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FC(3)97 b(Estrat\351gia)33 b(Algor\355tmica)2561 b(10)109 4088 y(4)97 b(Heur\355stica)33 b(Construtiv)-5 b(a)2562 b(12)255 4310 y FH(4.1)99 b(F)-8 b(ormaliza\347\343o)91 b(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(12)255 4532 y(4.2)99 b(Crit\351rios)32 b(gulosos)24 b(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(14)109 4851 y FC(5)k(Vizinhan\347as)33 b(e)g(Busca)h(Lo)s(cal)2402 b(16)255 5072 y FH(5.1)99 b(Estruturas)34 b(de)f(vizinhan\347a)48 b(.)i(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(16)255 5294 y(5.2)99 b(Heur\355sticas)32 b(de)i(busca)f(lo)s(cal)89 b(.)50 b(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(17)255 5515 y(5.3)99 b(Estruturas)34 b(de)f(dados)103 b(.)50 b(.)g(.)g(.)g(.)f(.)h (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)f(.)h(.)g(.)g(.)93 b(19)255 5737 y(5.4)99 b(Complexidade)32 b(assin)m(t\363tica)e(.)50 b(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(27)p eop %%Page: 8 10 8 9 bop 109 -28 a FB(Sum\341rio)3331 b(viii)p 109 9 3780 4 v 109 256 a FC(6)97 b(Otimiza\347\343o)31 b(do)i(Primeiro)d(Ob)5 b(jetiv)m(o)2110 b(29)255 477 y FH(6.1)99 b(Algoritmo)29 b(desen)m(v)m(olvido)40 b(.)50 b(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g (.)93 b(29)479 699 y(6.1.1)111 b FE(Iter)-5 b(ate)g(d)35 b(L)-5 b(o)g(c)g(al)34 b(Se)-5 b(ar)g(ch)74 b FH(.)49 b(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(29)479 920 y(6.1.2)111 b(P)m(erturba\347\343o)132 b(.)50 b(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.) g(.)g(.)93 b(30)479 1142 y(6.1.3)111 b(Busca)34 b(lo)s(cal)86 b(.)50 b(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.) h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(31)479 1363 y(6.1.4)111 b(In)m(tensi\034ca\347\343o)34 b(/)e(Div)m(ersi\034ca\347\343o)69 b(.)50 b(.)g(.)g(.)g(.)g(.)f(.)h(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(32)479 1585 y(6.1.5)111 b(Reinicializa\347\343o)93 b(.)50 b(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(32)479 1807 y(6.1.6)111 b(Crit\351rio)31 b(de)i(estagna\347\343o)80 b(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(33)479 2028 y(6.1.7)111 b(Estrutura)34 b(geral)d(do)h(algoritmo)j(.)50 b(.)g(.)g(.)g(.)g(.)g(.) f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(34)109 2347 y FC(7)k(Otimiza\347\343o)31 b(do)i(Segundo)g(e)f(T)-8 b(erceiro)33 b(Ob)5 b(jetiv)m(os)1629 b(37)255 2569 y FH(7.1)99 b FE(V)-7 b(ariable)34 b(Neighb)-5 b(orho)g(o)g(d)34 b(Se)-5 b(ar)g(ch)88 b FH(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.) h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(37)255 2790 y(7.2)99 b(Algoritmo)29 b(para)k(o)f(segundo)h(ob)5 b(jetiv)m(o)92 b(.)50 b(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(38)479 3012 y(7.2.1)111 b(P)m(erturba\347\343o)132 b(.)50 b(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.) g(.)g(.)93 b(39)479 3233 y(7.2.2)111 b(Busca)34 b(lo)s(cal)86 b(.)50 b(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.) h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(40)479 3455 y(7.2.3)111 b(In)m(tensi\034ca\347\343o)34 b(/)e(Div)m(ersi\034ca\347\343o)69 b(.)50 b(.)g(.)g(.)g(.)g(.)f(.)h(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(41)479 3677 y(7.2.4)111 b(Crit\351rio)31 b(de)i(estagna\347\343o)80 b(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(41)479 3898 y(7.2.5)111 b(Estrutura)34 b(geral)d(do)h(algoritmo)112 b(.)50 b(.)g(.)g(.)g(.)g(.) f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(42)255 4120 y(7.3)99 b(Algoritmo)29 b(para)k(o)f(terceiro)g(ob)5 b(jetiv)m(o)37 b(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(43)479 4341 y(7.3.1)111 b(Restaura\347\343o)33 b(da)f(viabilidade)109 b(.)50 b(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)f(.)h(.)g(.)g(.)93 b(44)479 4563 y(7.3.2)111 b(P)m (erturba\347\343o)132 b(.)50 b(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.) g(.)93 b(45)479 4784 y(7.3.3)111 b(Busca)34 b(lo)s(cal)86 b(.)50 b(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.) h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(46)479 5006 y(7.3.4)111 b(In)m(tensi\034ca\347\343o)34 b(/)e(Div)m(ersi\034ca\347\343o)69 b(.)50 b(.)g(.)g(.)g(.)g(.)f(.)h(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(46)479 5228 y(7.3.5)111 b(Estrutura)34 b(geral)d(do)h(algoritmo)j(.) 50 b(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) f(.)h(.)g(.)g(.)93 b(47)109 5547 y FC(8)k(Exp)s(erimen)m(tos)33 b(Computacionais)2233 b(49)255 5768 y FH(8.1)99 b(Desa\034o)34 b(R)m(O)m(ADEF)48 b(.)i(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.) g(.)93 b(49)p eop %%Page: 9 11 9 10 bop 109 -28 a FB(Sum\341rio)3381 b(ix)p 109 9 3780 4 v 255 256 a FH(8.2)99 b(Resultados)33 b(obtidos)79 b(.)50 b(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.) h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(52)109 575 y FC(9)k(Conclus\365)s(es)3065 b(61)109 894 y(Refer\352ncias)3192 b(63)p eop %%Page: 10 12 10 11 bop 1330 651 a FD(Lista)64 b(de)e(Figuras)255 1288 y FH(1.1)99 b(O\034cinas)33 b(da)f(linha)f(de)i(pro)s(du\347\343o)f(de) h(uma)f(f\341brica)f(de)i(carros.)g(.)50 b(.)g(.)g(.)g(.)g(.)g(.)f(.)h (.)g(.)g(.)141 b(1)255 1509 y(2.1)99 b(Seq\374\352ncia)34 b(de)f(carros)f(satisfazendo)h(a)f(restri\347\343o)g(de)h(capacidade)g (de)g(raz\343o)f FA(1)p Fz(=P)14 b FH(.)78 b(.)141 b(4)255 1731 y(2.2)99 b(Diferen\347a)33 b(en)m(tre)h(restri\347\365)s(es)e(de)h (capacidade)g(de)g(raz\365)s(es)g(1/3)f(e)g(2/6.)58 b(.)50 b(.)g(.)g(.)f(.)h(.)g(.)g(.)141 b(5)255 1952 y(2.3)99 b(Exemplos)46 b(de)g(seq\374\352ncias)i(de)e(carros)g(para)g(uma)f (restri\347\343o)g(de)h(capacidade)g(de)479 2115 y(raz\343o)32 b(1/5.)67 b(.)49 b(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) f(.)h(.)g(.)g(.)141 b(6)255 2336 y(2.4)99 b(C\341lculo)36 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b(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g (.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(20)255 3769 y(5.3)99 b(V)-8 b(etores)34 b(auxiliares)c(corresp)s(onden)m(tes)35 b(a)d(uma)g(solu\347\343o.)62 b(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g (.)f(.)h(.)g(.)g(.)93 b(21)255 3991 y(5.4)99 b(V)-8 b(etores)34 b(auxiliares)c(corresp)s(onden)m(tes)35 b(a)d(uma)g(solu\347\343o.)62 b(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(23)255 4212 y(5.5)99 b(A)m(tualiza\347\343o)31 b(do)i(v)m(etor)g(A)g (ap)s(\363s)f(a)g(remo)s(\347\343o)g(de)h(um)f(carro.)88 b(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(25)255 4434 y(6.1)99 b(Pseudo-c\363)s(digo)32 b(da)h (metaheur\355stica)e(ILS.)41 b(.)50 b(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(30)255 4655 y(6.2)99 b(Exemplo)32 b(de)h(funcionamen)m(to)f(da)g(p)s (erturba\347\343o.)97 b(.)50 b(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g (.)g(.)f(.)h(.)g(.)g(.)93 b(31)255 4877 y(6.3)99 b(Pseudo-c\363)s(digo) 32 b(do)h(algoritmo)c(para)j(otimizar)d(o)k(primeiro)d(ob)5 b(jetiv)m(o.)63 b(.)50 b(.)g(.)f(.)h(.)g(.)g(.)93 b(36)255 5099 y(7.1)99 b(Pseudo-c\363)s(digo)32 b(da)h(metaheur\355stica)e(VNS.) 68 b(.)50 b(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f (.)h(.)g(.)g(.)93 b(38)255 5320 y(7.2)99 b(Exemplo)32 b(de)h(funcionamen)m(to)f(da)g(p)s(erturba\347\343o)h(com)f(mo)m(vimen) m(tos)f FE(swap)p FH(.)37 b(.)49 b(.)h(.)g(.)g(.)93 b(39)255 5542 y(7.3)99 b(Pseudo-c\363)s(digo)32 b(do)h(algoritmo)c(para)j (otimizar)d(o)k(segundo)g(ob)5 b(jetiv)m(o.)79 b(.)50 b(.)g(.)f(.)h(.)g(.)g(.)93 b(44)255 5763 y(7.4)99 b(Pseudo-c\363)s (digo)32 b(do)h(algoritmo)c(para)j(otimizar)d(o)k(terceiro)f(ob)5 b(jetiv)m(o.)101 b(.)50 b(.)g(.)f(.)h(.)g(.)g(.)93 b(48)p eop %%Page: 11 13 11 12 bop 109 -28 a FB(Lista)30 b(de)h(Figuras)3063 b(xi)p 109 9 3780 4 v 255 256 a FH(8.1)99 b(Gr\341\034co)24 b(que)h(mostra)e(a)h(qualidade)f(da)h(solu\347\343o)g(em)g (fun\347\343o)g(do)g(temp)s(o)f(de)i(execu\347\343o)479 418 y(para)32 b(a)h(inst\342ncia)e Fy(025_38_1)p FH(.)81 b(.)49 b(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(59)255 640 y(8.2)99 b(Gr\341\034co)24 b(que)h(mostra)e(a)h(qualidade)f(da)h(solu\347\343o)g (em)g(fun\347\343o)g(do)g(temp)s(o)f(de)i(execu\347\343o)479 802 y(para)32 b(a)h(inst\342ncia)e Fy(024_V2_S22_J1)p FH(.)99 b(.)50 b(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(59)255 1024 y(8.3)99 b(Gr\341\034co)24 b(que)h(mostra)e(a)h(qualidade)f(da)h(solu\347\343o)g (em)g(fun\347\343o)g(do)g(temp)s(o)f(de)i(execu\347\343o)479 1186 y(para)32 b(a)h(inst\342ncia)e Fy(028_ch2_S23_J3)p FH(.)70 b(.)50 b(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(60)p eop %%Page: 12 14 12 13 bop 1326 651 a FD(Lista)64 b(de)e(T)-16 b(ab)5 b(elas)255 1288 y FH(8.1)99 b(Dados)33 b(das)g(inst\342ncias)f(dos)h (conjun)m(tos)g(de)h(teste)f(A)g(e)g(B.)92 b(.)50 b(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)f(.)h(.)g(.)g(.)93 b(51)255 1509 y(8.2)99 b(M\351dia)33 b(dos)f(resultados)h(obtidos)f(para)g(as)h(inst\342ncias) f(do)g(conjun)m(to)h(de)g(teste)h(A.)49 b(.)h(.)93 b(54)255 1731 y(8.3)99 b(M\351dia)33 b(dos)f(resultados)h(obtidos)f(para)g(as)h (inst\342ncias)f(do)g(conjun)m(to)h(de)g(teste)h(B.)53 b(.)d(.)93 b(55)255 1952 y(8.4)99 b(Melhor)32 b(solu\347\343o)g(encon)m (trada)i(para)e(as)g(inst\342ncias)g(do)h(conjun)m(to)g(de)g(teste)g (A.)69 b(.)50 b(.)g(.)93 b(56)255 2174 y(8.5)99 b(Melhor)32 b(solu\347\343o)g(encon)m(trada)i(para)e(as)g(inst\342ncias)g(do)h (conjun)m(to)g(de)g(teste)g(B.)73 b(.)50 b(.)g(.)93 b(56)255 2395 y(8.6)99 b(Dados)33 b(das)g(inst\342ncias)f(do)h(conjun)m(to)g(de) g(teste)g(X.)40 b(.)50 b(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) f(.)h(.)g(.)g(.)93 b(57)255 2617 y(8.7)99 b(M\351dia)33 b(dos)f(resultados)h(obtidos)f(para)g(as)h(inst\342ncias)f(do)g(conjun) m(to)h(de)g(teste)h(X.)49 b(.)h(.)93 b(57)p eop %%Page: 1 15 1 14 bop 109 726 a FD(Cap\355tulo)64 b(1)109 1390 y(In)-5 b(tro)5 b(du\347\343o)274 2087 y FH(O)35 b(problema)f(de)i (seq\374enciamen)m(to)g(de)g(carros)f(em)g(linhas)f(de)i(pro)s (du\347\343o)f(de)h(ind\372strias)e(auto-)109 2250 y(mobil\355sticas)29 b(\351)k(um)f(tip)s(o)f(m)m(uito)g(particular)f(de)k(problemas)d(de)i (escalonamen)m(to.)274 2471 y(O)28 b(n)m(\372mero)g(de)g(op)s(\347\365) s(es)h(disp)s(on\355v)m(eis)e(aos)h(compradores)g(tem)f(propiciado)g(o) h(crescimen)m(to)g(consi-)109 2634 y(der\341)m(v)m(el)d(da)g(div)m (ersidade)g(dos)g(carros)g(man)m(ufaturados.)40 b(Devido)25 b(aos)g(custos)g(da)g(linha)e(de)i(pro)s(du\347\343o,)109 2796 y(os)k(diferen)m(tes)g(v)m(e\355culos)g(s\343o)g(to)s(dos)g(mon)m (tados)f(usando)h(a)g(mesma)f(unidade)g(de)i(mon)m(tagem.)41 b(J\341)28 b(que)109 2959 y(qualquer)40 b(mo)s(di\034ca\347\343o)e(do)h (\035uxo)i(f\355sico)d(den)m(tro)i(da)g(f\341brica)e(implica)f(em)i (custo)h(m)m(uito)f(elev)-5 b(ado,)109 3121 y(m)m(uitos)42 b(esfor\347os)i(t\352m)f(sido)g(concen)m(trados)h(na)g (otimiza\347\343o)c(do)j(gerenciamen)m(to)g(de)h(recursos)h(de)109 3284 y(pro)s(du\347\343o.)d(Desta)31 b(forma,)d(os)i(clien)m(tes)g(p)s (o)s(dem)f(ser)h(supridos)g(com)f(os)h(carros)g(desejados)h(nas)f (datas)109 3446 y(acordadas)i(a)h(custos)g(mais)e(baixos.)274 3668 y(A)39 b(linha)f(de)i(pro)s(du\347\343o)f(p)s(o)s(de)g(ser)i (considerada)e(como)f(um)h(pro)s(cesso)i(de)e(man)m(ufatura)g(linear) 109 3830 y(comp)s(osta)30 b(p)s(or)g(tr\352s)i(o\034cinas)f(\()p FE(shops)8 b FH(\):)42 b(o\034cina)30 b(de)h(arma\347\343o)f(de)h (carro)s(ceria,)g(o\034cina)f(de)h(pin)m(tura)g(e)109 3993 y(o\034cina)g(de)j(mon)m(tagem,)d(como)g(ilustra)g(a)i(Figura)d (1.1.)211 5239 y currentpoint currentpoint translate 0.78845 0.78845 scale neg exch neg exch translate 211 5239 a @beginspecial 27 @llx 329 @lly 571 @urx 480 @ury 5440 @rwi @setspecial %%BeginDocument: shop.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 27 329 571 480 %%Creator: CorelDRAW 7 %%Title: %%CreationDate: Thu Jan 20 12:17:39 2005 %%DocumentProcessColors: Cyan Magenta Yellow Black %%DocumentSuppliedResources: (atend) %%EndComments %%BeginProlog /AutoFlatness true def /AutoSteps 0 def /CMYKMarks false def /UseLevel2 false def %Color profile: _DEFAULT.CCM - Gen. Profil -Sem %%BeginResource: procset wCorel7Dict 7.0 0 /wCorel7Dict 300 dict def wCorel7Dict begin % Copyright (c)1992-96 Corel Corporation % All rights reserved. v7.0 r1.0 /bd{bind def}bind def/ld{load def}bd/xd{exch def}bd/_ null def/rp{{pop}repeat} bd/@cp/closepath ld/@gs/gsave ld/@gr/grestore ld/@np/newpath ld/Tl/translate ld /$sv 0 def/@sv{/$sv save def}bd/@rs{$sv restore}bd/spg/showpage ld/showpage{} bd currentscreen/@dsp xd/$dsp/@dsp def/$dsa xd/$dsf xd/$sdf false def/$SDF false def/$Scra 0 def/SetScr/setscreen ld/setscreen{pop pop pop}bd/@ss{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if exch $Scra add exch load SetScr}bd /SepMode_5 where{pop}{/SepMode_5 0 def}ifelse/CurrentInkName_5 where{pop} {/CurrentInkName_5(Composite)def}ifelse/$ink_5 where{pop}{/$ink_5 -1 def} ifelse/$c 0 def/$m 0 def/$y 0 def/$k 0 def/$t 1 def/$n _ def/$o 0 def/$fil 0 def/$C 0 def/$M 0 def/$Y 0 def/$K 0 def/$T 1 def/$N _ def/$O 0 def/$PF false def/s1c 0 def/s1m 0 def/s1y 0 def/s1k 0 def/s1t 0 def/s1n _ def/$bkg false def /SK 0 def/SM 0 def/SY 0 def/SC 0 def/$op false def matrix currentmatrix/$ctm xd /$ptm matrix def/$ttm matrix def/$stm matrix def/$ffpnt true def /CorelDrawReencodeVect[16#0/grave 16#5/breve 16#6/dotaccent 16#8/ring 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl 16#88/circumflex/perthousand/Scaron/guilsinglleft/OE 16#91/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash 16#98/tilde/trademark/scaron/guilsinglright/oe 16#9F/Ydieresis 16#A1/exclamdown/cent/sterling/currency/yen/brokenbar/section 16#a8/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/minus/registered/macron 16#b0/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered 16#b8/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown 16#c0/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla 16#c8/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis 16#d0/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply 16#d8/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls 16#e0/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla 16#e8/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis 16#f0/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide 16#f8/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis]def /L2?/languagelevel where{pop languagelevel 2 ge}{false}ifelse def /@BeginSysCorelDict{systemdict/Corel30Dict known{systemdict/Corel30Dict get exec}if}bd/@EndSysCorelDict{systemdict/Corel30Dict known{end}if}bd AutoFlatness {/@ifl{dup currentflat exch sub 10 gt{ ([Error: PathTooComplex; OffendingCommand: AnyPaintingOperator]\n)print flush @np exit}{currentflat 2 add setflat}ifelse}bd/@fill/fill ld/fill{currentflat{ {@fill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@eofill/eofill ld/eofill {currentflat{{@eofill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@clip /clip ld/clip{currentflat{{@clip}stopped{@ifl}{exit}ifelse}bind loop setflat} bd/@eoclip/eoclip ld/eoclip{currentflat{{@eoclip}stopped{@ifl}{exit}ifelse} bind loop setflat}bd/@stroke/stroke ld/stroke{currentflat{{@stroke}stopped {@ifl}{exit}ifelse}bind loop setflat}bd}if L2?{/@ssa{true setstrokeadjust}bd}{ /@ssa{}bd}ifelse/d/setdash ld/j/setlinejoin ld/J/setlinecap ld/M/setmiterlimit ld/w/setlinewidth ld/O{/$o xd}bd/R{/$O xd}bd/W/eoclip ld/c/curveto ld/C/c ld/l /lineto ld/L/l ld/rl/rlineto ld/m/moveto ld/n/newpath ld/N/newpath ld/P{11 rp} bd/u{}bd/U{}bd/A{pop}bd/q/@gs ld/Q/@gr ld/&{}bd/@j{@sv @np}bd/@J{@rs}bd/g{1 exch sub/$k xd/$c 0 def/$m 0 def/$y 0 def/$t 1 def/$n _ def/$fil 0 def}bd/G{1 sub neg/$K xd _ 1 0 0 0/$C xd/$M xd/$Y xd/$T xd/$N xd}bd/k{1 index type /stringtype eq{/$t xd/$n xd}{/$t 0 def/$n _ def}ifelse/$k xd/$y xd/$m xd/$c xd /$fil 0 def}bd/K{1 index type/stringtype eq{/$T xd/$N xd}{/$T 0 def/$N _ def} ifelse/$K xd/$Y xd/$M xd/$C xd}bd/x/k ld/X/K ld/sf{1 index type/stringtype eq{ /s1t xd/s1n xd}{/s1t 0 def/s1n _ def}ifelse/s1k xd/s1y xd/s1m xd/s1c xd}bd/i{ dup 0 ne{setflat}{pop}ifelse}bd/v{4 -2 roll 2 copy 6 -2 roll c}bd/V/v ld/y{2 copy c}bd/Y/y ld/@w{matrix rotate/$ptm xd matrix scale $ptm dup concatmatrix /$ptm xd 1 eq{$ptm exch dup concatmatrix/$ptm xd}if 1 w}bd/@g{1 eq dup/$sdf xd {/$scp xd/$sca xd/$scf xd}if}bd/@G{1 eq dup/$SDF xd{/$SCP xd/$SCA xd/$SCF xd} if}bd/@D{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if 3 copy exch $Scra add exch load SetScr/$dsp xd/$dsa xd/$dsf xd}bd/$ngx{$SDF{$SCF SepMode_5 0 eq{$SCA} {$dsa}ifelse $SCP @ss}if}bd/p{/$pm xd 7 rp/$pyf xd/$pxf xd/$pn xd/$fil 1 def} bd/@MN{2 copy le{pop}{exch pop}ifelse}bd/@MX{2 copy ge{pop}{exch pop}ifelse}bd /InRange{3 -1 roll @MN @MX}bd/@sqr{dup 0 rl dup 0 exch rl neg 0 rl @cp}bd /currentscale{1 0 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt 0 1 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt}bd/@unscale{}bd/wDstChck{2 1 roll dup 3 -1 roll eq{1 add}if}bd /@dot{dup mul exch dup mul add 1 exch sub}bd/@lin{exch pop abs 1 exch sub}bd /cmyk2rgb{3{dup 5 -1 roll add 1 exch sub dup 0 lt{pop 0}if exch}repeat pop}bd /rgb2cmyk{3{1 exch sub 3 1 roll}repeat 3 copy @MN @MN 3{dup 5 -1 roll sub neg exch}repeat}bd/rgb2g{2 index .299 mul 2 index .587 mul add 1 index .114 mul add 4 1 roll pop pop pop}bd/WaldoColor_5 where{pop}{/SetRgb/setrgbcolor ld/GetRgb /currentrgbcolor ld/SetGry/setgray ld/GetGry/currentgray ld/SetRgb2 systemdict /setrgbcolor get def/GetRgb2 systemdict/currentrgbcolor get def/SetHsb systemdict/sethsbcolor get def/GetHsb systemdict/currenthsbcolor get def /rgb2hsb{SetRgb2 GetHsb}bd/hsb2rgb{3 -1 roll dup floor sub 3 1 roll SetHsb GetRgb2}bd/setcmykcolor where{pop/SetCmyk_5/setcmykcolor ld}{/SetCmyk_5{ cmyk2rgb SetRgb}bd}ifelse/currentcmykcolor where{pop/GetCmyk/currentcmykcolor ld}{/GetCmyk{GetRgb rgb2cmyk}bd}ifelse/setoverprint where{pop}{/setoverprint{ /$op xd}bd}ifelse/currentoverprint where{pop}{/currentoverprint{$op}bd}ifelse /@tc_5{5 -1 roll dup 1 ge{pop}{4{dup 6 -1 roll mul exch}repeat pop}ifelse}bd /@trp{exch pop 5 1 roll @tc_5}bd/setprocesscolor_5{SepMode_5 0 eq{SetCmyk_5}{0 4 $ink_5 sub index exch pop 5 1 roll pop pop pop pop SepsColor true eq{$ink_5 3 gt{1 sub neg SetGry}{0 0 0 4 $ink_5 roll SetCmyk_5}ifelse}{1 sub neg SetGry} ifelse}ifelse}bd/findcmykcustomcolor where{pop}{/findcmykcustomcolor{5 array astore}bd}ifelse/setcustomcolor where{pop}{/setcustomcolor{exch aload pop SepMode_5 0 eq{pop @tc_5 setprocesscolor_5}{CurrentInkName_5 eq{4 index}{0} ifelse 6 1 roll 5 rp 1 sub neg SetGry}ifelse}bd}ifelse/@scc_5{dup type /booleantype eq{setoverprint}{1 eq setoverprint}ifelse dup _ eq{pop setprocesscolor_5 pop}{findcmykcustomcolor exch setcustomcolor}ifelse SepMode_5 0 eq{true}{GetGry 1 eq currentoverprint and not}ifelse}bd/colorimage where{pop /ColorImage{colorimage}def}{/ColorImage{/ncolors xd pop/dataaq xd{dataaq ncolors dup 3 eq{/$dat xd 0 1 $dat length 3 div 1 sub{dup 3 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length 3 idiv getinterval pop}{4 eq{/$dat xd 0 1 $dat length 4 div 1 sub{dup 4 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div $dat 4 index 3 add get 255 div cmyk2rgb rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length ncolors idiv getinterval}if}ifelse}image}bd }ifelse/setcmykcolor{1 5 1 roll _ currentoverprint @scc_5/$ffpnt xd}bd /currentcmykcolor{0 0 0 0}bd/setrgbcolor{rgb2cmyk setcmykcolor}bd /currentrgbcolor{currentcmykcolor cmyk2rgb}bd/sethsbcolor{hsb2rgb setrgbcolor} bd/currenthsbcolor{currentrgbcolor rgb2hsb}bd/setgray{dup dup setrgbcolor}bd /currentgray{currentrgbcolor rgb2g}bd}ifelse/WaldoColor_5 true def/@sft{$tllx $pxf add dup $tllx gt{$pwid sub}if/$tx xd $tury $pyf sub dup $tury lt{$phei add}if/$ty xd}bd/@stb{pathbbox/$ury xd/$urx xd/$lly xd/$llx xd}bd/@ep{{cvx exec }forall}bd/@tp{@sv/$in true def 2 copy dup $lly le{/$in false def}if $phei sub $ury ge{/$in false def}if dup $urx ge{/$in false def}if $pwid add $llx le{/$in false def}if $in{@np 2 copy m $pwid 0 rl 0 $phei neg rl $pwid neg 0 rl 0 $phei rl clip @np $pn cvlit load aload pop 7 -1 roll 5 index sub 7 -1 roll 3 index sub Tl matrix currentmatrix/$ctm xd @ep pop pop pop pop}{pop pop}ifelse @rs}bd /@th{@sft 0 1 $tly 1 sub{dup $psx mul $tx add{dup $llx gt{$pwid sub}{exit} ifelse}loop exch $phei mul $ty exch sub 0 1 $tlx 1 sub{$pwid mul 3 copy 3 -1 roll add exch @tp pop}for pop pop}for}bd/@tv{@sft 0 1 $tlx 1 sub{dup $pwid mul $tx add exch $psy mul $ty exch sub{dup $ury lt{$phei add}{exit}ifelse}loop 0 1 $tly 1 sub{$phei mul 3 copy sub @tp pop}for pop pop}for}bd/$fm 0 def/wfill{1 $fm eq{fill}{eofill}ifelse}bd/wclip{1 $fm eq{clip}{eoclip}ifelse}bd/@pf{@gs $ctm setmatrix $pm concat @stb wclip Bburx Bbury $pm itransform/$tury xd/$turx xd Bbllx Bblly $pm itransform/$tlly xd/$tllx xd/$wid $turx $tllx sub def/$hei $tury $tlly sub def @gs $vectpat{1 0 0 0 0 _ $o @scc_5{wfill}if}{$t $c $m $y $k $n $o @scc_5{SepMode_5 0 eq $pfrg or{$tllx $tlly Tl $wid $hei scale <00> 8 1 false[8 0 0 1 0 0]{}imagemask}{/$bkg true def}ifelse}if}ifelse @gr $wid 0 gt $hei 0 gt and{$pn cvlit load aload pop/$pd xd 3 -1 roll sub/$phei xd exch sub /$pwid xd $wid $pwid div ceiling 1 add/$tlx xd $hei $phei div ceiling 1 add /$tly xd $psx 0 eq{@tv}{@th}ifelse}if @gr @np/$bkg false def}bd/@Pf{@sv SepMode_5 0 eq $Psc 0 ne or $ink_5 3 eq or{0 J 0 j[]0 d $t $c $m $y $k $n $o @scc_5 pop $ctm setmatrix 72 1000 div dup matrix scale dup concat dup Bburx exch Bbury exch itransform ceiling cvi/Bbury xd ceiling cvi/Bburx xd Bbllx exch Bblly exch itransform floor cvi/Bblly xd floor cvi/Bbllx xd $Prm aload pop $Psn load exec}{1 SetGry wfill}ifelse @rs @np}bd/F{matrix currentmatrix $sdf{$scf $sca $scp @ss}if $fil 1 eq{@pf}{$fil 2 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@EndSysCorelDict end %%DocumentSuppliedResources: procset wCorel7Dict %%EOF %%EndDocument @endspecial 211 5239 a currentpoint currentpoint translate 1 0.78845 div 1 0.78845 div scale neg exch neg exch translate 211 5239 a 549 5442 a FH(Figura)h(1.1:)43 b(O\034cinas)33 b(da)f(linha)f(de)i(pro)s(du\347\343o)f(de)h(uma)f (f\341brica)f(de)i(carros.)274 5829 y(P)m(ara)g(programar)d(a)j(linha)e (de)i(pro)s(du\347\343o,)f(o)g(trabalho)f(\351)i(dividido)e(em)h(duas)h (etapas:)p eop %%Page: 2 16 2 15 bop 109 -28 a FB(1)60 b(In)m(tro)s(du\347\343o)3201 b(2)p 109 9 3780 4 v 179 256 a FH(\(1\))49 b(determinar)c(o)h(dia)f(de) i(pro)s(du\347\343o)f(para)f(cada)i(carro)f(encomendado,)k(de)c(acordo) g(com)g(as)353 418 y(capacidades)23 b(da)f(linha)f(de)j(pro)s (du\347\343o)e(e)h(com)f(os)h(prazos)g(de)g(en)m(trega)h(prometidos)d (aos)i(clien)m(tes;)179 664 y(\(2\))49 b(escalonar)44 b(a)g(ordem)g(dos)h(carros)g(a)g(serem)g(pro)s(duzidos)f(na)g(linha)f (de)j(mon)m(tagem)d(a)h(cada)353 826 y(dia)39 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2969 y FH(carros)109 3132 y(com)47 b(a)h(op)s(\347\343o)f Fz(i)h FH(dev)m(em)h(ser)g(pro)s(duzidos)f(em)f(cada)h (subseq\374\352ncia)i(consecutiv)-5 b(a)49 b(de)f Fz(P)3557 3147 y Ft(i)3633 3132 y FH(carros)109 3294 y(na)38 b(linha)f(de)j(mon)m (tagem.)60 b(P)m(or)39 b(exemplo,)h(se)f(uma)f(determinada)g(op)s (\347\343o)g(est\341)h(asso)s(ciada)g(a)f(uma)109 3457 y(restri\347\343o)26 b(de)i(capacidade)f(de)h(raz\343o)f FA(1)p Fz(=)p FA(3)p FH(,)h(isto)e(signi\034ca)g(que)i(n\343o)f(dev)m (e)i(existir)e(mais)f(que)i(um)e(carro)109 3619 y(com)31 b(esta)i(op)s(\347\343o)e(em)h(qualquer)g(seq\374\352ncia)h(consecutiv) -5 b(a)33 b(de)f(3)g(carros.)43 b(De)33 b(forma)e(geral,)g(se)i(existe) 109 3782 y(uma)i(restri\347\343o)h(de)h(capacidade)f(de)h(raz\343o)f FA(1)p Fz(=P)49 b FH(para)36 b(uma)g(op)s(\347\343o,)h(dois)f(carros)g (com)g(esta)h(op)s(\347\343o)109 3944 y(dev)m(em)26 b(ser)g(separados)g (p)s(or)f(no)g(m\355nimo)d Fz(P)f Fs(\000)7 b FA(1)25 b FH(carros)h(consecutiv)m(os)h(que)f(n\343o)f(p)s(ossuam)g(esta)h(op)s (\347\343o)109 4107 y(\(v)m(er)33 b(Figura)e(2.1\).)1066 5429 y currentpoint currentpoint translate 0.61626 0.61626 scale neg exch neg exch translate 1066 5429 a @beginspecial 110 @llx 339 @lly 473 @urx 546 @ury 3630 @rwi @setspecial %%BeginDocument: restricao1.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 110 339 473 546 %%Creator: CorelDRAW 7 %%Title: %%CreationDate: Thu Jan 20 14:47:40 2005 %%DocumentProcessColors: Cyan Magenta Yellow Black %%DocumentSuppliedResources: (atend) %%EndComments %%BeginProlog /AutoFlatness true def /AutoSteps 0 def /CMYKMarks false def /UseLevel2 false def %Color profile: _DEFAULT.CCM - Gen. Profil -Sem %%BeginResource: procset wCorel7Dict 7.0 0 /wCorel7Dict 300 dict def wCorel7Dict begin % Copyright (c)1992-96 Corel Corporation % All rights reserved. v7.0 r1.0 /bd{bind def}bind def/ld{load def}bd/xd{exch def}bd/_ null def/rp{{pop}repeat} bd/@cp/closepath ld/@gs/gsave ld/@gr/grestore ld/@np/newpath ld/Tl/translate ld /$sv 0 def/@sv{/$sv save def}bd/@rs{$sv restore}bd/spg/showpage ld/showpage{} bd currentscreen/@dsp xd/$dsp/@dsp def/$dsa xd/$dsf xd/$sdf false def/$SDF false def/$Scra 0 def/SetScr/setscreen ld/setscreen{pop pop pop}bd/@ss{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if exch $Scra add exch load SetScr}bd /SepMode_5 where{pop}{/SepMode_5 0 def}ifelse/CurrentInkName_5 where{pop} {/CurrentInkName_5(Composite)def}ifelse/$ink_5 where{pop}{/$ink_5 -1 def} ifelse/$c 0 def/$m 0 def/$y 0 def/$k 0 def/$t 1 def/$n _ def/$o 0 def/$fil 0 def/$C 0 def/$M 0 def/$Y 0 def/$K 0 def/$T 1 def/$N _ def/$O 0 def/$PF false def/s1c 0 def/s1m 0 def/s1y 0 def/s1k 0 def/s1t 0 def/s1n _ def/$bkg false def /SK 0 def/SM 0 def/SY 0 def/SC 0 def/$op false def matrix currentmatrix/$ctm xd /$ptm matrix def/$ttm matrix def/$stm matrix def/$ffpnt true def /CorelDrawReencodeVect[16#0/grave 16#5/breve 16#6/dotaccent 16#8/ring 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl 16#88/circumflex/perthousand/Scaron/guilsinglleft/OE 16#91/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash 16#98/tilde/trademark/scaron/guilsinglright/oe 16#9F/Ydieresis 16#A1/exclamdown/cent/sterling/currency/yen/brokenbar/section 16#a8/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/minus/registered/macron 16#b0/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered 16#b8/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown 16#c0/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla 16#c8/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis 16#d0/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply 16#d8/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls 16#e0/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla 16#e8/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis 16#f0/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide 16#f8/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis]def /L2?/languagelevel where{pop languagelevel 2 ge}{false}ifelse def /@BeginSysCorelDict{systemdict/Corel30Dict known{systemdict/Corel30Dict get exec}if}bd/@EndSysCorelDict{systemdict/Corel30Dict known{end}if}bd AutoFlatness {/@ifl{dup currentflat exch sub 10 gt{ ([Error: PathTooComplex; OffendingCommand: AnyPaintingOperator]\n)print flush @np exit}{currentflat 2 add setflat}ifelse}bd/@fill/fill ld/fill{currentflat{ {@fill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@eofill/eofill ld/eofill {currentflat{{@eofill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@clip /clip ld/clip{currentflat{{@clip}stopped{@ifl}{exit}ifelse}bind loop setflat} bd/@eoclip/eoclip ld/eoclip{currentflat{{@eoclip}stopped{@ifl}{exit}ifelse} bind loop setflat}bd/@stroke/stroke ld/stroke{currentflat{{@stroke}stopped {@ifl}{exit}ifelse}bind loop setflat}bd}if L2?{/@ssa{true setstrokeadjust}bd}{ /@ssa{}bd}ifelse/d/setdash ld/j/setlinejoin ld/J/setlinecap ld/M/setmiterlimit ld/w/setlinewidth ld/O{/$o xd}bd/R{/$O xd}bd/W/eoclip ld/c/curveto ld/C/c ld/l /lineto ld/L/l ld/rl/rlineto ld/m/moveto ld/n/newpath ld/N/newpath ld/P{11 rp} bd/u{}bd/U{}bd/A{pop}bd/q/@gs ld/Q/@gr ld/&{}bd/@j{@sv @np}bd/@J{@rs}bd/g{1 exch sub/$k xd/$c 0 def/$m 0 def/$y 0 def/$t 1 def/$n _ def/$fil 0 def}bd/G{1 sub neg/$K xd _ 1 0 0 0/$C xd/$M xd/$Y xd/$T xd/$N xd}bd/k{1 index type /stringtype eq{/$t xd/$n xd}{/$t 0 def/$n _ def}ifelse/$k xd/$y xd/$m xd/$c xd /$fil 0 def}bd/K{1 index type/stringtype eq{/$T xd/$N xd}{/$T 0 def/$N _ def} ifelse/$K xd/$Y xd/$M xd/$C xd}bd/x/k ld/X/K ld/sf{1 index type/stringtype eq{ /s1t xd/s1n xd}{/s1t 0 def/s1n _ def}ifelse/s1k xd/s1y xd/s1m xd/s1c xd}bd/i{ dup 0 ne{setflat}{pop}ifelse}bd/v{4 -2 roll 2 copy 6 -2 roll c}bd/V/v ld/y{2 copy c}bd/Y/y ld/@w{matrix rotate/$ptm xd matrix scale $ptm dup concatmatrix /$ptm xd 1 eq{$ptm exch dup concatmatrix/$ptm xd}if 1 w}bd/@g{1 eq dup/$sdf xd {/$scp xd/$sca xd/$scf xd}if}bd/@G{1 eq dup/$SDF xd{/$SCP xd/$SCA xd/$SCF xd} if}bd/@D{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if 3 copy exch $Scra add exch load SetScr/$dsp xd/$dsa xd/$dsf xd}bd/$ngx{$SDF{$SCF SepMode_5 0 eq{$SCA} {$dsa}ifelse $SCP @ss}if}bd/p{/$pm xd 7 rp/$pyf xd/$pxf xd/$pn xd/$fil 1 def} bd/@MN{2 copy le{pop}{exch pop}ifelse}bd/@MX{2 copy ge{pop}{exch pop}ifelse}bd /InRange{3 -1 roll @MN @MX}bd/@sqr{dup 0 rl dup 0 exch rl neg 0 rl @cp}bd /currentscale{1 0 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt 0 1 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt}bd/@unscale{}bd/wDstChck{2 1 roll dup 3 -1 roll eq{1 add}if}bd /@dot{dup mul exch dup mul add 1 exch sub}bd/@lin{exch pop abs 1 exch sub}bd /cmyk2rgb{3{dup 5 -1 roll add 1 exch sub dup 0 lt{pop 0}if exch}repeat pop}bd /rgb2cmyk{3{1 exch sub 3 1 roll}repeat 3 copy @MN @MN 3{dup 5 -1 roll sub neg exch}repeat}bd/rgb2g{2 index .299 mul 2 index .587 mul add 1 index .114 mul add 4 1 roll pop pop pop}bd/WaldoColor_5 where{pop}{/SetRgb/setrgbcolor ld/GetRgb /currentrgbcolor ld/SetGry/setgray ld/GetGry/currentgray ld/SetRgb2 systemdict /setrgbcolor get def/GetRgb2 systemdict/currentrgbcolor get def/SetHsb systemdict/sethsbcolor get def/GetHsb systemdict/currenthsbcolor get def /rgb2hsb{SetRgb2 GetHsb}bd/hsb2rgb{3 -1 roll dup floor sub 3 1 roll SetHsb GetRgb2}bd/setcmykcolor where{pop/SetCmyk_5/setcmykcolor ld}{/SetCmyk_5{ cmyk2rgb SetRgb}bd}ifelse/currentcmykcolor where{pop/GetCmyk/currentcmykcolor ld}{/GetCmyk{GetRgb rgb2cmyk}bd}ifelse/setoverprint where{pop}{/setoverprint{ /$op xd}bd}ifelse/currentoverprint where{pop}{/currentoverprint{$op}bd}ifelse /@tc_5{5 -1 roll dup 1 ge{pop}{4{dup 6 -1 roll mul exch}repeat pop}ifelse}bd /@trp{exch pop 5 1 roll @tc_5}bd/setprocesscolor_5{SepMode_5 0 eq{SetCmyk_5}{0 4 $ink_5 sub index exch pop 5 1 roll pop pop pop pop SepsColor true eq{$ink_5 3 gt{1 sub neg SetGry}{0 0 0 4 $ink_5 roll SetCmyk_5}ifelse}{1 sub neg SetGry} ifelse}ifelse}bd/findcmykcustomcolor where{pop}{/findcmykcustomcolor{5 array astore}bd}ifelse/setcustomcolor where{pop}{/setcustomcolor{exch aload pop SepMode_5 0 eq{pop @tc_5 setprocesscolor_5}{CurrentInkName_5 eq{4 index}{0} ifelse 6 1 roll 5 rp 1 sub neg SetGry}ifelse}bd}ifelse/@scc_5{dup type /booleantype eq{setoverprint}{1 eq setoverprint}ifelse dup _ eq{pop setprocesscolor_5 pop}{findcmykcustomcolor exch setcustomcolor}ifelse SepMode_5 0 eq{true}{GetGry 1 eq currentoverprint and not}ifelse}bd/colorimage where{pop /ColorImage{colorimage}def}{/ColorImage{/ncolors xd pop/dataaq xd{dataaq ncolors dup 3 eq{/$dat xd 0 1 $dat length 3 div 1 sub{dup 3 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length 3 idiv getinterval pop}{4 eq{/$dat xd 0 1 $dat length 4 div 1 sub{dup 4 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div $dat 4 index 3 add get 255 div cmyk2rgb rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length ncolors idiv getinterval}if}ifelse}image}bd }ifelse/setcmykcolor{1 5 1 roll _ currentoverprint @scc_5/$ffpnt xd}bd /currentcmykcolor{0 0 0 0}bd/setrgbcolor{rgb2cmyk setcmykcolor}bd /currentrgbcolor{currentcmykcolor cmyk2rgb}bd/sethsbcolor{hsb2rgb setrgbcolor} bd/currenthsbcolor{currentrgbcolor rgb2hsb}bd/setgray{dup dup setrgbcolor}bd /currentgray{currentrgbcolor rgb2g}bd}ifelse/WaldoColor_5 true def/@sft{$tllx $pxf add dup $tllx gt{$pwid sub}if/$tx xd $tury $pyf sub dup $tury lt{$phei add}if/$ty xd}bd/@stb{pathbbox/$ury xd/$urx xd/$lly xd/$llx xd}bd/@ep{{cvx exec }forall}bd/@tp{@sv/$in true def 2 copy dup $lly le{/$in false def}if $phei sub $ury ge{/$in false def}if dup $urx ge{/$in false def}if $pwid add $llx le{/$in false def}if $in{@np 2 copy m $pwid 0 rl 0 $phei neg rl $pwid neg 0 rl 0 $phei rl clip @np $pn cvlit load aload pop 7 -1 roll 5 index sub 7 -1 roll 3 index sub Tl matrix currentmatrix/$ctm xd @ep pop pop pop pop}{pop pop}ifelse @rs}bd /@th{@sft 0 1 $tly 1 sub{dup $psx mul $tx add{dup $llx gt{$pwid sub}{exit} ifelse}loop exch $phei mul $ty exch sub 0 1 $tlx 1 sub{$pwid mul 3 copy 3 -1 roll add exch @tp pop}for pop pop}for}bd/@tv{@sft 0 1 $tlx 1 sub{dup $pwid mul $tx add exch $psy mul $ty exch sub{dup $ury lt{$phei add}{exit}ifelse}loop 0 1 $tly 1 sub{$phei mul 3 copy sub @tp pop}for pop pop}for}bd/$fm 0 def/wfill{1 $fm eq{fill}{eofill}ifelse}bd/wclip{1 $fm eq{clip}{eoclip}ifelse}bd/@pf{@gs $ctm setmatrix $pm concat @stb wclip Bburx Bbury $pm itransform/$tury xd/$turx xd Bbllx Bblly $pm itransform/$tlly xd/$tllx xd/$wid $turx $tllx sub def/$hei $tury $tlly sub def @gs $vectpat{1 0 0 0 0 _ $o @scc_5{wfill}if}{$t $c $m $y $k $n $o @scc_5{SepMode_5 0 eq $pfrg or{$tllx $tlly Tl $wid $hei scale <00> 8 1 false[8 0 0 1 0 0]{}imagemask}{/$bkg true def}ifelse}if}ifelse @gr $wid 0 gt $hei 0 gt and{$pn cvlit load aload pop/$pd xd 3 -1 roll sub/$phei xd exch sub /$pwid xd $wid $pwid div ceiling 1 add/$tlx xd $hei $phei div ceiling 1 add /$tly xd $psx 0 eq{@tv}{@th}ifelse}if @gr @np/$bkg false def}bd/@Pf{@sv SepMode_5 0 eq $Psc 0 ne or $ink_5 3 eq or{0 J 0 j[]0 d $t $c $m $y $k $n $o @scc_5 pop $ctm setmatrix 72 1000 div dup matrix scale dup concat dup Bburx exch Bbury exch itransform ceiling cvi/Bbury xd ceiling cvi/Bburx xd Bbllx exch Bblly exch itransform floor cvi/Bblly xd floor cvi/Bbllx xd $Prm aload pop $Psn load exec}{1 SetGry wfill}ifelse @rs @np}bd/F{matrix currentmatrix $sdf{$scf $sca $scp @ss}if $fil 1 eq{@pf}{$fil 2 eq{@ff}{$fil 3 eq{@Pf}{$t $c $m $y $k $n $o @scc_5{wfill}{@np}ifelse}ifelse}ifelse}ifelse $sdf{$dsf $dsa $dsp @ss}if setmatrix}bd/f{@cp F}bd/S{matrix currentmatrix $ctm setmatrix $SDF{$SCF $SCA $SCP @ss}if $T $C $M $Y $K $N $O @scc_5{matrix currentmatrix $ptm concat stroke setmatrix}{@np}ifelse $SDF{$dsf $dsa $dsp @ss}if setmatrix}bd/s{@cp S}bd/B{@gs F @gr S}bd/b{@cp B}bd/_E{5 array astore exch cvlit xd}bd/@cc{currentfile $dat readhexstring pop}bd/@sm{/$ctm $ctm currentmatrix def}bd/@E{/Bbury xd/Bburx xd /Bblly xd/Bbllx xd}bd/@c{@cp}bd/@p{/$fil 1 def 1 eq dup/$vectpat xd{/$pfrg true def}{@gs $t $c $m $y $k $n $o @scc_5/$pfrg xd @gr}ifelse/$pm xd/$psy xd/$psx xd /$pyf xd/$pxf xd/$pn xd}bd/@P{/$fil 3 def/$Psn xd/$Psc xd array astore/$Prm xd }bd/@ii{concat 3 index 3 index m 3 index 1 index l 2 copy l 1 index 3 index l 3 index 3 index l clip pop pop pop pop}bd/tcc{@cc}def/@i{@sm @gs @ii 6 index 1 ne {/$frg true def pop pop}{1 eq{s1t s1c s1m s1y s1k s1n $O @scc_5/$frg xd}{/$frg false def}ifelse 1 eq{@gs $ctm setmatrix F @gr}if}ifelse @np/$ury xd/$urx xd /$lly xd/$llx xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul 8 div ceiling cvi string def $bkg $frg or{$SDF{$SCF $SCA $SCP @ss}if $llx $lly Tl $urx $llx sub $ury $lly sub scale $bkg{$t $c $m $y $k $n $o @scc_5 pop}if $wid $hei abs $bts 1 eq{$bkg}{$bts}ifelse[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/tcc load $bts 1 eq{imagemask}{image}ifelse $SDF{$dsf $dsa $dsp @ss}if}{$hei abs{tcc pop} repeat}ifelse @gr $ctm setmatrix}bd/@I{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd /$llx xd/$ncl xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def $ngx $llx $lly Tl $urx $llx sub $ury $lly sub scale $wid $hei abs $bts[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/@cc load false $ncl ColorImage $SDF{$dsf $dsa $dsp @ss}if @gr $ctm setmatrix}bd/COMP 0 def L2?{ /@I_2{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd/$llx xd/$ncl xd/$bts xd/$hei xd /$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def 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86087 25701 84807 24958 c 83518 24214 82352 23123 81317 21693 c 80282 20254 79520 18589 79031 16689 c 78542 14788 78297 13095 78297 11599 c @c F %CHAR: 101947 0 (s) @t 104289 10000 m 109275 10310 L 109275 8871 109501 7648 109943 6642 c 110376 5635 111194 4807 112380 4158 c 113565 3518 114948 3198 116528 3198 c 118730 3198 120385 3641 121486 4516 c 122587 5400 123142 6444 123142 7639 c 123142 8495 122812 9313 122145 10085 c 121467 10856 119812 11806 117177 12935 c 114534 14073 112850 14864 112116 15325 c 110884 16077 109962 16961 109332 17987 c 108711 19003 108400 20179 108400 21496 c 108400 23810 109313 25795 111157 27451 c 112991 29106 115559 29934 118871 29934 c 122540 29934 125343 29078 127262 27385 c 129181 25682 130178 23443 130254 20668 C 125371 20339 L 125296 22107 124675 23500 123499 24525 c 122323 25560 120658 26068 118513 26068 c 116782 26068 115447 25673 114487 24892 c 113527 24102 113057 23246 113057 22324 c 113057 21402 113471 20593 114299 19897 c 114844 19417 116265 18683 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y(raz\365)s(es)d(menores,)h(ou)f (seja,)i(uma)d(restri\347\343o)h(da)g(capacidade)g(de)g(raz\343o)g FA(1)p Fz(=)p FA(5)f FH(\351)i(mais)e(restritiv)-5 b(a)33 b(que)109 581 y(uma)40 b(restri\347\343o)h(de)h(capacidade)f(de)h (raz\343o)e FA(2)p Fz(=)p FA(3)p FH(.)69 b(Dev)m(e-se)44 b(notar)c(tam)m(b)s(\351m)g(que)j(uma)d(raz\343o)h FA(1)p Fz(=)p FA(3)109 743 y FH(\351)f(diferen)m(te)g(de)g FA(2)p Fz(=)p FA(6)p FH(,)g(conforme)f(mostra)g(a)h(Figura)d(2.2.)65 b(A)39 b(seq\374\352ncia)i(\(a\))e(viola)f(a)i(restri\347\343o)f(de)109 906 y(capacidade)33 b(de)i(raz\343o)e FA(1)p Fz(=)p FA(3)p FH(,)h(mas)f(n\343o)h(viola)e(a)h(restri\347\343o)h(da)f(capacidade)h (de)g(raz\343o)g FA(2)p Fz(=)p FA(6)p FH(,)f(como)g(se)109 1068 y(p)s(o)s(de)f(v)m(er)i(na)e(seq\374\352ncia)i(\(b\).)861 2132 y currentpoint currentpoint translate 0.64845 0.64845 scale neg exch neg exch translate 861 2132 a @beginspecial 74 @llx 372 @lly 495 @urx 525 @ury 4210 @rwi @setspecial %%BeginDocument: razao.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 74 372 495 525 %%Creator: CorelDRAW 7 %%Title: %%CreationDate: Thu Jan 20 14:47:11 2005 %%DocumentProcessColors: Black %%DocumentSuppliedResources: (atend) %%EndComments %%BeginProlog /AutoFlatness true def /AutoSteps 0 def /CMYKMarks false def /UseLevel2 false def %Color profile: _DEFAULT.CCM - Gen. Profil -Sem %%BeginResource: procset wCorel7Dict 7.0 0 /wCorel7Dict 300 dict def wCorel7Dict begin % Copyright (c)1992-96 Corel Corporation % All rights reserved. v7.0 r1.0 /bd{bind def}bind def/ld{load def}bd/xd{exch def}bd/_ null def/rp{{pop}repeat} bd/@cp/closepath ld/@gs/gsave ld/@gr/grestore ld/@np/newpath ld/Tl/translate ld /$sv 0 def/@sv{/$sv save def}bd/@rs{$sv restore}bd/spg/showpage ld/showpage{} bd currentscreen/@dsp xd/$dsp/@dsp def/$dsa xd/$dsf xd/$sdf false def/$SDF false def/$Scra 0 def/SetScr/setscreen ld/setscreen{pop pop pop}bd/@ss{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if exch $Scra add exch load SetScr}bd /SepMode_5 where{pop}{/SepMode_5 0 def}ifelse/CurrentInkName_5 where{pop} {/CurrentInkName_5(Composite)def}ifelse/$ink_5 where{pop}{/$ink_5 -1 def} ifelse/$c 0 def/$m 0 def/$y 0 def/$k 0 def/$t 1 def/$n _ def/$o 0 def/$fil 0 def/$C 0 def/$M 0 def/$Y 0 def/$K 0 def/$T 1 def/$N _ def/$O 0 def/$PF false def/s1c 0 def/s1m 0 def/s1y 0 def/s1k 0 def/s1t 0 def/s1n _ def/$bkg false def /SK 0 def/SM 0 def/SY 0 def/SC 0 def/$op false def matrix currentmatrix/$ctm xd /$ptm matrix def/$ttm matrix def/$stm matrix def/$ffpnt true def /CorelDrawReencodeVect[16#0/grave 16#5/breve 16#6/dotaccent 16#8/ring 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl 16#88/circumflex/perthousand/Scaron/guilsinglleft/OE 16#91/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash 16#98/tilde/trademark/scaron/guilsinglright/oe 16#9F/Ydieresis 16#A1/exclamdown/cent/sterling/currency/yen/brokenbar/section 16#a8/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/minus/registered/macron 16#b0/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered 16#b8/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown 16#c0/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla 16#c8/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis 16#d0/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply 16#d8/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls 16#e0/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla 16#e8/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis 16#f0/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide 16#f8/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis]def /L2?/languagelevel where{pop languagelevel 2 ge}{false}ifelse def /@BeginSysCorelDict{systemdict/Corel30Dict known{systemdict/Corel30Dict get exec}if}bd/@EndSysCorelDict{systemdict/Corel30Dict known{end}if}bd AutoFlatness {/@ifl{dup currentflat exch sub 10 gt{ ([Error: PathTooComplex; OffendingCommand: AnyPaintingOperator]\n)print flush @np exit}{currentflat 2 add setflat}ifelse}bd/@fill/fill ld/fill{currentflat{ {@fill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@eofill/eofill ld/eofill {currentflat{{@eofill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@clip /clip ld/clip{currentflat{{@clip}stopped{@ifl}{exit}ifelse}bind loop setflat} bd/@eoclip/eoclip ld/eoclip{currentflat{{@eoclip}stopped{@ifl}{exit}ifelse} bind loop setflat}bd/@stroke/stroke ld/stroke{currentflat{{@stroke}stopped {@ifl}{exit}ifelse}bind loop setflat}bd}if L2?{/@ssa{true setstrokeadjust}bd}{ /@ssa{}bd}ifelse/d/setdash ld/j/setlinejoin ld/J/setlinecap ld/M/setmiterlimit ld/w/setlinewidth ld/O{/$o xd}bd/R{/$O xd}bd/W/eoclip ld/c/curveto ld/C/c ld/l /lineto ld/L/l ld/rl/rlineto ld/m/moveto ld/n/newpath ld/N/newpath ld/P{11 rp} bd/u{}bd/U{}bd/A{pop}bd/q/@gs ld/Q/@gr ld/&{}bd/@j{@sv @np}bd/@J{@rs}bd/g{1 exch sub/$k xd/$c 0 def/$m 0 def/$y 0 def/$t 1 def/$n _ def/$fil 0 def}bd/G{1 sub neg/$K xd _ 1 0 0 0/$C xd/$M xd/$Y xd/$T xd/$N xd}bd/k{1 index type /stringtype eq{/$t xd/$n xd}{/$t 0 def/$n _ def}ifelse/$k xd/$y xd/$m xd/$c xd /$fil 0 def}bd/K{1 index type/stringtype eq{/$T xd/$N xd}{/$T 0 def/$N _ def} ifelse/$K xd/$Y xd/$M xd/$C xd}bd/x/k ld/X/K ld/sf{1 index type/stringtype eq{ /s1t xd/s1n xd}{/s1t 0 def/s1n _ def}ifelse/s1k xd/s1y xd/s1m xd/s1c xd}bd/i{ dup 0 ne{setflat}{pop}ifelse}bd/v{4 -2 roll 2 copy 6 -2 roll c}bd/V/v ld/y{2 copy c}bd/Y/y ld/@w{matrix rotate/$ptm xd matrix scale $ptm dup concatmatrix /$ptm xd 1 eq{$ptm exch dup concatmatrix/$ptm xd}if 1 w}bd/@g{1 eq dup/$sdf xd {/$scp xd/$sca xd/$scf xd}if}bd/@G{1 eq dup/$SDF xd{/$SCP xd/$SCA xd/$SCF xd} if}bd/@D{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if 3 copy exch $Scra add exch load SetScr/$dsp xd/$dsa xd/$dsf xd}bd/$ngx{$SDF{$SCF SepMode_5 0 eq{$SCA} {$dsa}ifelse $SCP @ss}if}bd/p{/$pm xd 7 rp/$pyf xd/$pxf xd/$pn xd/$fil 1 def} bd/@MN{2 copy le{pop}{exch pop}ifelse}bd/@MX{2 copy ge{pop}{exch pop}ifelse}bd /InRange{3 -1 roll @MN @MX}bd/@sqr{dup 0 rl dup 0 exch rl neg 0 rl @cp}bd /currentscale{1 0 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt 0 1 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt}bd/@unscale{}bd/wDstChck{2 1 roll dup 3 -1 roll eq{1 add}if}bd /@dot{dup mul exch dup mul add 1 exch sub}bd/@lin{exch pop abs 1 exch sub}bd /cmyk2rgb{3{dup 5 -1 roll add 1 exch sub dup 0 lt{pop 0}if exch}repeat pop}bd /rgb2cmyk{3{1 exch sub 3 1 roll}repeat 3 copy @MN @MN 3{dup 5 -1 roll sub neg exch}repeat}bd/rgb2g{2 index .299 mul 2 index .587 mul add 1 index .114 mul add 4 1 roll pop pop pop}bd/WaldoColor_5 where{pop}{/SetRgb/setrgbcolor ld/GetRgb /currentrgbcolor ld/SetGry/setgray ld/GetGry/currentgray ld/SetRgb2 systemdict /setrgbcolor get def/GetRgb2 systemdict/currentrgbcolor get def/SetHsb systemdict/sethsbcolor get def/GetHsb systemdict/currenthsbcolor get def /rgb2hsb{SetRgb2 GetHsb}bd/hsb2rgb{3 -1 roll dup floor sub 3 1 roll SetHsb GetRgb2}bd/setcmykcolor where{pop/SetCmyk_5/setcmykcolor ld}{/SetCmyk_5{ cmyk2rgb SetRgb}bd}ifelse/currentcmykcolor where{pop/GetCmyk/currentcmykcolor ld}{/GetCmyk{GetRgb rgb2cmyk}bd}ifelse/setoverprint where{pop}{/setoverprint{ /$op xd}bd}ifelse/currentoverprint where{pop}{/currentoverprint{$op}bd}ifelse /@tc_5{5 -1 roll dup 1 ge{pop}{4{dup 6 -1 roll mul exch}repeat pop}ifelse}bd /@trp{exch pop 5 1 roll @tc_5}bd/setprocesscolor_5{SepMode_5 0 eq{SetCmyk_5}{0 4 $ink_5 sub index exch pop 5 1 roll pop pop pop pop SepsColor true eq{$ink_5 3 gt{1 sub neg SetGry}{0 0 0 4 $ink_5 roll SetCmyk_5}ifelse}{1 sub neg SetGry} ifelse}ifelse}bd/findcmykcustomcolor where{pop}{/findcmykcustomcolor{5 array astore}bd}ifelse/setcustomcolor where{pop}{/setcustomcolor{exch aload pop SepMode_5 0 eq{pop @tc_5 setprocesscolor_5}{CurrentInkName_5 eq{4 index}{0} ifelse 6 1 roll 5 rp 1 sub neg SetGry}ifelse}bd}ifelse/@scc_5{dup type /booleantype eq{setoverprint}{1 eq setoverprint}ifelse dup _ eq{pop setprocesscolor_5 pop}{findcmykcustomcolor exch setcustomcolor}ifelse SepMode_5 0 eq{true}{GetGry 1 eq currentoverprint and not}ifelse}bd/colorimage where{pop /ColorImage{colorimage}def}{/ColorImage{/ncolors xd pop/dataaq xd{dataaq ncolors dup 3 eq{/$dat xd 0 1 $dat length 3 div 1 sub{dup 3 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length 3 idiv getinterval pop}{4 eq{/$dat xd 0 1 $dat length 4 div 1 sub{dup 4 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div $dat 4 index 3 add get 255 div cmyk2rgb rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length ncolors idiv getinterval}if}ifelse}image}bd }ifelse/setcmykcolor{1 5 1 roll _ currentoverprint @scc_5/$ffpnt xd}bd /currentcmykcolor{0 0 0 0}bd/setrgbcolor{rgb2cmyk setcmykcolor}bd /currentrgbcolor{currentcmykcolor cmyk2rgb}bd/sethsbcolor{hsb2rgb setrgbcolor} bd/currenthsbcolor{currentrgbcolor rgb2hsb}bd/setgray{dup dup setrgbcolor}bd /currentgray{currentrgbcolor rgb2g}bd}ifelse/WaldoColor_5 true def/@sft{$tllx $pxf add dup $tllx gt{$pwid sub}if/$tx xd $tury $pyf sub dup $tury lt{$phei add}if/$ty xd}bd/@stb{pathbbox/$ury xd/$urx xd/$lly xd/$llx xd}bd/@ep{{cvx exec }forall}bd/@tp{@sv/$in true def 2 copy dup $lly le{/$in false def}if $phei sub $ury ge{/$in false def}if dup $urx ge{/$in false def}if $pwid add $llx le{/$in false def}if $in{@np 2 copy m $pwid 0 rl 0 $phei neg rl $pwid neg 0 rl 0 $phei rl clip @np $pn cvlit load aload pop 7 -1 roll 5 index sub 7 -1 roll 3 index sub Tl matrix currentmatrix/$ctm xd @ep pop pop pop pop}{pop pop}ifelse @rs}bd /@th{@sft 0 1 $tly 1 sub{dup $psx mul $tx add{dup $llx gt{$pwid sub}{exit} ifelse}loop exch $phei mul $ty exch sub 0 1 $tlx 1 sub{$pwid mul 3 copy 3 -1 roll add exch @tp pop}for pop pop}for}bd/@tv{@sft 0 1 $tlx 1 sub{dup $pwid mul $tx add exch $psy mul $ty exch sub{dup $ury lt{$phei add}{exit}ifelse}loop 0 1 $tly 1 sub{$phei mul 3 copy sub @tp pop}for pop pop}for}bd/$fm 0 def/wfill{1 $fm eq{fill}{eofill}ifelse}bd/wclip{1 $fm eq{clip}{eoclip}ifelse}bd/@pf{@gs $ctm setmatrix $pm concat @stb wclip Bburx Bbury $pm itransform/$tury xd/$turx xd Bbllx Bblly $pm itransform/$tlly xd/$tllx xd/$wid $turx $tllx sub def/$hei $tury $tlly sub def @gs $vectpat{1 0 0 0 0 _ $o @scc_5{wfill}if}{$t $c $m $y $k $n $o @scc_5{SepMode_5 0 eq $pfrg or{$tllx $tlly Tl $wid $hei scale <00> 8 1 false[8 0 0 1 0 0]{}imagemask}{/$bkg true def}ifelse}if}ifelse @gr $wid 0 gt $hei 0 gt and{$pn cvlit load aload pop/$pd xd 3 -1 roll sub/$phei xd exch sub /$pwid xd $wid $pwid div ceiling 1 add/$tlx xd $hei $phei div ceiling 1 add /$tly xd $psx 0 eq{@tv}{@th}ifelse}if @gr @np/$bkg false def}bd/@Pf{@sv SepMode_5 0 eq $Psc 0 ne or $ink_5 3 eq or{0 J 0 j[]0 d $t $c $m $y $k $n $o @scc_5 pop $ctm setmatrix 72 1000 div dup matrix scale dup concat dup Bburx exch Bbury exch itransform ceiling cvi/Bbury xd ceiling cvi/Bburx xd Bbllx exch Bblly exch itransform floor cvi/Bblly xd floor cvi/Bbllx xd $Prm aload pop $Psn load exec}{1 SetGry wfill}ifelse @rs @np}bd/F{matrix currentmatrix $sdf{$scf $sca $scp @ss}if $fil 1 eq{@pf}{$fil 2 eq{@ff}{$fil 3 eq{@Pf}{$t $c $m $y $k $n $o @scc_5{wfill}{@np}ifelse}ifelse}ifelse}ifelse $sdf{$dsf $dsa $dsp @ss}if setmatrix}bd/f{@cp F}bd/S{matrix currentmatrix $ctm setmatrix $SDF{$SCF $SCA $SCP @ss}if $T $C $M $Y $K $N $O @scc_5{matrix currentmatrix $ptm concat stroke setmatrix}{@np}ifelse $SDF{$dsf $dsa $dsp @ss}if setmatrix}bd/s{@cp S}bd/B{@gs F @gr S}bd/b{@cp B}bd/_E{5 array astore exch cvlit xd}bd/@cc{currentfile $dat readhexstring pop}bd/@sm{/$ctm $ctm currentmatrix def}bd/@E{/Bbury xd/Bburx xd /Bblly xd/Bbllx xd}bd/@c{@cp}bd/@p{/$fil 1 def 1 eq dup/$vectpat xd{/$pfrg true def}{@gs $t $c $m $y $k $n $o @scc_5/$pfrg xd @gr}ifelse/$pm xd/$psy xd/$psx xd /$pyf xd/$pxf xd/$pn xd}bd/@P{/$fil 3 def/$Psn xd/$Psc xd array astore/$Prm xd }bd/@ii{concat 3 index 3 index m 3 index 1 index l 2 copy l 1 index 3 index l 3 index 3 index l clip pop pop pop pop}bd/tcc{@cc}def/@i{@sm @gs @ii 6 index 1 ne {/$frg true def pop pop}{1 eq{s1t s1c s1m s1y s1k s1n $O @scc_5/$frg xd}{/$frg false def}ifelse 1 eq{@gs $ctm setmatrix F @gr}if}ifelse @np/$ury xd/$urx xd /$lly xd/$llx xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul 8 div ceiling cvi string def $bkg $frg or{$SDF{$SCF $SCA $SCP @ss}if $llx $lly Tl $urx $llx sub $ury $lly sub scale $bkg{$t $c $m $y $k $n $o @scc_5 pop}if $wid $hei abs $bts 1 eq{$bkg}{$bts}ifelse[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/tcc load $bts 1 eq{imagemask}{image}ifelse $SDF{$dsf $dsa $dsp @ss}if}{$hei abs{tcc pop} repeat}ifelse @gr $ctm setmatrix}bd/@I{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd /$llx xd/$ncl xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def $ngx $llx $lly Tl $urx $llx sub $ury $lly sub scale $wid $hei abs $bts[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/@cc load false $ncl ColorImage $SDF{$dsf $dsa $dsp @ss}if @gr $ctm setmatrix}bd/COMP 0 def L2?{ /@I_2{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd/$llx xd/$ncl xd/$bts xd/$hei xd /$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def 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Profil -Sem %%BeginResource: procset wCorel7Dict 7.0 0 /wCorel7Dict 300 dict def wCorel7Dict begin % Copyright (c)1992-96 Corel Corporation % All rights reserved. v7.0 r1.0 /bd{bind def}bind def/ld{load def}bd/xd{exch def}bd/_ null def/rp{{pop}repeat} bd/@cp/closepath ld/@gs/gsave ld/@gr/grestore ld/@np/newpath ld/Tl/translate ld /$sv 0 def/@sv{/$sv save def}bd/@rs{$sv restore}bd/spg/showpage ld/showpage{} bd currentscreen/@dsp xd/$dsp/@dsp def/$dsa xd/$dsf xd/$sdf false def/$SDF false def/$Scra 0 def/SetScr/setscreen ld/setscreen{pop pop pop}bd/@ss{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if exch $Scra add exch load SetScr}bd /SepMode_5 where{pop}{/SepMode_5 0 def}ifelse/CurrentInkName_5 where{pop} {/CurrentInkName_5(Composite)def}ifelse/$ink_5 where{pop}{/$ink_5 -1 def} ifelse/$c 0 def/$m 0 def/$y 0 def/$k 0 def/$t 1 def/$n _ def/$o 0 def/$fil 0 def/$C 0 def/$M 0 def/$Y 0 def/$K 0 def/$T 1 def/$N _ def/$O 0 def/$PF false def/s1c 0 def/s1m 0 def/s1y 0 def/s1k 0 def/s1t 0 def/s1n _ def/$bkg false def /SK 0 def/SM 0 def/SY 0 def/SC 0 def/$op false def matrix currentmatrix/$ctm xd /$ptm matrix def/$ttm matrix def/$stm matrix def/$ffpnt true def /CorelDrawReencodeVect[16#0/grave 16#5/breve 16#6/dotaccent 16#8/ring 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl 16#88/circumflex/perthousand/Scaron/guilsinglleft/OE 16#91/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash 16#98/tilde/trademark/scaron/guilsinglright/oe 16#9F/Ydieresis 16#A1/exclamdown/cent/sterling/currency/yen/brokenbar/section 16#a8/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/minus/registered/macron 16#b0/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered 16#b8/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown 16#c0/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla 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c 230742 -41985 231372 -44074 232623 -45522 c 233884 -46962 235427 -47686 237242 -47686 c 238955 -47686 240629 -47122 242285 -46002 c 243941 -44883 245229 -43265 246142 -41148 C @c 231645 -33904 m 248070 -33904 L 248089 -33387 248099 -33020 248099 -32804 c 248099 -30301 247478 -28382 246226 -27056 c 244975 -25720 243367 -25052 241401 -25052 c 239274 -25052 237327 -25795 235577 -27263 c 233818 -28730 232511 -30941 231645 -33904 C @c F %CHAR: 254166 -51101 (s) @t 256508 -41101 m 261494 -40791 L 261494 -42230 261720 -43453 262162 -44459 c 262595 -45466 263413 -46294 264599 -46943 c 265784 -47583 267167 -47903 268747 -47903 c 270949 -47903 272604 -47460 273705 -46585 c 274806 -45701 275361 -44657 275361 -43462 c 275361 -42606 275031 -41788 274364 -41016 c 273686 -40245 272031 -39295 269396 -38166 c 266753 -37028 265069 -36237 264335 -35776 c 263103 -35024 262181 -34140 261551 -33114 c 260930 -32098 260619 -30922 260619 -29605 c 260619 -27291 261532 -25306 263376 -23650 c 265210 -21995 267778 -21167 271090 -21167 c 274759 -21167 277562 -22023 279481 -23716 c 281400 -25419 282397 -27658 282473 -30433 C 277590 -30762 L 277515 -28994 276894 -27601 275718 -26576 c 274542 -25541 272877 -25033 270732 -25033 c 269001 -25033 267666 -25428 266706 -26209 c 265746 -26999 265276 -27855 265276 -28777 c 265276 -29699 265690 -30508 266518 -31204 c 267063 -31684 268484 -32418 270789 -33406 c 274608 -35061 277016 -36369 278004 -37319 c 279585 -38843 280375 -40706 280375 -42888 c 280375 -44337 279933 -45767 279039 -47159 c 278145 -48552 276791 -49671 274956 -50508 c 273131 -51346 270977 -51760 268493 -51760 c 265116 -51760 262237 -50922 259867 -49257 c 257496 -47583 256377 -44864 256508 -41101 C @c F T %%PageTrailer @rs @rs %%Trailer @EndSysCorelDict end %%DocumentSuppliedResources: procset wCorel7Dict %%EOF %%EndDocument @endspecial 546 4371 a currentpoint currentpoint translate 1 0.60837 div 1 0.60837 div scale neg exch neg exch translate 546 4371 a 109 4575 a FH(Figura)d(2.3:)43 b(Exemplos)31 b(de)h(seq\374\352ncias)h(de)e(carros)h(para)f(uma)f (restri\347\343o)h(de)h(capacidade)f(de)h(raz\343o)109 4695 y(1/5.)274 5072 y(O)47 b(n)m(\372mero)g(total)e(de)i (viola\347\365)s(es)f(de)h(restri\347\365)s(es)h(de)f(capacidade)g (\351)g(a)g(soma)f(do)h(n)m(\372mero)g(de)109 5234 y(viola\347\365)s (es)31 b(de)i(cada)g(restri\347\343o)f(em)g(to)s(das)g(as)h (seq\374\352ncias)h(consecutiv)-5 b(as)33 b(do)g(dia)e(de)i(pro)s (du\347\343o.)274 5456 y(Quando)j(o)f(dia)g(de)i(pro)s(du\347\343o)f (atual)e(\351)i(escalonado,)h(c)m(hamado)e(de)i(dia)e(D,)h(os)g (\372ltimos)e(carros)109 5618 y(do)h(dia)f(de)i(pro)s(du\347\343o)e(an) m(terior,)i(c)m(hamado)e(dia)g(D-1,)i(dev)m(em)g(ser)g(lev)-5 b(ados)35 b(em)f(considera\347\343o)i(para)109 5781 y(a)41 b(computa\347\343o)g(do)g(n)m(\372mero)h(de)g(viola\347\365)s(es)e(de)j (restri\347\365)s(es)e(de)i(capacidade)e(no)h(dia)e(de)i(pro)s (du\347\343o)109 5943 y(D.)35 b(Em)m(b)s(ora)g(ainda)f(n\343o)h(tenham) g(sido)g(pro)s(duzidos)g(p)s(or)f(algum)g(motiv)m(o,)g(estes)j(carros)e (do)g(dia)g(de)p eop %%Page: 7 21 7 20 bop 109 -28 a FB(2.2)60 b(Requisitos)30 b(de)h(mon)m(tagem)2594 b(7)p 109 9 3780 4 v 109 256 a FH(pro)s(du\347\343o)39 b(D-1)g(j\341)g(foram)e(escalonados)j(e,)h(p)s(ortan)m(to,)f(suas)h(p)s (osi\347\365)s(es)e(n\343o)g(p)s(o)s(dem)f(ser)i(alteradas)109 418 y(quando)e(o)f(dia)g(de)h(pro)s(du\347\343o)f(D)h(est\341)g(sendo)h (escalonado.)58 b(Quando)38 b(computando)f(o)g(n)m(\372mero)h(de)109 581 y(viola\347\365)s(es,)23 b(as)h(seq\374\352ncias)g(consideradas)f (dev)m(em,)j(en)m(t\343o,)f(come\347ar)e(no)g(dia)f(de)h(pro)s (du\347\343o)g(D-1.)40 b(P)m(ara)109 743 y(uma)33 b(restri\347\343o)g (de)i(capacidade)f(de)g(raz\343o)g Fz(N)r(=P)14 b FH(,)34 b(a)f(primeira)f(seq\374\352ncia)j(considerada)f(con)m(t\351m)g(os)109 906 y Fz(P)39 b Fs(\000)27 b FA(1)39 b FH(\372ltimos)d(carros)j (escalonados)g(do)f(dia)g(de)h(pro)s(du\347\343o)g(D-1)f(e)h(o)g (primeiro)d(carro)i(do)h(dia)f(D.)109 1068 y(A)32 b(Figura)f(2.4)h (mostra)g(um)g(exemplo)f(do)i(n)m(\372mero)f(de)h(viola\347\365)s(es)e (em)i(to)s(das)f(seq\374\352ncias)i(para)e(uma)109 1231 y(restri\347\343o)44 b(de)g(capacidade)h(de)g(raz\343o)f FA(1)p Fz(=)p FA(5)p FH(.)78 b(Na)44 b(\034gura,)j(observ)-5 b(a-se)46 b(que)f(a)f(primeira)e(seq\374\352ncia)109 1393 y(con)m(tabilizada)30 b(tem)i(exatamen)m(te)h(quatro)g(carros)f (do)h(dia)e(D-1)i(e)g(um)e(carro)i(do)f(dia)g(D.)803 3300 y currentpoint currentpoint translate 0.61813 0.61813 scale neg exch neg exch translate 803 3300 a @beginspecial 2 @llx 229 @lly 466 @urx 550 @ury 4640 @rwi @setspecial %%BeginDocument: restricao3.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 2 229 466 550 %%Creator: CorelDRAW 7 %%Title: %%CreationDate: Thu Jan 20 14:48:53 2005 %%DocumentProcessColors: Cyan Magenta Yellow Black %%DocumentSuppliedResources: (atend) %%EndComments %%BeginProlog /AutoFlatness true def /AutoSteps 0 def /CMYKMarks false def /UseLevel2 false def %Color profile: _DEFAULT.CCM - Gen. Profil -Sem %%BeginResource: procset wCorel7Dict 7.0 0 /wCorel7Dict 300 dict def wCorel7Dict begin % Copyright (c)1992-96 Corel Corporation % All rights reserved. v7.0 r1.0 /bd{bind def}bind def/ld{load def}bd/xd{exch def}bd/_ null def/rp{{pop}repeat} bd/@cp/closepath ld/@gs/gsave ld/@gr/grestore ld/@np/newpath ld/Tl/translate ld /$sv 0 def/@sv{/$sv save def}bd/@rs{$sv restore}bd/spg/showpage ld/showpage{} bd currentscreen/@dsp xd/$dsp/@dsp def/$dsa xd/$dsf xd/$sdf false def/$SDF false def/$Scra 0 def/SetScr/setscreen ld/setscreen{pop pop pop}bd/@ss{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if exch $Scra add exch load SetScr}bd /SepMode_5 where{pop}{/SepMode_5 0 def}ifelse/CurrentInkName_5 where{pop} {/CurrentInkName_5(Composite)def}ifelse/$ink_5 where{pop}{/$ink_5 -1 def} ifelse/$c 0 def/$m 0 def/$y 0 def/$k 0 def/$t 1 def/$n _ def/$o 0 def/$fil 0 def/$C 0 def/$M 0 def/$Y 0 def/$K 0 def/$T 1 def/$N _ def/$O 0 def/$PF false def/s1c 0 def/s1m 0 def/s1y 0 def/s1k 0 def/s1t 0 def/s1n _ def/$bkg false def /SK 0 def/SM 0 def/SY 0 def/SC 0 def/$op false def matrix currentmatrix/$ctm xd /$ptm matrix def/$ttm matrix def/$stm matrix def/$ffpnt true def /CorelDrawReencodeVect[16#0/grave 16#5/breve 16#6/dotaccent 16#8/ring 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl 16#88/circumflex/perthousand/Scaron/guilsinglleft/OE 16#91/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash 16#98/tilde/trademark/scaron/guilsinglright/oe 16#9F/Ydieresis 16#A1/exclamdown/cent/sterling/currency/yen/brokenbar/section 16#a8/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/minus/registered/macron 16#b0/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered 16#b8/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown 16#c0/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla 16#c8/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis 16#d0/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply 16#d8/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls 16#e0/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla 16#e8/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis 16#f0/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide 16#f8/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis]def /L2?/languagelevel where{pop languagelevel 2 ge}{false}ifelse def /@BeginSysCorelDict{systemdict/Corel30Dict known{systemdict/Corel30Dict get exec}if}bd/@EndSysCorelDict{systemdict/Corel30Dict known{end}if}bd AutoFlatness {/@ifl{dup currentflat exch sub 10 gt{ ([Error: PathTooComplex; OffendingCommand: AnyPaintingOperator]\n)print flush @np exit}{currentflat 2 add setflat}ifelse}bd/@fill/fill ld/fill{currentflat{ {@fill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@eofill/eofill ld/eofill {currentflat{{@eofill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@clip /clip ld/clip{currentflat{{@clip}stopped{@ifl}{exit}ifelse}bind loop setflat} bd/@eoclip/eoclip ld/eoclip{currentflat{{@eoclip}stopped{@ifl}{exit}ifelse} bind loop setflat}bd/@stroke/stroke ld/stroke{currentflat{{@stroke}stopped {@ifl}{exit}ifelse}bind loop setflat}bd}if L2?{/@ssa{true setstrokeadjust}bd}{ /@ssa{}bd}ifelse/d/setdash ld/j/setlinejoin ld/J/setlinecap ld/M/setmiterlimit ld/w/setlinewidth ld/O{/$o xd}bd/R{/$O xd}bd/W/eoclip ld/c/curveto ld/C/c ld/l /lineto ld/L/l ld/rl/rlineto ld/m/moveto ld/n/newpath ld/N/newpath ld/P{11 rp} bd/u{}bd/U{}bd/A{pop}bd/q/@gs ld/Q/@gr ld/&{}bd/@j{@sv @np}bd/@J{@rs}bd/g{1 exch sub/$k xd/$c 0 def/$m 0 def/$y 0 def/$t 1 def/$n _ def/$fil 0 def}bd/G{1 sub neg/$K xd _ 1 0 0 0/$C xd/$M xd/$Y xd/$T xd/$N xd}bd/k{1 index type /stringtype eq{/$t xd/$n xd}{/$t 0 def/$n _ def}ifelse/$k xd/$y xd/$m xd/$c xd /$fil 0 def}bd/K{1 index type/stringtype eq{/$T xd/$N xd}{/$T 0 def/$N _ def} ifelse/$K xd/$Y xd/$M xd/$C xd}bd/x/k ld/X/K ld/sf{1 index type/stringtype eq{ /s1t xd/s1n xd}{/s1t 0 def/s1n _ def}ifelse/s1k xd/s1y xd/s1m xd/s1c xd}bd/i{ dup 0 ne{setflat}{pop}ifelse}bd/v{4 -2 roll 2 copy 6 -2 roll c}bd/V/v ld/y{2 copy c}bd/Y/y ld/@w{matrix rotate/$ptm xd matrix scale $ptm dup concatmatrix /$ptm xd 1 eq{$ptm exch dup concatmatrix/$ptm xd}if 1 w}bd/@g{1 eq dup/$sdf xd {/$scp xd/$sca xd/$scf xd}if}bd/@G{1 eq dup/$SDF xd{/$SCP xd/$SCA xd/$SCF xd} if}bd/@D{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if 3 copy exch $Scra add exch load SetScr/$dsp xd/$dsa xd/$dsf xd}bd/$ngx{$SDF{$SCF SepMode_5 0 eq{$SCA} {$dsa}ifelse $SCP @ss}if}bd/p{/$pm xd 7 rp/$pyf xd/$pxf xd/$pn xd/$fil 1 def} bd/@MN{2 copy le{pop}{exch pop}ifelse}bd/@MX{2 copy ge{pop}{exch pop}ifelse}bd /InRange{3 -1 roll @MN @MX}bd/@sqr{dup 0 rl dup 0 exch rl neg 0 rl @cp}bd /currentscale{1 0 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt 0 1 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt}bd/@unscale{}bd/wDstChck{2 1 roll dup 3 -1 roll eq{1 add}if}bd /@dot{dup mul exch dup mul add 1 exch sub}bd/@lin{exch pop abs 1 exch sub}bd /cmyk2rgb{3{dup 5 -1 roll add 1 exch sub dup 0 lt{pop 0}if exch}repeat pop}bd /rgb2cmyk{3{1 exch sub 3 1 roll}repeat 3 copy @MN @MN 3{dup 5 -1 roll sub neg exch}repeat}bd/rgb2g{2 index .299 mul 2 index .587 mul add 1 index .114 mul add 4 1 roll pop pop pop}bd/WaldoColor_5 where{pop}{/SetRgb/setrgbcolor ld/GetRgb /currentrgbcolor ld/SetGry/setgray ld/GetGry/currentgray ld/SetRgb2 systemdict /setrgbcolor get def/GetRgb2 systemdict/currentrgbcolor get def/SetHsb systemdict/sethsbcolor get def/GetHsb systemdict/currenthsbcolor get def /rgb2hsb{SetRgb2 GetHsb}bd/hsb2rgb{3 -1 roll dup floor sub 3 1 roll SetHsb GetRgb2}bd/setcmykcolor where{pop/SetCmyk_5/setcmykcolor ld}{/SetCmyk_5{ cmyk2rgb SetRgb}bd}ifelse/currentcmykcolor where{pop/GetCmyk/currentcmykcolor ld}{/GetCmyk{GetRgb rgb2cmyk}bd}ifelse/setoverprint where{pop}{/setoverprint{ /$op xd}bd}ifelse/currentoverprint where{pop}{/currentoverprint{$op}bd}ifelse /@tc_5{5 -1 roll dup 1 ge{pop}{4{dup 6 -1 roll mul exch}repeat pop}ifelse}bd /@trp{exch pop 5 1 roll @tc_5}bd/setprocesscolor_5{SepMode_5 0 eq{SetCmyk_5}{0 4 $ink_5 sub index exch pop 5 1 roll pop pop pop pop SepsColor true eq{$ink_5 3 gt{1 sub neg SetGry}{0 0 0 4 $ink_5 roll SetCmyk_5}ifelse}{1 sub neg SetGry} ifelse}ifelse}bd/findcmykcustomcolor where{pop}{/findcmykcustomcolor{5 array astore}bd}ifelse/setcustomcolor where{pop}{/setcustomcolor{exch aload pop SepMode_5 0 eq{pop @tc_5 setprocesscolor_5}{CurrentInkName_5 eq{4 index}{0} ifelse 6 1 roll 5 rp 1 sub neg SetGry}ifelse}bd}ifelse/@scc_5{dup type /booleantype eq{setoverprint}{1 eq setoverprint}ifelse dup _ eq{pop setprocesscolor_5 pop}{findcmykcustomcolor exch setcustomcolor}ifelse SepMode_5 0 eq{true}{GetGry 1 eq currentoverprint and not}ifelse}bd/colorimage where{pop /ColorImage{colorimage}def}{/ColorImage{/ncolors xd 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c 274139 22258 275136 19473 275136 15983 c 275136 13189 274440 10442 273057 7733 c 271664 5024 269745 2944 267281 1486 c 264816 38 262238 -687 259538 -687 c 256095 -687 253273 423 251062 2643 c 248842 4873 247723 7846 247685 11571 C @c F T %%PageTrailer @rs @rs %%Trailer @EndSysCorelDict end %%DocumentSuppliedResources: procset wCorel7Dict %%EOF %%EndDocument @endspecial 803 3300 a currentpoint currentpoint translate 1 0.61813 div 1 0.61813 div scale neg exch neg exch translate 803 3300 a 109 3504 a FH(Figura)d(2.4:)43 b(C\341lculo)30 b(do)h(n)m(\372mero)h(de)f(viola\347\365)s(es)g(de)g (uma)g(restri\347\343o)g(de)h(capacidade)f(de)h(raz\343o)f(1/5)109 3624 y(em)h(uma)g(dada)g(seq\374\352ncia.)274 4011 y(O)43 b(dia)f(de)h(pro)s(du\347\343o)g(seguin)m(te,)k(c)m(hamado)42 b(de)i(D+1,)i(p)s(or)c(sua)i(v)m(ez,)j(\351)c(ignorado)f(duran)m(te)h (o)109 4173 y(escalonamen)m(to)27 b(do)h(dia)g(D.)g(No)g(en)m(tan)m (to,)i(as)e(viola\347\365)s(es)f(decorren)m(tes)k(dos)d(\372ltimos)e (carros)i(do)h(dia)e(D)109 4336 y(s\343o)i(computadas)g(como)f(se)i(os) f(primeiros)e(carros)i(do)g(dia)g(D+1)g(n\343o)g(estiv)m(essem)h(asso)s (ciados)f(com)f(a)109 4498 y(restri\347\343o.)41 b(Ou)27 b(seja,)h(para)f(uma)f(restri\347\343o)h(de)h(capacidade)f(de)g (raz\343o)g Fz(N)r(=P)14 b FH(,)27 b(as)h(\372ltimas)d (seq\374\352ncias)109 4661 y(computadas)k(t\352m,)h(na)f(realidade,)g (tamanhos)g Fz(P)g Fs(\000)16 b FA(1)p Fz(;)h(P)29 b Fs(\000)16 b FA(2)p Fz(;)h(:)g(:)g(:)f(;)h(N)27 b FA(+)16 b(1)p FH(.)42 b(O)29 b(n)m(\372mero)g(de)h(viola\347\365)s(es)109 4823 y(de)42 b(uma)g(restri\347\343o)g(con)m(tin)m(ua)g(sendo)h(a)f (diferen\347a)g(do)h(n)m(\372mero)f(de)h(carros)f(asso)s(ciados)g(com)g (esta)109 4986 y(restri\347\343o)36 b(na)g(seq\374\352ncia)i(menos)e(o) h(n)m(umerador)f(da)g(restri\347\343o)g(se)i(a)e(diferen\347a)g(\351)h (p)s(ositiv)-5 b(a,)36 b(e)h(zero,)109 5148 y(caso)e(con)m(tr\341rio.) 51 b(O)35 b(in)m(tuito)e(deste)k(m\351to)s(do)d(de)i(computa\347\343o)e (\351)i(dar)f(o)g(mesmo)f(p)s(eso)i(\340s)f(viola\347\365)s(es)109 5311 y(decorren)m(tes)43 b(dos)e(\372ltimos)e(carros)i(do)g(dia)f(D)h (e)h(\340s)f(viola\347\365)s(es)f(dos)h(carros)g(an)m(teriores,)i (j\341)e(que)h(as)109 5473 y(viola\347\365)s(es)33 b(causadas)j(p)s (elos)e(carros)h(in)m(termedi\341rios)d(aparecem)j(em)f(v)-5 b(\341rias)34 b(seq\374\352ncias)i(consecuti-)109 5636 y(v)-5 b(as.)43 b(A)31 b(\034m)g(de)h(facilitar)c(o)j(en)m(tendimen)m (to,)h(a)f(Figura)e(2.5)i(mostra)f(a)h(con)m(tin)m(ua\347\343o)g(do)h (exemplo)e(da)109 5799 y(Figura)h(2.4,)h(calculando)f(as)i (viola\347\365)s(es)e(adicionais)f(causadas)k(p)s(elas)e(\372ltimas)e (seq\374\352ncias.)p eop %%Page: 8 22 8 21 bop 109 -28 a FB(2.3)60 b(Tip)s(os)31 b(de)f(problema)2819 b(8)p 109 9 3780 4 v 729 1337 a currentpoint currentpoint translate 0.62439 0.62439 scale neg exch neg exch translate 729 1337 a @beginspecial 2 @llx 323 @lly 490 @urx 550 @ury 4880 @rwi @setspecial %%BeginDocument: restricao4.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 2 323 490 550 %%Creator: CorelDRAW 7 %%Title: %%CreationDate: Thu Jan 20 14:49:26 2005 %%DocumentProcessColors: Cyan Magenta Yellow Black %%DocumentSuppliedResources: (atend) %%EndComments %%BeginProlog /AutoFlatness true def /AutoSteps 0 def /CMYKMarks false def /UseLevel2 false def %Color profile: _DEFAULT.CCM - Gen. Profil -Sem %%BeginResource: procset wCorel7Dict 7.0 0 /wCorel7Dict 300 dict def wCorel7Dict begin % Copyright (c)1992-96 Corel Corporation % All rights reserved. v7.0 r1.0 /bd{bind def}bind def/ld{load def}bd/xd{exch def}bd/_ null def/rp{{pop}repeat} bd/@cp/closepath ld/@gs/gsave ld/@gr/grestore ld/@np/newpath ld/Tl/translate ld /$sv 0 def/@sv{/$sv save def}bd/@rs{$sv restore}bd/spg/showpage ld/showpage{} bd currentscreen/@dsp xd/$dsp/@dsp def/$dsa xd/$dsf xd/$sdf false def/$SDF false def/$Scra 0 def/SetScr/setscreen ld/setscreen{pop pop pop}bd/@ss{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if exch $Scra add exch load SetScr}bd /SepMode_5 where{pop}{/SepMode_5 0 def}ifelse/CurrentInkName_5 where{pop} {/CurrentInkName_5(Composite)def}ifelse/$ink_5 where{pop}{/$ink_5 -1 def} ifelse/$c 0 def/$m 0 def/$y 0 def/$k 0 def/$t 1 def/$n _ def/$o 0 def/$fil 0 def/$C 0 def/$M 0 def/$Y 0 def/$K 0 def/$T 1 def/$N _ def/$O 0 def/$PF false def/s1c 0 def/s1m 0 def/s1y 0 def/s1k 0 def/s1t 0 def/s1n _ def/$bkg false def /SK 0 def/SM 0 def/SY 0 def/SC 0 def/$op false def matrix currentmatrix/$ctm xd /$ptm matrix def/$ttm matrix def/$stm matrix def/$ffpnt true def /CorelDrawReencodeVect[16#0/grave 16#5/breve 16#6/dotaccent 16#8/ring 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl 16#88/circumflex/perthousand/Scaron/guilsinglleft/OE 16#91/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash 16#98/tilde/trademark/scaron/guilsinglright/oe 16#9F/Ydieresis 16#A1/exclamdown/cent/sterling/currency/yen/brokenbar/section 16#a8/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/minus/registered/macron 16#b0/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered 16#b8/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown 16#c0/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla 16#c8/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis 16#d0/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply 16#d8/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls 16#e0/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla 16#e8/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis 16#f0/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide 16#f8/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis]def /L2?/languagelevel where{pop languagelevel 2 ge}{false}ifelse def /@BeginSysCorelDict{systemdict/Corel30Dict known{systemdict/Corel30Dict get exec}if}bd/@EndSysCorelDict{systemdict/Corel30Dict known{end}if}bd AutoFlatness {/@ifl{dup currentflat exch sub 10 gt{ ([Error: PathTooComplex; OffendingCommand: AnyPaintingOperator]\n)print flush @np exit}{currentflat 2 add setflat}ifelse}bd/@fill/fill ld/fill{currentflat{ {@fill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@eofill/eofill ld/eofill {currentflat{{@eofill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@clip /clip ld/clip{currentflat{{@clip}stopped{@ifl}{exit}ifelse}bind loop setflat} bd/@eoclip/eoclip ld/eoclip{currentflat{{@eoclip}stopped{@ifl}{exit}ifelse} bind loop setflat}bd/@stroke/stroke ld/stroke{currentflat{{@stroke}stopped {@ifl}{exit}ifelse}bind loop setflat}bd}if L2?{/@ssa{true setstrokeadjust}bd}{ /@ssa{}bd}ifelse/d/setdash ld/j/setlinejoin ld/J/setlinecap ld/M/setmiterlimit ld/w/setlinewidth ld/O{/$o xd}bd/R{/$O xd}bd/W/eoclip ld/c/curveto ld/C/c ld/l /lineto ld/L/l ld/rl/rlineto ld/m/moveto ld/n/newpath ld/N/newpath ld/P{11 rp} bd/u{}bd/U{}bd/A{pop}bd/q/@gs ld/Q/@gr ld/&{}bd/@j{@sv @np}bd/@J{@rs}bd/g{1 exch sub/$k xd/$c 0 def/$m 0 def/$y 0 def/$t 1 def/$n _ def/$fil 0 def}bd/G{1 sub neg/$K xd _ 1 0 0 0/$C xd/$M xd/$Y xd/$T xd/$N xd}bd/k{1 index type /stringtype eq{/$t xd/$n xd}{/$t 0 def/$n _ def}ifelse/$k xd/$y xd/$m xd/$c xd /$fil 0 def}bd/K{1 index type/stringtype eq{/$T xd/$N xd}{/$T 0 def/$N _ def} ifelse/$K xd/$Y xd/$M xd/$C xd}bd/x/k ld/X/K ld/sf{1 index type/stringtype eq{ /s1t xd/s1n xd}{/s1t 0 def/s1n _ def}ifelse/s1k xd/s1y xd/s1m xd/s1c xd}bd/i{ dup 0 ne{setflat}{pop}ifelse}bd/v{4 -2 roll 2 copy 6 -2 roll c}bd/V/v ld/y{2 copy c}bd/Y/y ld/@w{matrix rotate/$ptm xd matrix scale $ptm dup concatmatrix /$ptm xd 1 eq{$ptm exch dup concatmatrix/$ptm xd}if 1 w}bd/@g{1 eq dup/$sdf xd {/$scp xd/$sca xd/$scf xd}if}bd/@G{1 eq dup/$SDF xd{/$SCP xd/$SCA xd/$SCF xd} if}bd/@D{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if 3 copy exch $Scra add exch load SetScr/$dsp xd/$dsa xd/$dsf xd}bd/$ngx{$SDF{$SCF SepMode_5 0 eq{$SCA} {$dsa}ifelse $SCP @ss}if}bd/p{/$pm xd 7 rp/$pyf xd/$pxf xd/$pn xd/$fil 1 def} bd/@MN{2 copy le{pop}{exch pop}ifelse}bd/@MX{2 copy ge{pop}{exch pop}ifelse}bd /InRange{3 -1 roll @MN @MX}bd/@sqr{dup 0 rl dup 0 exch rl neg 0 rl @cp}bd /currentscale{1 0 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt 0 1 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt}bd/@unscale{}bd/wDstChck{2 1 roll dup 3 -1 roll eq{1 add}if}bd /@dot{dup mul exch dup mul add 1 exch sub}bd/@lin{exch pop abs 1 exch sub}bd /cmyk2rgb{3{dup 5 -1 roll add 1 exch sub dup 0 lt{pop 0}if exch}repeat pop}bd /rgb2cmyk{3{1 exch sub 3 1 roll}repeat 3 copy @MN @MN 3{dup 5 -1 roll sub neg exch}repeat}bd/rgb2g{2 index .299 mul 2 index .587 mul add 1 index .114 mul add 4 1 roll pop pop pop}bd/WaldoColor_5 where{pop}{/SetRgb/setrgbcolor ld/GetRgb /currentrgbcolor ld/SetGry/setgray ld/GetGry/currentgray ld/SetRgb2 systemdict /setrgbcolor get def/GetRgb2 systemdict/currentrgbcolor get def/SetHsb systemdict/sethsbcolor get def/GetHsb systemdict/currenthsbcolor get def /rgb2hsb{SetRgb2 GetHsb}bd/hsb2rgb{3 -1 roll dup floor sub 3 1 roll SetHsb GetRgb2}bd/setcmykcolor where{pop/SetCmyk_5/setcmykcolor ld}{/SetCmyk_5{ cmyk2rgb SetRgb}bd}ifelse/currentcmykcolor where{pop/GetCmyk/currentcmykcolor ld}{/GetCmyk{GetRgb rgb2cmyk}bd}ifelse/setoverprint where{pop}{/setoverprint{ /$op xd}bd}ifelse/currentoverprint where{pop}{/currentoverprint{$op}bd}ifelse /@tc_5{5 -1 roll dup 1 ge{pop}{4{dup 6 -1 roll mul exch}repeat pop}ifelse}bd /@trp{exch pop 5 1 roll @tc_5}bd/setprocesscolor_5{SepMode_5 0 eq{SetCmyk_5}{0 4 $ink_5 sub index exch pop 5 1 roll pop pop pop pop SepsColor true eq{$ink_5 3 gt{1 sub neg SetGry}{0 0 0 4 $ink_5 roll SetCmyk_5}ifelse}{1 sub neg SetGry} ifelse}ifelse}bd/findcmykcustomcolor where{pop}{/findcmykcustomcolor{5 array astore}bd}ifelse/setcustomcolor where{pop}{/setcustomcolor{exch aload pop SepMode_5 0 eq{pop @tc_5 setprocesscolor_5}{CurrentInkName_5 eq{4 index}{0} ifelse 6 1 roll 5 rp 1 sub neg SetGry}ifelse}bd}ifelse/@scc_5{dup type /booleantype eq{setoverprint}{1 eq setoverprint}ifelse dup _ eq{pop setprocesscolor_5 pop}{findcmykcustomcolor exch setcustomcolor}ifelse SepMode_5 0 eq{true}{GetGry 1 eq currentoverprint and not}ifelse}bd/colorimage where{pop /ColorImage{colorimage}def}{/ColorImage{/ncolors xd 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b(da)h(literatura)2727 b(9)p 109 9 3780 4 v 109 256 a FH(ob)5 b(jetiv)m(os.)45 b(Desta)34 b(forma,)e(pretende-se)i(que)g(a)f(melhor)f(solu\347\343o)g (seja)h(aquela)g(com)f(o)h(menor)g(v)-5 b(alor)109 418 y(do)29 b(primeiro)e(ob)5 b(jetiv)m(o,)31 b(em)e(seguida,)h(com)f(o)g (menor)h(v)-5 b(alor)28 b(do)h(segundo)i(e,)f(p)s(or)g(\034m,)f(com)g (o)h(menor)109 581 y(v)-5 b(alor)31 b(do)h(terceiro)g(ob)5 b(jetiv)m(o.)109 972 y Fx(2.4)155 b(Revis\343o)53 b(da)f(literatura)274 1293 y FH(A)36 b(v)m(ers\343o)i(cl\341ssica)d(do)h(PSC)i(foi)d (primeiramen)m(te)f(descrita)i(p)s(or)g(P)m(arello)f(et)h(al)f([10])h (como)g(um)109 1455 y(tip)s(o)30 b(particular)g(de)i(problema)f(de)h (escalonamen)m(to)f(em)h(linhas)e(de)j(pro)s(du\347\343o)e(de)i(carros) f(e)g(en)m(v)m(olv)m(e)109 1618 y(somen)m(te)44 b(a)g(otimiza\347\343o) e(de)i(viola\347\365)s(es)f(de)i(restri\347\365)s(es)f(de)h (capacidade.)78 b(O)44 b(problema)f(tem)h(sido)109 1780 y(ab)s(ordado)38 b(freq\374en)m(temen)m(te)i(usando)f(t\351cnicas)h(de) f(programa\347\343o)e(p)s(or)h(restri\347\365)s(es)h([1)o(,)g(7],)h (que)g(ex-)109 1943 y(ploram)g(o)j(espa\347o)g(de)g(busca)h(de)f(uma)f (maneira)e(sistem\341tica.)73 b(A)42 b(\034m)g(de)h(reduzir)g(o)f (espa\347o)i(de)109 2105 y(busca,)e(esta)e(estrat\351gia)e(\351)i(com)m (binada)e(com)h(t\351cnicas)h(de)g(\034ltragem)e(para)h(restringir)f(o) h(dom\355nio)109 2268 y(das)28 b(v)-5 b(ari\341)m(v)m(eis)27 b([11].)42 b(Mesmo)28 b(assim,)g(em)f(algumas)f(inst\342ncias,)i(estas) h(ab)s(ordagens)f(n\343o)g(conseguem)109 2430 y(reduzir)37 b(o)h(dom\355nio)d(su\034cien)m(temen)m(te)k(de)f(forma)e(a)h(tornar)g (a)h(busca)g(completa)f(trat\341)m(v)m(el.)58 b(Dian)m(te)109 2593 y(disto,)25 b(o)e(problema)f(tem)h(atra\355do)f(a)i(aten\347\343o) g(para)f(o)g(desen)m(v)m(olvimen)m(to)i(de)f(estrat\351gias)f(que)i (buscam)109 2755 y(solu\347\365)s(es)32 b(apro)m(ximadas)g([2,)g(5,)h (13)o(,)g(14)o(,)g(15)o(].)274 2977 y(A)44 b(NP-completude)f(do)h (problema)f(de)h(decis\343o)g(asso)s(ciado)f(ao)h(PSC)g(cl\341ssico)g (foi)e(primeira-)109 3139 y(men)m(te)29 b(demonstrada)f(p)s(or)g(Gen)m (t)h([4],)h(atra)m(v)m(\351s)g(de)f(uma)f(transforma\347\343o)f(do)i (problema)e(do)i(caminho)109 3302 y(hamiltoniano.)53 b(Gen)m(t)38 b(tam)m(b)s(\351m)e(a\034rma)g(que)i(o)f(problema)f(p)s (ertence)i(a)f(NP)-8 b(,)38 b(sugerindo)f(que)h(uma)109 3464 y(seq\374\352ncia)29 b(de)g(carros)g(\351)f(um)g(certi\034cado)g (apropriado.)41 b(Kis)27 b([8])i(apresen)m(ta)g(uma)f(no)m(v)-5 b(a)28 b(pro)m(v)-5 b(a)28 b(de)h(que)109 3627 y(o)j(problema)f(\351)i (NP-completo.)274 3848 y(No)38 b(en)m(tan)m(to,)i(to)s(dos)d(os)h (trabalhos)f(citados)h(consideram)f(a)g(v)m(ers\343o)i(cl\341ssica)e (do)h(problema,)g(e)109 4011 y(n\343o)32 b(a)g(v)m(ers\343o)i(que)f (\351)g(tema)f(de)h(estudo)g(desta)g(disserta\347\343o.)p eop %%Page: 10 24 10 23 bop 109 726 a FD(Cap\355tulo)64 b(3)109 1390 y(Estrat\351gia)g (Algor\355tmica)274 2092 y FH(A)47 b(\034m)f(de)h(resolv)m(er)g(de)h (maneira)d(mais)g(e\034cien)m(te)j(o)e(PSC,)i(\351)f(imp)s(ortan)m(te)e (observ)-5 b(ar)47 b(cuida-)109 2255 y(dosamen)m(te)37 b(suas)g(caracter\355sticas)f(e)h(p)s(eculiaridades,)g(o)f(que)i(p)s (ossibilita)33 b(fundamen)m(tar)k(e)g(melhor)109 2417 y(a)5 b(justar)35 b(a)f(estrat\351gia)g(que)i(ir\341)e(resolv)m (\352-lo.)49 b(Como)34 b(o)h(problema)e(em)h(estudo)i(\351)f(m)m(uito)f (rico)f(no)i(que)109 2580 y(se)k(refere)h(a)e(tais)g (caracter\355sticas,)i(elas)e(serviram)g(como)g(base)h(para)g(o)f(pro)5 b(jeto)39 b(da)g(estrat\351gia)f(de)109 2742 y(solu\347\343o)32 b(empregada.)274 2964 y(O)e(PSC)h(\351)g(um)f(problema)f(que)i(visa)f (\340)g(otimiza\347\343o)d(de)k(tr\352s)g(ob)5 b(jetiv)m(os)31 b(tratados)f(com)f(n\355v)m(eis)i(de)109 3126 y(prioridade)e(diferen)m (tes,)j(atra)m(v)m(\351s)g(de)f(p)s(esos)g(a)g(eles)f(asso)s(ciados)h (na)f(fun\347\343o)h(ob)5 b(jetiv)m(o.)43 b(Denomina-se)109 3289 y(de)27 b(subproblema)g(o)g(tratamen)m(to)f(da)h(otimiza\347\343o) e(separada)i(de)h(cada)f(ob)5 b(jetiv)m(o.)42 b(Como)26 b(a)h(diferen\347a)109 3451 y(en)m(tre)32 b(os)f(p)s(esos)h(dev)m(e)g (ser)g(relativ)-5 b(amen)m(te)29 b(grande)i(para)g(enfatizar)f(seus)i (diferen)m(tes)g(n\355v)m(eis)f(de)h(prio-)109 3614 y(ridade,)g(a)g (id\351ia)f(de)j(atacar)e(os)h(subproblemas)f(do)h(PSC)g(separadamen)m (te)h(p)s(or)e(ordem)g(decrescen)m(te)109 3776 y(de)h(prioridade)e (torna-se)h(uma)g(estrat\351gia)g(vi\341)m(v)m(el)g(e)h(adequada.)274 3998 y(No)39 b(en)m(tan)m(to,)i(outra)e(caracter\355stica)f(do)h (problema)f(exerce)j(o)e(pap)s(el)f(principal)f(no)i(sup)s(orte)g(a)109 4160 y(essa)28 b(id\351ia.)41 b(Quando)27 b(resolv)m(endo)i(os)e (subproblemas)h(separadamen)m(te,)h(\351)f(m)m(uito)e(com)m(um)h (existirem)109 4323 y(m)m(uitas)k(solu\347\365)s(es)h(de)g(mesmo)f (custo,)i(o)f(que)h(se)f(denomina)f(de)i(um)e(empate.)43 b(P)m(ara)32 b(o)g(subproblema)109 4485 y(de)39 b(minimizar)34 b(as)39 b(tro)s(cas)f(de)h(cores,)i(que)e(\351)g(um)f(problema)f(mais)g (simples,)i(esta)f(caracter\355stica)g(\351)109 4648 y(facilmen)m(te)g(notada,)j(p)s(or)e(exemplo,)h(atra)m(v)m(\351s)h(da)f (p)s(erm)m(uta\347\343o)f(de)h(grup)s(os)f(de)h(carros)g(de)g(mesma)109 4810 y(cor.)57 b(P)m(ara)37 b(o)g(subproblema)g(de)h(minimizar)33 b(viola\347\365)s(es)j(de)h(restri\347\365)s(es)h(de)g(capacidade)f(de) h(alta)d(ou)109 4973 y(baixa)e(prioridade,)f(isto)i(p)s(o)s(der)f(ser)i (observ)-5 b(ado)34 b(no)g(exemplo)f(da)h(Figura)e(3.1,)i(onde)g (tem-se)g(v)-5 b(\341rias)109 5135 y(seq\374encias)32 b(com)e(o)h(mesmo)f(n)m(\372mero)h(de)g(viola\347\365)s(es)f(para)g (uma)h(restri\347\343o)f(de)h(capacidade)g(de)h(raz\343o)109 5298 y(1/4.)42 b(Mesmo)33 b(quando)g(o)f(n)m(\372mero)h(de)g (restri\347\365)s(es)g(aumen)m(ta,)f(os)h(empates)g(ainda)e(acon)m (tecem.)274 5520 y(O)k(ob)5 b(jetiv)m(o)35 b(\351)h(tirar)d(pro)m(v)m (eito)i(destes)i(empates,)f(explorando)f(solu\347\365)s(es)g(diferen)m (tes)h(no)f(espa\347o)109 5682 y(de)e(busca,)g(mas)f(de)h(mesma)f (qualidade.)42 b(Em)32 b(virtude)h(disto,)f(dividir)f(o)h(PSC)h(em)g (subproblemas)f(e)109 5845 y(atac\341-los)f(separadamen)m(te)i(p)s (ermite)e(apro)m(v)m(eitar)h(de)h(forma)e(mais)h(e\034cien)m(te)h(os)g (empates.)p eop %%Page: 11 25 11 24 bop 109 -28 a FB(3)60 b(Estrat\351gia)32 b(Algor\355tmica)2687 b(11)p 109 9 3780 4 v 867 1337 a currentpoint currentpoint translate 0.62439 0.62439 scale neg exch neg exch translate 867 1337 a @beginspecial 28 @llx 323 @lly 463 @urx 550 @ury 4350 @rwi @setspecial %%BeginDocument: empates.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 28 323 463 550 %%Creator: CorelDRAW 7 %%Title: %%CreationDate: Thu Jan 20 14:46:35 2005 %%DocumentProcessColors: Black %%DocumentSuppliedResources: (atend) %%EndComments %%BeginProlog /AutoFlatness true def /AutoSteps 0 def /CMYKMarks false def /UseLevel2 false def %Color profile: _DEFAULT.CCM - Gen. Profil -Sem %%BeginResource: procset wCorel7Dict 7.0 0 /wCorel7Dict 300 dict def wCorel7Dict begin % Copyright (c)1992-96 Corel Corporation % All rights reserved. v7.0 r1.0 /bd{bind def}bind def/ld{load def}bd/xd{exch def}bd/_ null def/rp{{pop}repeat} bd/@cp/closepath ld/@gs/gsave ld/@gr/grestore ld/@np/newpath ld/Tl/translate ld /$sv 0 def/@sv{/$sv save def}bd/@rs{$sv restore}bd/spg/showpage ld/showpage{} bd currentscreen/@dsp xd/$dsp/@dsp def/$dsa xd/$dsf xd/$sdf false def/$SDF false def/$Scra 0 def/SetScr/setscreen ld/setscreen{pop pop pop}bd/@ss{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if exch $Scra add exch load SetScr}bd /SepMode_5 where{pop}{/SepMode_5 0 def}ifelse/CurrentInkName_5 where{pop} {/CurrentInkName_5(Composite)def}ifelse/$ink_5 where{pop}{/$ink_5 -1 def} ifelse/$c 0 def/$m 0 def/$y 0 def/$k 0 def/$t 1 def/$n _ def/$o 0 def/$fil 0 def/$C 0 def/$M 0 def/$Y 0 def/$K 0 def/$T 1 def/$N _ def/$O 0 def/$PF false def/s1c 0 def/s1m 0 def/s1y 0 def/s1k 0 def/s1t 0 def/s1n _ def/$bkg false def /SK 0 def/SM 0 def/SY 0 def/SC 0 def/$op false def matrix currentmatrix/$ctm xd /$ptm matrix def/$ttm matrix def/$stm matrix def/$ffpnt true def /CorelDrawReencodeVect[16#0/grave 16#5/breve 16#6/dotaccent 16#8/ring 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl 16#88/circumflex/perthousand/Scaron/guilsinglleft/OE 16#91/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash 16#98/tilde/trademark/scaron/guilsinglright/oe 16#9F/Ydieresis 16#A1/exclamdown/cent/sterling/currency/yen/brokenbar/section 16#a8/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/minus/registered/macron 16#b0/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered 16#b8/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown 16#c0/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla 16#c8/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis 16#d0/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply 16#d8/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls 16#e0/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla 16#e8/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis 16#f0/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide 16#f8/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis]def /L2?/languagelevel where{pop languagelevel 2 ge}{false}ifelse def /@BeginSysCorelDict{systemdict/Corel30Dict known{systemdict/Corel30Dict get exec}if}bd/@EndSysCorelDict{systemdict/Corel30Dict known{end}if}bd AutoFlatness {/@ifl{dup currentflat exch sub 10 gt{ ([Error: PathTooComplex; OffendingCommand: AnyPaintingOperator]\n)print flush @np exit}{currentflat 2 add setflat}ifelse}bd/@fill/fill ld/fill{currentflat{ {@fill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@eofill/eofill ld/eofill {currentflat{{@eofill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@clip /clip ld/clip{currentflat{{@clip}stopped{@ifl}{exit}ifelse}bind loop setflat} bd/@eoclip/eoclip ld/eoclip{currentflat{{@eoclip}stopped{@ifl}{exit}ifelse} bind loop setflat}bd/@stroke/stroke ld/stroke{currentflat{{@stroke}stopped {@ifl}{exit}ifelse}bind loop setflat}bd}if L2?{/@ssa{true setstrokeadjust}bd}{ /@ssa{}bd}ifelse/d/setdash ld/j/setlinejoin ld/J/setlinecap ld/M/setmiterlimit ld/w/setlinewidth ld/O{/$o xd}bd/R{/$O xd}bd/W/eoclip ld/c/curveto ld/C/c ld/l /lineto ld/L/l ld/rl/rlineto ld/m/moveto ld/n/newpath ld/N/newpath ld/P{11 rp} bd/u{}bd/U{}bd/A{pop}bd/q/@gs ld/Q/@gr ld/&{}bd/@j{@sv @np}bd/@J{@rs}bd/g{1 exch sub/$k xd/$c 0 def/$m 0 def/$y 0 def/$t 1 def/$n _ def/$fil 0 def}bd/G{1 sub neg/$K xd _ 1 0 0 0/$C xd/$M xd/$Y xd/$T xd/$N xd}bd/k{1 index type /stringtype eq{/$t xd/$n xd}{/$t 0 def/$n _ def}ifelse/$k xd/$y xd/$m xd/$c xd /$fil 0 def}bd/K{1 index type/stringtype eq{/$T xd/$N xd}{/$T 0 def/$N _ def} ifelse/$K xd/$Y xd/$M xd/$C xd}bd/x/k ld/X/K ld/sf{1 index type/stringtype eq{ /s1t xd/s1n xd}{/s1t 0 def/s1n _ def}ifelse/s1k xd/s1y xd/s1m xd/s1c xd}bd/i{ dup 0 ne{setflat}{pop}ifelse}bd/v{4 -2 roll 2 copy 6 -2 roll c}bd/V/v ld/y{2 copy c}bd/Y/y ld/@w{matrix rotate/$ptm xd matrix scale $ptm dup concatmatrix /$ptm xd 1 eq{$ptm exch dup concatmatrix/$ptm xd}if 1 w}bd/@g{1 eq dup/$sdf xd {/$scp xd/$sca xd/$scf xd}if}bd/@G{1 eq dup/$SDF xd{/$SCP xd/$SCA xd/$SCF xd} if}bd/@D{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if 3 copy exch $Scra add exch load SetScr/$dsp xd/$dsa xd/$dsf xd}bd/$ngx{$SDF{$SCF SepMode_5 0 eq{$SCA} {$dsa}ifelse $SCP @ss}if}bd/p{/$pm xd 7 rp/$pyf xd/$pxf xd/$pn xd/$fil 1 def} bd/@MN{2 copy le{pop}{exch pop}ifelse}bd/@MX{2 copy ge{pop}{exch pop}ifelse}bd /InRange{3 -1 roll @MN @MX}bd/@sqr{dup 0 rl dup 0 exch rl neg 0 rl @cp}bd /currentscale{1 0 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt 0 1 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt}bd/@unscale{}bd/wDstChck{2 1 roll dup 3 -1 roll eq{1 add}if}bd /@dot{dup mul exch dup mul add 1 exch sub}bd/@lin{exch pop abs 1 exch sub}bd /cmyk2rgb{3{dup 5 -1 roll add 1 exch sub dup 0 lt{pop 0}if exch}repeat pop}bd /rgb2cmyk{3{1 exch sub 3 1 roll}repeat 3 copy @MN @MN 3{dup 5 -1 roll sub neg exch}repeat}bd/rgb2g{2 index .299 mul 2 index .587 mul add 1 index .114 mul add 4 1 roll pop pop pop}bd/WaldoColor_5 where{pop}{/SetRgb/setrgbcolor ld/GetRgb /currentrgbcolor ld/SetGry/setgray ld/GetGry/currentgray ld/SetRgb2 systemdict /setrgbcolor get def/GetRgb2 systemdict/currentrgbcolor get def/SetHsb systemdict/sethsbcolor get def/GetHsb systemdict/currenthsbcolor get def /rgb2hsb{SetRgb2 GetHsb}bd/hsb2rgb{3 -1 roll dup floor sub 3 1 roll SetHsb GetRgb2}bd/setcmykcolor where{pop/SetCmyk_5/setcmykcolor ld}{/SetCmyk_5{ cmyk2rgb SetRgb}bd}ifelse/currentcmykcolor where{pop/GetCmyk/currentcmykcolor ld}{/GetCmyk{GetRgb rgb2cmyk}bd}ifelse/setoverprint where{pop}{/setoverprint{ /$op xd}bd}ifelse/currentoverprint where{pop}{/currentoverprint{$op}bd}ifelse /@tc_5{5 -1 roll dup 1 ge{pop}{4{dup 6 -1 roll mul exch}repeat pop}ifelse}bd /@trp{exch pop 5 1 roll @tc_5}bd/setprocesscolor_5{SepMode_5 0 eq{SetCmyk_5}{0 4 $ink_5 sub index exch pop 5 1 roll pop pop pop pop SepsColor true eq{$ink_5 3 gt{1 sub neg SetGry}{0 0 0 4 $ink_5 roll SetCmyk_5}ifelse}{1 sub neg SetGry} ifelse}ifelse}bd/findcmykcustomcolor where{pop}{/findcmykcustomcolor{5 array astore}bd}ifelse/setcustomcolor where{pop}{/setcustomcolor{exch aload pop SepMode_5 0 eq{pop @tc_5 setprocesscolor_5}{CurrentInkName_5 eq{4 index}{0} ifelse 6 1 roll 5 rp 1 sub neg SetGry}ifelse}bd}ifelse/@scc_5{dup type /booleantype eq{setoverprint}{1 eq setoverprint}ifelse dup _ eq{pop setprocesscolor_5 pop}{findcmykcustomcolor exch setcustomcolor}ifelse SepMode_5 0 eq{true}{GetGry 1 eq currentoverprint and not}ifelse}bd/colorimage where{pop /ColorImage{colorimage}def}{/ColorImage{/ncolors xd pop/dataaq xd{dataaq ncolors dup 3 eq{/$dat xd 0 1 $dat length 3 div 1 sub{dup 3 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length 3 idiv getinterval pop}{4 eq{/$dat xd 0 1 $dat length 4 div 1 sub{dup 4 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div $dat 4 index 3 add get 255 div cmyk2rgb rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length ncolors idiv getinterval}if}ifelse}image}bd }ifelse/setcmykcolor{1 5 1 roll _ currentoverprint @scc_5/$ffpnt xd}bd /currentcmykcolor{0 0 0 0}bd/setrgbcolor{rgb2cmyk setcmykcolor}bd /currentrgbcolor{currentcmykcolor cmyk2rgb}bd/sethsbcolor{hsb2rgb setrgbcolor} bd/currenthsbcolor{currentrgbcolor rgb2hsb}bd/setgray{dup dup setrgbcolor}bd /currentgray{currentrgbcolor rgb2g}bd}ifelse/WaldoColor_5 true def/@sft{$tllx $pxf add dup $tllx gt{$pwid sub}if/$tx xd $tury $pyf sub dup $tury lt{$phei add}if/$ty xd}bd/@stb{pathbbox/$ury xd/$urx xd/$lly xd/$llx xd}bd/@ep{{cvx exec }forall}bd/@tp{@sv/$in true def 2 copy dup $lly le{/$in false def}if $phei sub $ury ge{/$in false def}if dup $urx ge{/$in false def}if $pwid add $llx le{/$in false def}if $in{@np 2 copy m $pwid 0 rl 0 $phei neg rl $pwid neg 0 rl 0 $phei rl clip @np $pn cvlit load aload pop 7 -1 roll 5 index sub 7 -1 roll 3 index sub Tl matrix currentmatrix/$ctm xd @ep pop pop pop pop}{pop pop}ifelse @rs}bd /@th{@sft 0 1 $tly 1 sub{dup $psx mul $tx add{dup $llx gt{$pwid sub}{exit} ifelse}loop exch $phei mul $ty exch sub 0 1 $tlx 1 sub{$pwid mul 3 copy 3 -1 roll add exch @tp pop}for pop pop}for}bd/@tv{@sft 0 1 $tlx 1 sub{dup $pwid mul $tx add exch $psy mul $ty exch sub{dup $ury lt{$phei add}{exit}ifelse}loop 0 1 $tly 1 sub{$phei mul 3 copy sub @tp pop}for pop pop}for}bd/$fm 0 def/wfill{1 $fm eq{fill}{eofill}ifelse}bd/wclip{1 $fm eq{clip}{eoclip}ifelse}bd/@pf{@gs $ctm setmatrix $pm concat @stb wclip Bburx Bbury $pm itransform/$tury xd/$turx xd Bbllx Bblly $pm itransform/$tlly xd/$tllx xd/$wid $turx $tllx sub def/$hei $tury $tlly sub def @gs $vectpat{1 0 0 0 0 _ $o @scc_5{wfill}if}{$t $c $m $y $k $n $o @scc_5{SepMode_5 0 eq $pfrg or{$tllx $tlly Tl $wid $hei scale <00> 8 1 false[8 0 0 1 0 0]{}imagemask}{/$bkg true def}ifelse}if}ifelse @gr $wid 0 gt $hei 0 gt and{$pn cvlit load aload pop/$pd xd 3 -1 roll sub/$phei xd exch sub /$pwid xd $wid $pwid div ceiling 1 add/$tlx xd $hei $phei div ceiling 1 add /$tly xd $psx 0 eq{@tv}{@th}ifelse}if @gr @np/$bkg false def}bd/@Pf{@sv SepMode_5 0 eq $Psc 0 ne or $ink_5 3 eq or{0 J 0 j[]0 d $t $c $m $y $k $n $o @scc_5 pop $ctm setmatrix 72 1000 div dup matrix scale dup concat dup Bburx exch Bbury exch itransform ceiling cvi/Bbury xd ceiling cvi/Bburx xd Bbllx exch Bblly exch itransform floor cvi/Bblly xd floor cvi/Bbllx xd $Prm aload pop $Psn load exec}{1 SetGry wfill}ifelse @rs @np}bd/F{matrix currentmatrix $sdf{$scf $sca $scp @ss}if $fil 1 eq{@pf}{$fil 2 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Fz(\031)g FA(=)p Fz(<)27 b(c)2554 5905 y Ft(i)2578 5914 y Fo(1)2617 5890 y Fz(;)17 b(c)2703 5905 y Ft(i)2727 5914 y Fo(2)2765 5890 y Fz(;)g(:)g(:)g(:)f(;)h(c)3026 5905 y Ft(i)3050 5917 y Fn(k)3120 5890 y Fz(>)p FH(;)p eop %%Page: 13 27 13 26 bop 109 -28 a FB(4.1)60 b(F)-8 b(ormaliza\347\343o)2998 b(13)p 109 9 3780 4 v 254 256 a Fs(\017)49 b FH(o)41 b(n)m(\372mero)h(de)g(carros)g(que)g(uma)f(seq\374\352ncia)i Fz(\031)j FH(con)m(t\351m)c(\351)g(c)m(hamado)f Fw(tamanho)h FH(de)g Fz(\031)k FH(e)c(\351)353 418 y(denotado)32 b(p)s(or)g Fs(j)p Fz(\031)t Fs(j)p FH(;)254 664 y Fs(\017)49 b FH(a)32 b Fw(concatena\347\343o)i FH(de)g(duas)f(seq\374\352ncias)i Fz(\031)2001 679 y Fq(1)2074 664 y FH(e)e Fz(\031)2205 679 y Fq(2)2278 664 y FH(\351)g(a)g(seq\374\352ncia)h(formada)d(p)s (elos)i(carros)g(de)353 826 y Fz(\031)408 841 y Fq(1)480 826 y FH(seguidos)g(p)s(elos)f(carros)g(de)h Fz(\031)1585 841 y Fq(2)1658 826 y FH(e)g(\351)f(denotada)h(p)s(or)f Fz(\031)2463 841 y Fq(1)2503 826 y Fs(j)p 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Fz(;)17 b(c)2085 1911 y Ft(i)2109 1920 y Fo(2)2147 1896 y Fz(;)g(:)g(:)g(:)f(;)h(c)2408 1911 y Ft(i)2432 1923 y Fn(k)2526 1896 y Fz(>)47 b FH(\351)h(o)f(n)m (\372mero)g(de)g(restri\347\365)s(es)h(de)353 2059 y(capacidade)32 b(violadas)f(e)i(\351)g(dado)f(p)s(or)1263 2434 y Fz(custo)p FA(\()p Fz(\031)t FA(\))27 b(=)1795 2310 y Ft(m)1755 2339 y Fr(X)1765 2549 y Ft(j)t Fq(=1)2035 2339 y Fr(X)1925 2547 y Fn(\031)1963 2533 y Fm(0)1986 2547 y Fo(:)p Fm(j)p Fn(\031)2061 2533 y Fm(0)2082 2547 y(j)p Fo(=)p Fn(q)r Fo(\()p Fn(o)2233 2563 y(j)2265 2547 y Fo(\))2034 2624 y Fn(\031)2072 2610 y Fm(0)2094 2624 y(\022)p Fn(\031)2316 2434 y FE(viola\347\343o)t FA(\()p Fz(\031)2762 2393 y Fl(0)2785 2434 y Fz(;)17 b(o)2876 2449 y Ft(j)2913 2434 y FA(\))p Fz(;)353 2775 y FH(onde)1173 2971 y FE(viola\347\343o)5 b FA(\()p Fz(\031)1620 2929 y Fl(0)1643 2971 y Fz(;)17 b(o)1734 2986 y Ft(j)1770 2971 y FA(\))28 b(=)1939 2800 y Fr(\()2061 2897 y FA(0)k FH(,)h(se)g Fz(r)s FA(\()p Fz(\031)2460 2861 y Fl(0)2483 2897 y Fz(;)17 b(o)2574 2912 y Ft(j)2610 2897 y FA(\))28 b Fs(\024)g Fz(p)p FA(\()p Fz(o)2915 2912 y Ft(j)2951 2897 y FA(\);)2061 3059 y(1)k FH(,)h(caso)g(con)m(tr\341rio.)274 3327 y(P)m(ara)g(efeito)f(de)i (simpli\034ca\347\343o,)c(o)j(n)m(\372mero)g(de)h(carros)f(que)h (requerem)f(uma)g(op)s(\347\343o)f Fz(o)3504 3342 y Ft(j)3573 3327 y FH(no)h(con-)109 3490 y(jun)m(to)f(formado)f(p)s(or)h(to)s(dos)h (os)f(carros)h Fz(C)40 b FH(tam)m(b)s(\351m)31 b(\351)i(dado)f(p)s(or) 1519 3780 y Fz(r)s FA(\()p Fz(C)r(;)17 b(o)1767 3795 y Ft(j)1802 3780 y FA(\))27 b(=)2021 3655 y Ft(n)1971 3685 y Fr(X)1986 3895 y Ft(i)p Fq(=1)2131 3780 y Fz(r)s FA(\()p Fz(c)2258 3795 y Ft(i)2286 3780 y Fz(;)17 b(o)2377 3795 y Ft(j)2413 3780 y FA(\))p Fz(:)274 4141 y FH(Al\351m)27 b(da)h(nota\347\343o)g(acima,)f(existe)i(um)e(conceito)h(imp)s(ortan)m (te)f(utilizado)e(p)s(ela)i(heur\355stica)h(cons-)109 4303 y(trutiv)-5 b(a)38 b(c)m(hamado)i Fw(taxa)47 b(de)f (utiliza\347\343o)38 b FH(das)i(op)s(\347\365)s(es)g([13].)66 b(Este)41 b(conceito)f(determina,)h(jun)m(ta-)109 4466 y(men)m(te)28 b(com)g(o)f(n)m(\372mero)h(de)h(carros)f(a)g(serem)h(pro) s(duzidos)f(e)g(o)g(n)m(\372mero)g(de)g(con\034gura\347\365)s(es)h (diferen)m(tes)109 4628 y(de)43 b(op)s(\347\365)s(es,)i(a)e (di\034culdade)f(de)h(uma)f(inst\342ncia)f(do)i(problema.)72 b(A)43 b(taxa)g(de)g(utiliza\347\343o)d(de)j(uma)109 4791 y(op)s(\347\343o)31 b Fz(o)434 4806 y Ft(j)502 4791 y FH(em)g(um)g(conjun)m(to)h(ou)f(uma)g(seq\374\352ncia)i(de)f(carros)f (\351)h(a)f(raz\343o)h(do)f(n)m(\372mero)g(de)h(carros)g(que)109 4953 y(demandam)24 b Fz(o)647 4968 y Ft(j)710 4953 y FH(na)h(seq\374\352ncia)i(em)f(rela\347\343o)f(ao)g(n)m(\372mero)h (m\341ximo)d(de)k(carros)f(que)h(p)s(o)s(dem)e(demandar)109 5116 y Fz(o)156 5131 y Ft(j)216 5116 y FH(nesta)g(seq\374\352ncia)h(de) e(mo)s(do)f(a)h(satisfazer)h(a)f(restri\347\343o)f(de)i(capacidade)f (asso)s(ciada.)40 b(F)-8 b(ormalmen)m(te,)109 5279 y(a)32 b(taxa)g(de)h(utiliza\347\343o)d(de)j(uma)f(op)s(\347\343o)g Fz(o)1651 5294 y Ft(j)1720 5279 y FH(no)g(conjun)m(to)h(de)g(carros)g Fz(C)40 b FH(\351)32 b(de\034nida)h(p)s(or)1345 5556 y Fz(taxaU)10 b(til)r FA(\()p Fz(o)1797 5571 y Ft(j)1836 5556 y FA(\))28 b(=)2015 5489 y Fz(r)s FA(\()p Fz(C)r(;)17 b(o)2263 5504 y Ft(j)2298 5489 y FA(\))23 b Fs(\001)e Fz(q)t FA(\()p Fz(o)2540 5504 y Ft(j)2577 5489 y FA(\))p 2015 5533 600 4 v 2146 5625 a Fz(n)h Fs(\001)g Fz(p)p FA(\()p Fz(o)2410 5640 y Ft(j)2446 5625 y FA(\))2624 5556 y Fz(:)p eop %%Page: 14 28 14 27 bop 109 -28 a FB(4.2)60 b(Crit\351rios)32 b(gulosos)2859 b(14)p 109 9 3780 4 v 274 256 a FH(Escrev)m(endo)35 b(de)e(outra)f (forma,)f(a)i(taxa)f(de)h(utiliza\347\343o)d(tam)m(b)s(\351m)h(\351)i (de\034nida)g(p)s(or)1150 527 y Fz(taxaU)10 b(til)r FA(\()p Fz(o)1602 542 y Ft(j)1641 527 y FA(\))27 b(=)1810 387 y Fr(\022)1893 460 y Fz(r)s FA(\()p Fz(C)r(;)17 b(o)2141 475 y Ft(j)2176 460 y FA(\))p 1893 504 322 4 v 2025 596 a Fz(n)2224 387 y Fr(\023)g(\036\022)2502 460 y Fz(p)p FA(\()p Fz(o)2636 475 y Ft(j)2672 460 y FA(\))p 2502 504 209 4 v 2503 596 a Fz(q)t FA(\()p Fz(o)2635 611 y Ft(j)2671 596 y FA(\))2720 387 y Fr(\023)2820 527 y Fz(:)274 859 y FH(Ou)36 b(seja,)h(a)f(taxa)g(de)h(utiliza\347\343o)c(\351)j (dada)g(p)s(ela)f(raz\343o)h(do)g(n)m(\372mero)g(de)g(carros)h (demandando)e(a)109 1022 y(op)s(\347\343o)f(na)i(seq\374\352ncia)g(p)s (elo)f(n)m(\372mero)g(de)h(carros)f(da)g(seq\374\352ncia)i(dividida)c (p)s(ela)i(raz\343o)f(da)i(restri\347\343o)109 1184 y(corresp)s(onden)m (te.)83 b(Isto)46 b(signi\034ca)e(que,)50 b(se)c(a)f(taxa)g(de)h (utiliza\347\343o)c(\351)k(maior)d(que)j(1,)i(a)d(raz\343o)g(do)109 1347 y(n)m(umerador)28 b(\351)g(maior)e(que)j(a)f(raz\343o)g(do)g (denominador)f(e,)j(conseq\374en)m(temen)m(te,)i(a)c(demanda)g(\351)g (maior)109 1509 y(que)41 b(a)g(capacidade,)h(logo,)f(a)g (restri\347\343o)f(ser\341)h(violada.)66 b(Se,)43 b(ao)d(con)m (tr\341rio,)i(a)e(taxa)h(de)g(utiliza\347\343o)109 1672 y(\351)36 b(m)m(uito)f(p)s(equena)i(e)g(pr\363)m(xima)e(de)i(0,)g(a)e (demanda)h(\351)h(m)m(uito)e(baixa)g(em)h(rela\347\343o)f(\340)h (capacidade)g(da)109 1834 y(linha)30 b(de)k(pro)s(du\347\343o.)109 2226 y Fx(4.2)155 b(Crit\351rios)55 b(gulosos)274 2546 y FH(A)28 b(heur\355stica)f(constr\363i)g(a)g(solu\347\343o)g(inicial)d (escolhendo)k(iterativ)-5 b(amen)m(te)26 b(o)h(pr\363)m(ximo)g(carro)g (a)g(ser)109 2709 y(escalonado)g(na)h(seq\374\352ncia)h(de)g(acordo)f (com)f(algum)f(crit\351rio)g(guloso.)41 b(O)28 b(crit\351rio)f(guloso)g (adotado)g(\351)109 2871 y(o)h(mais)f(in)m(tuitiv)m(o:)40 b(em)28 b(cada)h(itera\347\343o,)f(escolhe-se)h(o)g(carro)f(que)i (causa)f(o)f(menor)g(n)m(\372mero)h(de)g(no)m(v)-5 b(as)109 3034 y(viola\347\365)s(es)37 b(de)h(restri\347\365)s(es.)61 b(De)39 b(uma)e(maneira)f(mais)h(formal,)g(dada)h(uma)f (seq\374\352ncia)j(parcial)c Fz(\031)t FH(,)j(o)109 3196 y(pr\363)m(ximo)31 b(carro)h Fz(c)779 3211 y Ft(i)840 3196 y FH(a)g(ser)h(escolhido)f(\351)h(aquele)g(que)g(minimiza)258 3487 y FE(novasViola\347\365)-5 b(es)6 b FA(\()p Fz(\031)t(;)17 b(c)1089 3502 y Ft(i)1117 3487 y FA(\))28 b(=)1327 3362 y Ft(m)1286 3392 y Fr(X)1297 3602 y Ft(j)t Fq(=1)1447 3487 y Fz(r)s FA(\()p Fz(c)1574 3502 y Ft(i)1601 3487 y Fz(;)17 b(o)1692 3502 y Ft(j)1729 3487 y FA(\))22 b Fs(\001)f FE(viola\347\343o)5 b FA(\()p FE(ultimosCarr)-5 b(os)8 b FA(\()p Fz(\031)t Fs(j)27 b Fz(<)g(c)3127 3502 y Ft(i)3183 3487 y Fz(>;)17 b(q)t FA(\()p Fz(o)3435 3502 y Ft(j)3471 3487 y FA(\)\))p Fz(;)g(o)3638 3502 y Ft(j)3674 3487 y FA(\))p Fz(;)195 3920 y FH(onde)32 b FE(ultimosCarr)-5 b(os)8 b FA(\()p Fz(\031)1128 3879 y Fl(0)1151 3920 y Fz(;)17 b(k)s FA(\))27 b(=)1418 3750 y Fr(\()1540 3847 y FH(seq\374\352ncia)33 b(com)f(os)h(\372ltimos)d Fz(k)36 b FH(carros)d(de)g Fz(\031)3213 3810 y Fl(0)3236 3847 y Fz(;)49 b FH(se)33 b Fs(j)p Fz(\031)3513 3810 y Fl(0)3536 3847 y Fs(j)28 b(\025)g Fz(k)1540 4009 y(\031)1599 3973 y Fl(0)1622 4009 y FH(,)k(caso)h(con)m(tr\341rio.)274 4248 y(No)23 b(en)m(tan)m(to,)i(freq\374en)m(temen)m(te)g(existem)d(v) -5 b(\341rios)22 b(carros)h(candidatos)f(que)i(minimizam)18 b(o)k(n)m(\372mero)109 4410 y(de)45 b(no)m(v)-5 b(as)46 b(viola\347\365)s(es.)79 b(Dian)m(te)45 b(disto,)j(um)c(segundo)i (crit\351rio)d(guloso)h(\351)i(adotado)e(para)h(resolv)m(er)109 4573 y(os)f(empates.)78 b(Este)45 b(crit\351rio)e(\351)h(um)f(p)s(ouco) h(mais)f(elab)s(orado,)i(p)s(ois)f(fa)m(v)m(orece)h(uma)e (distribui\347\343o)109 4735 y(eq\374itativ)-5 b(a)39 b(das)i(op)s(\347\365)s(es.)69 b(A)41 b(distribui\347\343o)e(\351)i (baseada)g(na)g(seguin)m(te)g(id\351ia:)59 b(se)41 b(o)g(n)m(\372mero)g (m\351dio)109 4898 y(de)d(carros)h(que)g(demandam)e(uma)g(op)s (\347\343o)h(\351)g(menor)f(na)h(seq\374\352ncia)i(em)d (constru\347\343o)i Fz(\031)j FH(do)c(que)h(no)109 5060 y(conjun)m(to)33 b(total)f(de)i(carros)g Fz(C)7 b FH(,)33 b(en)m(t\343o)h(estes)h(carros)e(s\343o)h(fa)m(v)m(orecidos)f(para)g (en)m(trar)h(na)f(seq\374\352ncia)i(e)109 5223 y(vice-v)m(ersa.)44 b(Mais)32 b(formalmen)m(te,)f(escolhe-se)i(o)g(carro)f Fz(c)2239 5238 y Ft(i)2299 5223 y FH(que)i(minimiza)29 b(a)j(fun\347\343o:)636 5513 y Fz(\021)684 5528 y Ft(D)r(E)804 5513 y FA(\()p Fz(c)884 5528 y Ft(i)912 5513 y Fz(;)17 b(\031)t FA(\))27 b(=)1225 5389 y Ft(m)1184 5419 y Fr(X)1195 5629 y Ft(j)t Fq(=1)1344 5373 y Fr(\032)1419 5513 y FA(\()p Fz(r)s FA(\()p Fz(c)1584 5528 y Ft(i)1612 5513 y Fz(;)17 b(o)1703 5528 y Ft(j)1739 5513 y FA(\))28 b(=)f(0\))32 b FH(X)m(OR)2294 5373 y Fr(\022)2378 5446 y Fz(r)s FA(\()p Fz(C)r(;)17 b(o)2626 5461 y Ft(j)2661 5446 y FA(\))p 2378 5490 322 4 v 2509 5582 a Fz(n)2737 5513 y(>)2850 5446 y(r)s FA(\()p Fz(\031)t(;)g(o)3085 5461 y Ft(j)3121 5446 y FA(\))p 2850 5490 309 4 v 2947 5582 a Fs(j)p Fz(\031)t Fs(j)3169 5373 y Fr(\023\033)3333 5513 y Fz(:)109 5828 y FH(O)25 b(primeiro)e(carro)i(a)g(ser)h(escalonado)f(\351)h(escolhido) f(aleatoriamen)m(te)e(en)m(tre)j(os)g(carros)f(com)g(o)g(n)m(\372mero)p eop %%Page: 15 29 15 28 bop 109 -28 a FB(4.2)60 b(Crit\351rios)32 b(gulosos)2859 b(15)p 109 9 3780 4 v 109 256 a FH(m\341ximo)30 b(de)j(op)s(\347\365)s (es,)g(uma)e(v)m(ez)j(que)g(a)e(f\363rm)m(ula)f(acima)g(n\343o)h(p)s(o) s(de)g(ser)h(aplicada)e(quando)i Fs(j)p Fz(\031)t Fs(j)27 b FA(=)h(0)p FH(.)274 477 y(Ainda)41 b(que)h(o)f(crit\351rio)f(acima)g (seja)h(utilizado)e(para)i(quebrar)h(os)g(empates,)i(n\343o)d(\351)g (raro)g(que)109 640 y(empates)29 b(p)s(ersistam.)42 b(Neste)30 b(caso,)g(um)f(terceiro)g(crit\351rio)e(guloso)h(\351)i(utilizado,)d (fa)m(v)m(orecendo)k(carros)109 802 y(que)k(requerem)f(op)s(\347\365)s (es)h(com)e(alta)f(taxa)i(de)h(utiliza\347\343o.)45 b(Isto)34 b(\351)g(feito)f(atra)m(v)m(\351s)i(da)f(soma)f(das)i(taxas)109 965 y(de)f(utiliza\347\343o)d(das)k(op)s(\347\365)s(es)f(requeridas)h (p)s(or)e(cada)h(carro.)48 b(No)33 b(en)m(tan)m(to,)i(a)f(taxa)g(de)g (utiliza\347\343o)e(ora)109 1127 y(considerada)e(\351)h(din\342mica,)d (p)s(ois)h(\351)i(atualizada)d(sempre)j(que)g(um)f(carro)g(\351)h (adicionado)d(\340)i(seq\374\352ncia.)109 1290 y(A)k(taxa)g(de)h (utiliza\347\343o)d(din\342mica)g(de)i(uma)g(op)s(\347\343o)g Fz(o)2107 1305 y Ft(j)2177 1290 y FH(em)g(rela\347\343o)g(\340)g (seq\374\352ncia)h(parcial)e Fz(\031)38 b FH(\351)c(dada)109 1452 y(p)s(ela)d(seguin)m(te)i(fun\347\343o:)964 1714 y Fz(taxaU)10 b(til)r(D)s(in)p FA(\()p Fz(o)1591 1729 y Ft(j)1630 1714 y Fz(;)17 b(\031)t FA(\))27 b(=)1912 1647 y([)p Fz(r)s FA(\()p Fz(C)r(;)17 b(o)2187 1662 y Ft(j)2222 1647 y FA(\))22 b Fs(\000)h Fz(r)s FA(\()p Fz(\031)t(;)17 b(o)2617 1662 y Ft(j)2653 1647 y FA(\)])22 b Fs(\001)g Fz(q)t FA(\()p Fz(o)2922 1662 y Ft(j)2958 1647 y FA(\))p 1912 1691 1084 4 v 2139 1783 a([)p Fz(n)h Fs(\000)g(j)p Fz(\031)t Fs(j)p FA(])e Fs(\001)h Fz(p)p FA(\()p Fz(o)2694 1798 y Ft(j)2730 1783 y FA(\))3006 1714 y Fz(:)109 1987 y FH(Este)32 b(crit\351rio)e(de)i(desempate)g (\351)g(c)m(hamado)f(de)g(soma)g(de)h(taxas)g(de)g(utiliza\347\343o)c (din\342micas)i(e)i(\351)f(dado)109 2150 y(p)s(or:)1036 2340 y Fz(\021)1084 2355 y Ft(S)t(D)1195 2340 y FA(\()p Fz(c)1275 2355 y Ft(i)1303 2340 y Fz(;)17 b(\031)t FA(\))27 b(=)1615 2216 y Ft(m)1575 2246 y Fr(X)1585 2456 y Ft(j)t Fq(=1)1735 2340 y Fz(r)s FA(\()p Fz(c)1862 2355 y Ft(i)1890 2340 y Fz(;)17 b(o)1981 2355 y Ft(j)2017 2340 y FA(\))22 b Fs(\001)g Fz(taxaU)10 b(til)r(D)s(in)p FA(\()p Fz(o)2754 2355 y Ft(j)2793 2340 y Fz(;)17 b(\031)t FA(\))p Fz(:)274 2668 y FH(Escolhe-se,)43 b(en)m(t\343o,)g(o)c(carro)h(ainda)f(n\343o)h (escalonado)g(que)h(maximiza)d Fz(\021)3072 2683 y Ft(S)t(D)3182 2668 y FH(.)67 b(Se)40 b(os)h(empates)109 2831 y(p)s(ersistirem)21 b(ap)s(\363s)i(esta)g(segunda)g(ten)m(tativ)-5 b(a)22 b(de)h(desempate,)j(um)c(carro)g(\351)i(escolhido)d(aleatoriamen)m(te) 109 2994 y(den)m(tre)33 b(os)g(carros)g(candidatos.)p eop %%Page: 16 30 16 29 bop 109 726 a FD(Cap\355tulo)64 b(5)109 1390 y(Vizinhan\347as)f (e)g(Busca)g(Lo)5 b(cal)274 2087 y FH(As)34 b(heur\355sticas)f(de)g (busca)h(lo)s(cal)d(utilizadas)g(nos)i(algoritmos)d(desen)m(v)m (olvidos)35 b(para)e(a)f(otimiza-)109 2250 y(\347\343o)k(de)i(cada)f (ob)5 b(jetiv)m(o)37 b(s\343o)g(essencialmen)m(te)g(baseadas)h(na)f (mesma)f(id\351ia)g(e)h(aplicam)d(os)k(mesmos)109 2412 y(mo)m(vimen)m(tos)30 b(para)h(obter)g(solu\347\365)s(es)g(vizinhas.)43 b(P)m(or)32 b(isso,)f(as)g(principais)f(caracter\355sticas)g(que)j (essas)109 2575 y(heur\355sticas)26 b(p)s(ossuem)h(em)f(com)m(um)f (s\343o)i(apresen)m(tadas)h(neste)f(cap\355tulo,)f(em)m(b)s(ora)g(as)h (caracter\355sticas)109 2737 y(esp)s(ec\355\034cas)33 b(de)g(cada)g(busca)g(lo)s(cal)e(sejam)h(descritas)h(nos)g (cap\355tulos)e(dedicados)i(a)f(cada)h(algoritmo.)109 3129 y Fx(5.1)155 b(Estruturas)53 b(de)f(vizinhan\347a)274 3449 y FH(Os)38 b(mo)m(vimen)m(tos)g(aplicados)e(p)s(elas)i (heur\355sticas)g(de)h(busca)g(lo)s(cal)c(s\343o)j(baseados)h(em)f (duas)h(es-)109 3612 y(truturas)32 b(de)i(vizinhan\347a:)254 3916 y Fs(\017)49 b FE(Swap)34 b FH(\025)29 b(Nesta)h(vizinhan\347a,)f (um)g(mo)m(vimen)m(to)f(corresp)s(onde)i(a)f(in)m(v)m(erter)h(as)g(p)s (osi\347\365)s(es)f(de)h(dois)353 4079 y(carros)45 b(e)i(\351)f (de\034nido)f(p)s(or)h(um)f(par)h(de)g(p)s(osi\347\365)s(es)f FA(\()p Fz(i;)17 b(j)6 b FA(\))p FH(.)83 b(Em)46 b(uma)f (seq\374\352ncia)i(de)f(carros)353 4241 y Fz(\031)d FA(=)p Fz(<)c(c)684 4256 y Ft(k)721 4265 y Fo(1)760 4241 y Fz(;)17 b(:)g(:)g(:)e(;)i(c)1020 4256 y Ft(k)1057 4264 y Fn(n)1143 4241 y Fz(>)p FH(,)41 b(a)e(aplica\347\343o)f(do)h(mo)m(vimen)m(to)f Fz(sw)s(ap)p FA(\()p Fz(\031)t(;)17 b(i;)g(j)6 b FA(\))39 b FH(resulta)g(na)g(seq\374\352ncia)353 4404 y Fz(\031)412 4368 y Fl(0)462 4404 y FA(=)p Fz(<)28 b(c)684 4419 y Ft(k)721 4428 y Fo(1)759 4404 y Fz(;)17 b(:)g(:)g(:)f(;)h(c)1020 4419 y Ft(k)1057 4429 y Fn(i)p Fm(\000)p Fo(1)1165 4404 y Fz(;)g(c)1251 4419 y Ft(k)1288 4429 y Fn(j)1325 4404 y Fz(;)g(c)1411 4419 y Ft(k)1448 4429 y Fn(i)p Fo(+1)1555 4404 y Fz(;)g(:)g(:)g(:)e(;)i(c)1815 4419 y Ft(k)1852 4429 y Fn(j)s Fm(\000)p Fo(1)1967 4404 y Fz(;)g(c)2053 4419 y Ft(k)2090 4429 y Fn(i)2120 4404 y Fz(;)g(c)2206 4419 y Ft(k)2243 4429 y Fn(j)s Fo(+1)2356 4404 y Fz(;)g(:)g(:)g(:)f(;)h (c)2617 4419 y Ft(k)2654 4427 y Fn(n)2727 4404 y Fz(>)p FH(.)254 4649 y Fs(\017)49 b FE(Shift)i FH(\025)42 b(Nesta)h (vizinhan\347a,)h(um)d(mo)m(vimen)m(to)g(tam)m(b)s(\351m)g(\351)h (represen)m(tado)i(p)s(or)e(um)g(par)g(de)353 4812 y(p)s(osi\347\365)s (es)36 b FA(\()p Fz(i;)17 b(j)6 b FA(\))37 b FH(e)h(corresp)s(onde)g(a) e(remo)m(v)m(er)i(um)f(carro)f(de)i(sua)f(p)s(osi\347\343o)f(atual)g Fz(i)h FH(e)h(inseri-lo)353 4974 y(em)f(uma)h(no)m(v)-5 b(a)38 b(p)s(osi\347\343o)f Fz(j)6 b FH(.)60 b(Na)38 b(seq\374\352ncia)h(de)g(carros)f Fz(\031)j FA(=)p Fz(<)c(c)2812 4989 y Ft(k)2849 4998 y Fo(1)2888 4974 y Fz(;)17 b(:)g(:)g(:)f(;)h(c) 3149 4989 y Ft(k)3186 4997 y Fn(n)3269 4974 y Fz(>)p FH(,)39 b(a)f(aplica\347\343o)353 5137 y(do)24 b(mo)m(vimen)m(to)g Fz(shif)11 b(t)p FA(\()p Fz(\031)t(;)17 b(i;)g(j)6 b FA(\))24 b FH(resulta)g(na)h(seq\374\352ncia)h Fz(\031)2457 5101 y Fl(0)2508 5137 y FA(=)p Fz(<)h(c)2729 5152 y Ft(k)2766 5161 y Fo(1)2805 5137 y Fz(;)17 b(:)g(:)g(:)e(;)i(c)3065 5152 y Ft(k)3102 5162 y Fn(i)p Fm(\000)p Fo(1)3211 5137 y Fz(;)25 b(c)3305 5152 y Ft(k)3342 5162 y Fn(i)p Fo(+1)3449 5137 y Fz(;)17 b(:)g(:)g(:)f(;)h(c)3710 5152 y Ft(k)3747 5162 y Fn(j)s Fm(\000)p Fo(1)3861 5137 y Fz(;)353 5299 y(c)395 5314 y Ft(k)432 5324 y Fn(j)468 5299 y Fz(;)g(c)554 5314 y Ft(k)591 5324 y Fn(i)621 5299 y Fz(;)g(c)707 5314 y Ft(k)744 5324 y Fn(j)s Fo(+1)857 5299 y Fz(;)g(:)g(:)g(:)f(;)h(c)1118 5314 y Ft(k)1155 5322 y Fn(n)1229 5299 y Fz(>)p FH(,)25 b(se)f Fz(i)k(<)f(j)6 b FH(,)26 b(ou)d Fz(\031)1910 5263 y Fl(0)1961 5299 y FA(=)p Fz(<)k(c)2182 5314 y Ft(k)2219 5323 y Fo(1)2258 5299 y Fz(;)17 b(:)g(:)g(:)f(;)h(c)2519 5314 y Ft(k)2556 5324 y Fn(j)s Fm(\000)p Fo(1)2670 5299 y Fz(;)g(c)2756 5314 y Ft(k)2793 5324 y Fn(i)2823 5299 y Fz(;)g(c)2909 5314 y Ft(k)2946 5324 y Fn(j)2982 5299 y Fz(;)24 b(c)3075 5314 y Ft(k)3112 5324 y Fn(j)s Fo(+1)3225 5299 y Fz(;)17 b(:)g(:)g(:)f(;)h(c)3486 5314 y Ft(k)3523 5324 y Fn(i)p Fm(\000)p Fo(1)3631 5299 y Fz(;)g(c)3717 5314 y Ft(k)3754 5324 y Fn(i)p Fo(+1)3861 5299 y Fz(;)353 5462 y(:)g(:)g(:)f(;)h(c)570 5477 y Ft(k)607 5485 y Fn(n)680 5462 y Fz(>)p FH(,)33 b(se)g Fz(i)28 b(>)g(j)6 b FH(.)p eop %%Page: 17 31 17 30 bop 109 -28 a FB(5.2)60 b(Heur\355sticas)31 b(de)g(busca)f(lo)s (cal)2493 b(17)p 109 9 3780 4 v 109 256 a Fx(5.2)155 b(Heur\355sticas)55 b(de)d(busca)f(lo)t(cal)274 576 y FH(As)35 b(buscas)g(lo)s(cais)e(aplicam)f(mo)m(vimen)m(tos)h(dos)h(tip) s(os)g FE(swap)39 b FH(ou)34 b FE(shift)p FH(,)h(escolhendo,)g(para)f (cada)109 738 y(p)s(osi\347\343o,)g(o)h(mo)m(vimen)m(to)e(que)j(pro)s (duz)f(a)f(maior)f(redu\347\343o)i(na)g(fun\347\343o)g(de)g(custo.)51 b(Quando)34 b(existem)109 901 y(empates,)g(os)g(mo)m(vimen)m(tos)e (s\343o)i(guardados)f(em)h(uma)e(lista)g(de)i(candidatos)g(e)g(o)f(mo)m (vimen)m(to)f(a)h(ser)109 1063 y(aplicado)23 b(\351)i(escolhido)f (aleatoriamen)m(te)f(den)m(tre)j(estes.)42 b(A)25 b(busca)h(termina)d (quando)j(n\343o)e(se)i(consegue)109 1226 y(melhorar)k(a)j (solu\347\343o)f(atual)f(ap)s(\363s)h(to)s(dos)h(os)f(mo)m(vimen)m(tos) g(terem)g(sido)g(a)m(v)-5 b(aliados.)274 1447 y(O)28 b(pseudo-c\363)s(digo)f(da)i(busca)g(lo)s(cal)d(que)j(aplica)d(mo)m (vimen)m(tos)h Fz(sw)s(ap)h FH(\351)h(descrito)f(na)g(Figura)e(5.1.)109 1610 y(A)38 b(v)-5 b(ari\341)m(v)m(el)36 b Fz(\036)i FH(receb)s(e)h(o)f(custo)g(da)g(solu\347\343o)f(atual)f(no)i(in\355cio) e(de)i(cada)g(itera\347\343o)e(da)i(busca)h(\(linha)109 1772 y(2\),)45 b(que)f(corresp)s(onde)g(a)f(uma)f(itera\347\343o)g(do)h (la\347o)f Fw(rep)s(eat)h FH(que)h(come\347a)f(na)g(linha)e(1.)74 b(Em)43 b(uma)109 1935 y(itera\347\343o)f(da)i(busca,)j(pro)s(cura-se)d (o)g(melhor)e(mo)m(vimen)m(to)g(a)i(ser)g(realizado)e(para)h(cada)h (carro)f(da)109 2097 y(solu\347\343o,)c(o)e(que)i(\351)g(feito)e(den)m (tro)h(do)g(la\347o)f Fw(for)i FH(da)f(linha)e(3.)60 b(Nas)38 b(linhas)f(4)h(e)g(5,)h(inicializam-se)34 b(as)109 2260 y(v)-5 b(ari\341)m(v)m(eis)30 b FA(\001)584 2224 y Fl(\003)654 2260 y FH(e)g Fz(L)p FH(,)i(que)f(corresp)s(ondem,)g (resp)s(ectiv)-5 b(amen)m(te,)32 b(\340)e(menor)g(v)-5 b(aria\347\343o)29 b(de)i(custo)g(causada)109 2422 y(p)s(or)46 b(um)g(mo)m(vimen)m(to)f(e)i(\340)f(lista)f(de)i(mo)m(vimen)m(tos)e (candidatos)h(a)g(serem)h(aplicados)e(na)i(solu\347\343o)109 2585 y(\(to)s(dos)32 b(os)g(mo)m(vimen)m(tos)f(desta)i(lista)e(causam)h (a)g(mesma)f(v)-5 b(aria\347\343o)30 b(no)j(custo)f(da)h (solu\347\343o\).)42 b(O)32 b(la\347o)109 2748 y Fw(for)38 b FH(da)g(linha)e(6)i(visita)e(cada)i(p)s(osi\347\343o)f(da)h (seq\374\352ncia)h(em)f(busca)h(do)f(melhor)e(mo)m(vimen)m(to)h(para)g (o)109 2910 y(carro)c(da)g(p)s(osi\347\343o)g(considerada.)46 b(O)34 b(c\341lculo)e(da)h(v)-5 b(aria\347\343o)32 b(de)i(custo)h (decorren)m(te)g(da)e(aplica\347\343o)f(de)109 3073 y(cada)37 b(mo)m(vimen)m(to,)h(que)g(\351)g(armazenado)f(na)h(v)-5 b(ari\341)m(v)m(el)36 b FA(\001)p FH(,)j(\351)f(feito)f(na)g(linha)f(7) h(do)h(pseudo-c\363)s(digo.)109 3235 y(Este)g(c\341lculo)e(\351)i (descrito)f(em)g(detalhes)h(na)f(Se\347\343o)h(5.3.)58 b(Em)37 b(seguida,)h(realiza-se)e(a)h(a)m(v)-5 b(alia\347\343o)35 b(do)109 3398 y(mo)m(vimen)m(to:)59 b(se)42 b FA(\001)f FH(for)g(menor)f(que)i(a)f(menor)f(v)-5 b(aria\347\343o)40 b(de)i(custo)f(at\351)g(o)g(momen)m(to,)h FA(\001)3558 3361 y Fl(\003)3639 3398 y FH(\(linha)109 3560 y(8\),)36 b(atualiza-se)f(a)h(lista)e(de)j(mo)m(vimen)m(tos)e(\(linhas)g(9\))g(e) i(a)f(melhor)e(v)-5 b(aria\347\343o)35 b(de)i(custo)f(\(linha)f(10\);) 109 3723 y(se)i FA(\001)e(=)f(\001)534 3686 y Fl(\003)574 3723 y FH(,)j(este)h(mo)m(vimen)m(to)d(\351)i(adicionado)e(na)h(lista)f (de)i(mo)m(vimen)m(tos)f(candidatos)g(\(linha)f(12\).)109 3885 y(Ap)s(\363s)24 b(a)g(a)m(v)-5 b(alia\347\343o)22 b(de)i(to)s(dos)g(os)g(mo)m(vimen)m(tos)g(para)f(uma)h(determinada)f(p) s(osi\347\343o,)i(um)e(mo)m(vimen)m(to)g(\351)109 4048 y(escolhido)g(aleatoriamen)m(te)e(a)j(partir)f(da)g(lista)g(de)h(mo)m (vimen)m(tos)f(candidatos)g(\(linha)f(15\))i(e)g(\351)g(aplicado)109 4210 y(\340)g(solu\347\343o)g(atual)f(\(linha)g(16\).)40 b(O)24 b(algoritmo)d(termina)i(quando)i(a)f(solu\347\343o)g(n\343o)g (\351)h(aprimorada)d(dep)s(ois)109 4373 y(de)33 b(se)g(a)m(v)-5 b(aliar)30 b(to)s(das)j(as)f(tro)s(cas)h(p)s(oss\355v)m(eis)g(para)f (to)s(dos)g(os)h(carros)g(na)f(seq\374\352ncia)i(\(linha)c(18\).)274 4594 y(O)f(pro)s(cedimen)m(to)f(de)h(busca)h(lo)s(cal)d(que)j(aplica)d (mo)m(vimen)m(tos)h(do)h(tip)s(o)e FE(shift)39 b FH(p)s(o)s(de)28 b(ser)i(descrito,)109 4757 y(em)e(linhas)g(gerais,)i(de)f(forma)f (an\341loga)f(\340)i(busca)h(lo)s(cal)d(com)h(mo)m(vimen)m(tos)g FE(swap)p FH(.)42 b(O)29 b(pseudo-c\363)s(digo)109 4919 y(da)40 b(Figura)f(5.1)g(\351)i(facilmen)m(te)e(adaptado)h (alterando-se)f(ap)s(enas)i(as)f(linhas)g(7)g(e)g(16.)67 b(Na)40 b(linha)e(7,)109 5082 y(a)e(v)-5 b(ari\341)m(v)m(el)37 b FA(\001)g FH(receb)s(e)h(a)f(v)-5 b(aria\347\343o)35 b(no)i(custo)h(da)f(solu\347\343o)f(decorren)m(te)j(de)e(se)h(remo)m(v) m(er)g(o)f(carro)f(da)109 5244 y(p)s(osi\347\343o)e Fz(i)h FH(e)g(reinseri-lo)e(na)h(p)s(osi\347\343o)g Fz(j)6 b FH(.)51 b(Na)35 b(linha)e(16,)i(aplica-se)e(o)i(mo)m(vimen)m(to)e Fz(shif)11 b(t)p FA(\()p Fz(\031)t(;)17 b(i;)g(k)s FA(\))35 b FH(na)109 5407 y(solu\347\343o)25 b(atual)g Fz(\031)t FH(,)i(onde)f Fz(k)j FH(\351)e(a)e(p)s(osi\347\343o)g(escolhida)h (aleatoriamen)m(te)d(den)m(tre)28 b(as)e(p)s(osi\347\365)s(es)g (candidatas)109 5569 y(para)32 b(reinserir)g(o)g(carro)g(da)h(p)s (osi\347\343o)e Fz(i)p FH(.)274 5791 y(Uma)36 b(caracter\355stica)g (imp)s(ortan)m(te)f(dos)i(m\351to)s(dos)g(de)g(busca)h(lo)s(cal)d (utilizados)f(\351)k(que,)h(ev)m(en)m(tu-)p eop %%Page: 18 32 18 31 bop 109 -28 a FB(5.2)60 b(Heur\355sticas)31 b(de)g(busca)f(lo)s (cal)2493 b(18)p 109 9 3780 4 v 596 159 2805 4 v 596 2820 4 2661 v 657 351 a Fw(pro)s(cedure)33 b Fk(BuscaLocal)p FH(\(Solu\347\343o)h Fz(\031)t FH(\);)657 472 y(1)105 b Fw(rep)s(eat)657 592 y FH(2)260 b Fz(\036)27 b Fs( )g Fz(custo)p FA(\()p Fz(\031)t FA(\))657 713 y FH(3)260 b Fw(for)37 b Fv(i)32 b Fj(=)g(1)p Fv(;)19 b(:)g(:)g(:)g(;)g Fi(j)p Fv(\031)t Fi(j)37 b Fw(do)657 833 y FH(4)414 b FA(\001)1201 797 y Fl(\003)1268 833 y Fs( )28 b(1)657 953 y FH(5)414 b Fz(L)28 b Fs( )f(;)657 1074 y FH(6)414 b Fw(for)37 b Fv(j)h Fj(=)32 b(1)p Fv(;)19 b(:)g(:)g(:)g(;)g Fi(j)p Fv(\031)t Fi(j)37 b Fw(do)657 1194 y FH(7)568 b FA(\001)28 b Fs( )33 b FH(custo)g(de)g(tro)s(car)f(os)g(carros)h(das) g(p)s(osi\347\365)s(es)f Fz(i)h FH(e)g Fz(j)657 1314 y FH(8)568 b Fw(if)37 b Fj(\001)32 b Fv(<)g Fj(\001)1716 1278 y Fh(\003)1799 1314 y Fw(then)657 1435 y FH(9)723 b Fz(L)28 b Fs( )f(f)p Fz(j)6 b Fs(g)657 1555 y FH(10)674 b FA(\001)1510 1519 y Fl(\003)1577 1555 y Fs( )28 b FA(\001)657 1676 y FH(11)519 b Fw(else)37 b(if)g Fj(\001)32 b(=)g(\001)1929 1639 y Fh(\003)2012 1676 y Fw(then)657 1796 y FH(12)674 b Fz(L)28 b Fs( )f Fz(L)c Fs([)f(f)p Fz(j)6 b Fs(g)657 1916 y FH(13)519 b Fw(end-if)657 2037 y FH(14)365 b Fw(end-for)657 2157 y FH(15)g(Escolher)33 b Fz(k)e Fs(2)d Fz(L)33 b FH(aleatoriamen)m(te)657 2278 y(16)365 b Fz(\031)32 b Fs( )27 b Fz(sw)s(ap)p FA(\()p Fz(\031)t(;)17 b(i;)g(k)s FA(\))657 2398 y FH(17)211 b Fw(end-for)657 2518 y FH(18)56 b Fw(un)m(til)36 b Fv(\036)c Fj(=)g Fv(custo)p Fj(\()p Fv(\031)t Fj(\))657 2639 y FH(19)56 b Fw(return)37 b Fv(\031)657 2759 y Fw(end)c Fk(BuscaLocal)p FH(;)p 3397 2820 V 596 2823 2805 4 v 328 3091 a(Figura)e(5.1:)43 b(Pseudo-c\363)s(digo)32 b(da)g(heur\355stica)g(de)h(busca)h(lo)s(cal)c (com)i(mo)m(vimen)m(tos)g FE(swap)p FH(.)109 3376 y(almen)m(te,)j(a)h (solu\347\343o)e(ainda)h(p)s(o)s(de)g(ser)i(melhorada)c(se)k(mais)d (itera\347\365)s(es)h(forem)g(executadas)i(ap)s(\363s)e(a)109 3539 y(condi\347\343o)j(de)g(parada.)61 b(Isto)39 b(p)s(o)s(de)f(acon)m (tecer)i(p)s(ois)e(a)g(busca)h(quase)h(sempre)f(se)g(mo)m(v)m(e)g(para) f(uma)109 3701 y(no)m(v)-5 b(a)40 b(solu\347\343o,)h(mesmo)f(quando)g (n\343o)g(consegue)i(reduzir)e(o)g(custo)g(da)g(solu\347\343o)g(atual,) h(aplicando)109 3864 y(mo)m(vimen)m(tos)28 b(da)i(lista)d(de)j (candidatos)f(decorren)m(te)i(dos)f(empates.)43 b(Dian)m(te)29 b(disto,)h(\351)g(p)s(erfeitamen)m(te)109 4026 y(p)s(oss\355v)m(el)f (que)h(a)g(solu\347\343o)e(seja)i(aprimorada)d(nas)j(itera\347\365)s (es)f(seguin)m(tes.)44 b(No)29 b(en)m(tan)m(to,)i(de\034niu-se)f(um)109 4189 y(crit\351rio)35 b(de)i(parada)f(que)i(p)s(ermite)d(que)j(o)e(pro) s(cedimen)m(to)g(seja)h(executado)h(den)m(tro)g(de)f(um)f(temp)s(o)109 4351 y(computacional)30 b(aceit\341)m(v)m(el.)274 4573 y(A)d(descri\347\343o)g(geral)e(apresen)m(tada)j(dos)f(pro)s(cedimen)m (tos)g(de)g(busca)h(lo)s(cal)c(esconde)29 b(alguns)d(asp)s(ec-)109 4735 y(tos)32 b(que)h(dizem)e(resp)s(eito,)h(principalmen)m(te,)f (\340s)h(estruturas)h(de)g(dados)f(utilizadas.)42 b(Estes)33 b(asp)s(ectos)109 4898 y(t\352m)c(um)g(pap)s(el)g(imp)s(ortan)m(te)f (na)i(a)m(v)-5 b(alia\347\343o)27 b(e)j(na)g(aplica\347\343o)e(dos)i (mo)m(vimen)m(tos.)42 b(O)29 b(uso)h(de)h(estrutu-)109 5061 y(ras)k(de)h(dados)g(e\034cien)m(tes,)i(al\351m)c(de)i(outras)f (otimiza\347\365)s(es)f(na)h(implemen)m(ta\347\343o)e(das)j(buscas)h (lo)s(cais,)109 5223 y(p)s(ermitiu)f(obter)j(uma)f(complexidade)f (computacional)g(de)i(temp)s(o)f(reduzida,)i(conforme)e(p)s(o)s(de-se) 109 5386 y(observ)-5 b(ar)33 b(nas)g(se\347\365)s(es)g(seguin)m(tes.)p eop %%Page: 19 33 19 32 bop 109 -28 a FB(5.3)60 b(Estruturas)32 b(de)e(dados)2718 b(19)p 109 9 3780 4 v 109 256 a Fx(5.3)155 b(Estruturas)53 b(de)f(dados)274 576 y FH(As)28 b(estruturas)h(de)f(dados)g(para)f (represen)m(tar)j(as)d(informa\347\365)s(es)f(e)i(a)g(solu\347\343o)f (atual)f(do)i(problema)109 738 y(s\343o)37 b(um)g(asp)s(ecto)h(imp)s (ortan)m(te)e(no)h(pro)5 b(jeto)38 b(do)f(algoritmo)d(a)j(ser)h(desen)m (v)m(olvido)g(e)g(t\352m)f(um)g(pap)s(el)109 901 y(crucial)43 b(na)i(sua)g(complexidade)e(e,)48 b(conseq\374en)m(temen)m(te,)j(no)45 b(seu)g(desemp)s(enho.)81 b(As)45 b(estruturas)109 1063 y(de)32 b(dados)h(dev)m(em)g(ser)g(e\034cien)m(tes)h(do)e(p)s(on)m(to)g (de)h(vista)f(das)g(op)s(era\347\365)s(es)h(que)g(dev)m(er\343o)g(ser)g (realizadas)109 1226 y(sobre)22 b(elas.)40 b(Muita)21 b(aten\347\343o)g(e)h(esfor\347o)g(foram)f(dedicados)h(\340s)g (estruturas)g(de)h(dados,)h(principalmen)m(te)109 1388 y(observ)-5 b(ando-se)36 b(os)f(m\351to)s(dos)f(de)i(busca)g(lo)s(cal)d (aplicados,)h(uma)g(v)m(ez)j(que,)f(normalmen)m(te,)f(esta)g(\351)g(a) 109 1551 y(parte)41 b(do)g(algoritmo)d(que)k(demanda)f(mais)f(temp)s (o.)69 b(F)-8 b(oram)39 b(utilizadas,)j(al\351m)e(da)h(estrutura)h(de) 109 1713 y(dados)35 b(principal,)e(que)i(armazena)f(a)g(solu\347\343o)g (corren)m(te,)j(outras)d(estruturas)i(de)f(dados)g(auxiliares,)109 1876 y(para)d(armazenar)g(informa\347\365)s(es)f(adicionais)f(sobre)j (a)f(solu\347\343o.)274 2097 y(Uma)37 b(solu\347\343o)g(para)h(o)g (problema,)f(ou)h(seja,)i(uma)d(seq\374\352ncia)i(formada)e(p)s(or)g (to)s(dos)h(os)g(carros)109 2260 y(escalonados,)48 b(\351)e(represen)m (tada)h(p)s(or)e(um)g(v)m(etor,)k(onde)d(cada)g(p)s(osi\347\343o)e (guarda)h(um)g(n)m(\372mero)g(que)109 2422 y(represen)m(ta)28 b(o)f(carro)f(que)i(dev)m(e)g(ser)g(pro)s(duzido)e(naquela)h(p)s (osi\347\343o)f(ao)g(longo)f(do)i(dia)f(pro)s(du\347\343o.)41 b(Este)109 2585 y(n)m(\372mero)32 b(\351)h(o)f(\355ndice)g(referen)m (te)i(ao)e(carro)h(na)f(estrutura)h(de)h(dados)e(que)i(armazena)e(as)h (informa\347\365)s(es)109 2748 y(sobre)f(to)s(dos)g(os)g(carros)f(do)h (problema,)f(tais)g(como)f(as)i(op)s(\347\365)s(es)g(requeridas)h(e)f (a)f(cor)h(a)g(ser)g(usada)g(na)109 2910 y(pin)m(tura.)274 3132 y(A)m(dicionalmen)m(te,)23 b(tr\352s)h(v)m(etores)h(s\343o)e (utilizados)e(para)i(cada)g(uma)g(das)g(restri\347\365)s(es)h(de)f (capacidade)109 3294 y(do)46 b(problema.)83 b(Estes)47 b(v)m(etores)h(auxiliam)43 b(na)j(a)m(v)-5 b(alia\347\343o)44 b(da)i(v)-5 b(aria\347\343o)45 b(de)i(custo)f(causada)h(p)s(ela)109 3457 y(aplica\347\343o)32 b(de)i(um)g(mo)m(vimen)m(to)e(na)i (solu\347\343o,)g(no)g(que)h(diz)f(resp)s(eito)g(\340s)g(viola\347\365) s(es)f(de)h(restri\347\365)s(es)h(de)109 3619 y(capacidade.)68 b(O)41 b(primeiro)e(v)m(etor)i(asso)s(ciado)g(a)f(uma)h (restri\347\343o)f(de)i(capacidade)f(de)g(raz\343o)g Fz(N)r(=P)14 b FH(,)109 3782 y(denominado)40 b(v)m(etor)i Fz(A)p FH(,)h(armazena)e(o)g(n)m(\372mero)g(de)h(carros)f(que)h (requerem)g(a)f(op)s(\347\343o)g(asso)s(ciada)f(\340)109 3944 y(restri\347\343o)k(em)g(cada)h(seq\374\352ncia)h(consecutiv)-5 b(a)45 b(da)f(solu\347\343o)h(corren)m(te.)80 b(O)45 b(v)-5 b(alor)43 b(armazenado)h(na)109 4107 y(p)s(osi\347\343o)36 b Fz(i)i FH(deste)h(v)m(etor)f(represen)m(ta)h(o)f(n)m(\372mero)f(de)h (carros)g(asso)s(ciados)f(\340)g(restri\347\343o)h(na)f (seq\374\352ncia)109 4269 y(de)i Fs(j)p Fz(P)14 b Fs(j)38 b FH(carros)i(consecutiv)m(os)h(que)f(come\347a)f(na)g(p)s (osi\347\343o)f Fz(i)p FH(.)64 b(O)39 b(exemplo)g(da)g(Figura)e(5.2)i (a)5 b(juda)39 b(a)109 4432 y(en)m(tender)j(melhor)e(os)h(v)-5 b(alores)41 b(que)h(s\343o)f(armazenados)g(em)f Fz(A)p FH(.)69 b(Neste)43 b(exemplo,)f(a)f(restri\347\343o)g(de)109 4594 y(capacidade)36 b(considerada)h(tem)f(raz\343o)g FA(1)p Fz(=)p FA(4)p FH(.)55 b(As)38 b(seq\374\352ncias)g(consideradas) f(ao)f(longo)f(da)i(solu\347\343o)109 4757 y(s\343o)c(ilustradas)g(na)g (\034gura)h(e)g(o)f(n)m(\372mero)h(de)g(carros)g(asso)s(ciados)f(\340)h (restri\347\343o)f(em)g(cada)h(seq\374\352ncia)h(e)109 4919 y(a)d(p)s(osi\347\343o)g(corresp)s(onden)m(te)j(no)e(v)m(etor)h (de)f(seq\374\352ncias)i(p)s(o)s(dem)d(ser)h(vistos)g(ao)g(lado.)43 b(P)m(or)34 b(exemplo,)109 5082 y(na)46 b(primeira)e(p)s(osi\347\343o)i (do)g(v)m(etor)h(tem-se)g(o)f(v)-5 b(alor)45 b(3,)50 b(que)d(corresp)s(onde)h(ao)e(n)m(\372mero)g(de)h(carros)109 5244 y(asso)s(ciados)d(\340)g(restri\347\343o)g(na)g(seq\374\352ncia)i (formada)d(p)s(elos)h(quatro)g(primeiros)f(carros)h(da)h (solu\347\343o.)109 5407 y(Na)35 b(segunda)i(p)s(osi\347\343o)e(do)h(v) m(etor)h(de)f(seq\374\352ncias,)j(\351)d(armazenado)g(o)f(v)-5 b(alor)35 b(2,)h(corresp)s(ondendo)i(ao)109 5569 y(n)m(\372mero)32 b(de)g(carros)g(asso)s(ciados)g(\340)g(restri\347\343o)g(na)g (seq\374\352ncia)h(que)g(come\347a)f(no)g(carro)g(escalonado)f(na)109 5732 y(segunda)i(p)s(osi\347\343o,)f(e)h(assim)e(sucessiv)-5 b(amen)m(te,)34 b(at\351)f(a)f(\372ltima)e(seq\374\352ncia)k(da)e (solu\347\343o.)p eop %%Page: 20 34 20 33 bop 109 -28 a FB(5.3)60 b(Estruturas)32 b(de)e(dados)2718 b(20)p 109 9 3780 4 v 908 2046 a currentpoint currentpoint translate 0.5361 0.5361 scale neg exch neg exch translate 908 2046 a @beginspecial 2 @llx 113 @lly 490 @urx 536 @ury 4880 @rwi @setspecial %%BeginDocument: ed_vetorA.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 2 113 490 536 %%Creator: CorelDRAW 7 %%Title: %%CreationDate: Mon Feb 07 12:51:16 2005 %%DocumentProcessColors: Black %%DocumentSuppliedResources: (atend) %%EndComments %%BeginProlog /AutoFlatness true def /AutoSteps 0 def /CMYKMarks false def /UseLevel2 false def %Color profile: _DEFAULT.CCM - Gen. Profil -Sem %%BeginResource: procset wCorel7Dict 7.0 0 /wCorel7Dict 300 dict def wCorel7Dict begin % Copyright (c)1992-96 Corel Corporation % All rights reserved. v7.0 r1.0 /bd{bind def}bind def/ld{load def}bd/xd{exch def}bd/_ null def/rp{{pop}repeat} bd/@cp/closepath ld/@gs/gsave ld/@gr/grestore ld/@np/newpath ld/Tl/translate ld /$sv 0 def/@sv{/$sv save def}bd/@rs{$sv restore}bd/spg/showpage ld/showpage{} bd currentscreen/@dsp xd/$dsp/@dsp def/$dsa xd/$dsf xd/$sdf false def/$SDF false def/$Scra 0 def/SetScr/setscreen ld/setscreen{pop pop pop}bd/@ss{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if exch $Scra add exch load SetScr}bd /SepMode_5 where{pop}{/SepMode_5 0 def}ifelse/CurrentInkName_5 where{pop} {/CurrentInkName_5(Composite)def}ifelse/$ink_5 where{pop}{/$ink_5 -1 def} ifelse/$c 0 def/$m 0 def/$y 0 def/$k 0 def/$t 1 def/$n _ def/$o 0 def/$fil 0 def/$C 0 def/$M 0 def/$Y 0 def/$K 0 def/$T 1 def/$N _ def/$O 0 def/$PF false def/s1c 0 def/s1m 0 def/s1y 0 def/s1k 0 def/s1t 0 def/s1n _ def/$bkg false def /SK 0 def/SM 0 def/SY 0 def/SC 0 def/$op false def matrix currentmatrix/$ctm xd /$ptm matrix def/$ttm matrix def/$stm matrix def/$ffpnt true def /CorelDrawReencodeVect[16#0/grave 16#5/breve 16#6/dotaccent 16#8/ring 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl 16#88/circumflex/perthousand/Scaron/guilsinglleft/OE 16#91/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash 16#98/tilde/trademark/scaron/guilsinglright/oe 16#9F/Ydieresis 16#A1/exclamdown/cent/sterling/currency/yen/brokenbar/section 16#a8/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/minus/registered/macron 16#b0/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered 16#b8/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown 16#c0/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla 16#c8/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis 16#d0/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply 16#d8/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls 16#e0/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla 16#e8/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis 16#f0/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide 16#f8/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis]def /L2?/languagelevel where{pop languagelevel 2 ge}{false}ifelse def /@BeginSysCorelDict{systemdict/Corel30Dict known{systemdict/Corel30Dict get exec}if}bd/@EndSysCorelDict{systemdict/Corel30Dict known{end}if}bd AutoFlatness {/@ifl{dup currentflat exch sub 10 gt{ ([Error: PathTooComplex; OffendingCommand: AnyPaintingOperator]\n)print flush @np exit}{currentflat 2 add setflat}ifelse}bd/@fill/fill ld/fill{currentflat{ {@fill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@eofill/eofill ld/eofill {currentflat{{@eofill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@clip /clip ld/clip{currentflat{{@clip}stopped{@ifl}{exit}ifelse}bind loop setflat} bd/@eoclip/eoclip ld/eoclip{currentflat{{@eoclip}stopped{@ifl}{exit}ifelse} bind loop setflat}bd/@stroke/stroke ld/stroke{currentflat{{@stroke}stopped {@ifl}{exit}ifelse}bind loop setflat}bd}if L2?{/@ssa{true setstrokeadjust}bd}{ /@ssa{}bd}ifelse/d/setdash ld/j/setlinejoin ld/J/setlinecap ld/M/setmiterlimit ld/w/setlinewidth ld/O{/$o xd}bd/R{/$O xd}bd/W/eoclip ld/c/curveto ld/C/c ld/l /lineto ld/L/l ld/rl/rlineto ld/m/moveto ld/n/newpath ld/N/newpath ld/P{11 rp} bd/u{}bd/U{}bd/A{pop}bd/q/@gs ld/Q/@gr ld/&{}bd/@j{@sv @np}bd/@J{@rs}bd/g{1 exch sub/$k xd/$c 0 def/$m 0 def/$y 0 def/$t 1 def/$n _ def/$fil 0 def}bd/G{1 sub neg/$K xd _ 1 0 0 0/$C xd/$M xd/$Y xd/$T xd/$N xd}bd/k{1 index type /stringtype eq{/$t xd/$n xd}{/$t 0 def/$n _ def}ifelse/$k xd/$y xd/$m xd/$c xd /$fil 0 def}bd/K{1 index type/stringtype eq{/$T xd/$N xd}{/$T 0 def/$N _ def} ifelse/$K xd/$Y xd/$M xd/$C xd}bd/x/k ld/X/K ld/sf{1 index type/stringtype eq{ /s1t xd/s1n xd}{/s1t 0 def/s1n _ def}ifelse/s1k xd/s1y xd/s1m xd/s1c xd}bd/i{ dup 0 ne{setflat}{pop}ifelse}bd/v{4 -2 roll 2 copy 6 -2 roll c}bd/V/v ld/y{2 copy c}bd/Y/y ld/@w{matrix rotate/$ptm xd matrix scale $ptm dup concatmatrix /$ptm xd 1 eq{$ptm exch dup concatmatrix/$ptm xd}if 1 w}bd/@g{1 eq dup/$sdf xd {/$scp xd/$sca xd/$scf xd}if}bd/@G{1 eq dup/$SDF xd{/$SCP xd/$SCA xd/$SCF xd} if}bd/@D{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if 3 copy exch $Scra add exch load SetScr/$dsp xd/$dsa xd/$dsf xd}bd/$ngx{$SDF{$SCF SepMode_5 0 eq{$SCA} {$dsa}ifelse $SCP @ss}if}bd/p{/$pm xd 7 rp/$pyf xd/$pxf xd/$pn xd/$fil 1 def} bd/@MN{2 copy le{pop}{exch pop}ifelse}bd/@MX{2 copy ge{pop}{exch pop}ifelse}bd /InRange{3 -1 roll @MN @MX}bd/@sqr{dup 0 rl dup 0 exch rl neg 0 rl @cp}bd /currentscale{1 0 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt 0 1 dtransform matrix defaultmatrix 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-862709 22164 -861175 23123 -860187 c 24497 -858748 25503 -857346 26124 -855963 c 26547 -855032 26764 -854007 26764 -852906 c 26764 -851053 26105 -849482 24788 -848184 c 23481 -846885 21863 -846236 19953 -846236 c 18062 -846236 16406 -846895 14995 -848212 c 13575 -849519 12568 -851636 11957 -854534 C 7084 -853819 L 7563 -850234 8956 -847412 11261 -845343 c 13565 -843273 16435 -842238 19868 -842238 c 22164 -842238 24252 -842718 26115 -843677 c 27977 -844628 29379 -845973 30320 -847704 c 31251 -849425 31722 -851213 31722 -853047 c 31722 -855728 30771 -858315 28852 -860789 c 27676 -862332 24224 -865371 18495 -869915 c 16030 -871862 14196 -873461 12992 -874712 c 11787 -875954 10884 -877130 10282 -878240 C 28363 -878240 L 27394 -882812 L 3311 -882812 L @c F %CHAR: 0 -1008928 (1) @t 13584 -1008928 m 19981 -978420 L 17225 -980584 13349 -982324 8354 -983632 C 9285 -979107 L 11769 -978119 14214 -976821 16632 -975222 c 19050 -973622 20865 -972230 22079 -971035 c 22813 -970301 23509 -969408 24167 -968354 C 27065 -968354 L 18608 -1008928 L 13584 -1008928 L @c F %CHAR: 0 -1135044 (1) @t 13584 -1135044 m 19981 -1104536 L 17225 -1106700 13349 -1108440 8354 -1109748 C 9285 -1105223 L 11769 -1104235 14214 -1102937 16632 -1101338 c 19050 -1099738 20865 -1098346 22079 -1097151 c 22813 -1096417 23509 -1095524 24167 -1094470 C 27065 -1094470 L 18608 -1135044 L 13584 -1135044 L @c F T %%PageTrailer @rs @rs %%Trailer @EndSysCorelDict end %%DocumentSuppliedResources: procset wCorel7Dict %%EOF %%EndDocument @endspecial 908 2046 a currentpoint currentpoint translate 1 0.5361 div 1 0.5361 div scale neg exch neg exch translate 908 2046 a 109 2249 a FH(Figura)40 b(5.2:)60 b(V)-8 b(etor)42 b(que)g(guarda)f(o)h(n)m(\372mero)f(de)h (carros)g(asso)s(ciados)f(a)g(uma)g(restri\347\343o)g(em)g(cada)109 2369 y(seq\374\352ncia.)274 2762 y(O)28 b(segundo)i(v)m(etor)f (utilizado,)d(denominado)i(v)m(etor)h Fz(B)5 b FH(,)29 b(armazena)f(em)g(cada)h(p)s(osi\347\343o)e(o)h(n)m(\372mero)109 2925 y(de)i(seq\374\352ncias)i(em)e(que)h(o)f(n)m(\372mero)g(de)g (carros)h(asso)s(ciados)e(a)h(uma)g(certa)g(restri\347\343o)g(na)g (seq\374\352ncia)h(\351)109 3087 y(maior)22 b(que)k(o)e(n)m(umerador)h (da)g(raz\343o)f(desta)h(restri\347\343o,)h(ou)f(seja,)h(o)f(n)m (\372mero)g(de)g(seq\374\352ncias)h(que)g(est\343o)109 3250 y(violando)j(a)i(restri\347\343o)f(desde)j(o)d(in\355cio)f(da)i (solu\347\343o)f(at\351)h(aquela)g(p)s(osi\347\343o.)42 b(O)30 b(v)-5 b(alor)30 b(armazenado)g(na)109 3412 y(p)s(osi\347\343o)h Fz(i)i FH(do)g(v)m(etor)g Fz(B)38 b FH(asso)s(ciado)32 b(a)g(uma)g(restri\347\343o)g(de)i(raz\343o)e Fz(N)r(=P)46 b FH(corresp)s(onde)34 b(ao)e(n)m(\372mero)h(de)109 3575 y(seq\374\352ncias)g(que)g(violam)c(esta)k(restri\347\343o,)f (considerando-se)g(a)g(seq\374\352ncia)h(que)g(come\347a)e(na)h(p)s (osi\347\343o)109 3738 y(1)d(at\351)g(a)h(seq\374\352ncia)g(da)g(p)s (osi\347\343o)e Fz(i)p FH(.)43 b(Prosseguindo-se)30 b(com)f(o)h(mesmo)e (exemplo)h(da)h(\034gura)f(an)m(terior,)109 3900 y(tem-se)36 b(na)g(Figura)e(5.3)i(o)g(v)m(etor)g Fz(B)42 b FH(referen)m(te)37 b(\340)f(mesma)f(restri\347\343o)h(de)h(capacidade)f(de)g(raz\343o)g FA(1)p Fz(=)p FA(4)109 4063 y FH(para)25 b(a)h(mesma)f(solu\347\343o)g (utilizada.)38 b(Com)26 b(o)f(aux\355lio)f(do)h(v)m(etor)i Fz(A)p FH(,)g(que)g(guarda)e(o)h(n)m(\372mero)g(de)g(carros)109 4225 y(asso)s(ciados)37 b(\340)g(restri\347\343o)f(em)h(cada)g (seq\374\352ncia,)j(p)s(o)s(de-se)d(v)m(er)i(que)f(a)f(primeira)d(p)s (osi\347\343o)j(de)g Fz(B)43 b FH(tem)109 4388 y(o)d(v)-5 b(alor)40 b(1,)j(o)e(que)h(corresp)s(onde)g(a)f(uma)f(seq\374\352ncia)j (violando)c(a)i(restri\347\343o)f(at\351)i(esta)f(p)s(osi\347\343o)f (do)109 4550 y(v)m(etor)c Fz(A)p FH(,)h(ou)e(seja,)i(uma)e (seq\374\352ncia)i(que)g(p)s(ossui)e(v)-5 b(alor)34 b(em)i Fz(A)f FH(maior)f(que)j(um)e(\(n)m(umerador\).)52 b(Na)109 4713 y(segunda)39 b(p)s(osi\347\343o,)g(o)g(v)-5 b(alor)37 b(armazenado)h(\351)g(2,)i(corresp)s(ondendo)g(\340s)f(duas)g (primeiras)e(seq\374\352ncias)109 4875 y(e,)k(na)e(terceira)g(p)s (osi\347\343o,)h(tem-se)f(tr\352s)h(seq\374\352ncias)h(violando)d(a)h (restri\347\343o)g(at\351)g(esta)h(p)s(osi\347\343o.)62 b(Na)109 5038 y(quarta)36 b(p)s(osi\347\343o,)f(o)h(v)-5 b(alor)34 b(con)m(tin)m(ua)i(igual)e(a)h(tr\352s,)j(p)s(ois)d(a)g (seq\374\352ncia)i(desta)g(p)s(osi\347\343o)e(n\343o)g(viola)f(a)109 5200 y(restri\347\343o.)43 b(Desta)33 b(forma,)e(to)s(das)i(as)f(p)s (osi\347\365)s(es)h(de)g Fz(B)k FH(s\343o)c(calculadas.)274 5422 y(O)43 b(terceiro)f(v)m(etor,)k(denominado)c(v)m(etor)h Fz(C)7 b FH(,)46 b(\351)d(constru\355do)g(de)g(forma)e(an\341loga)g(ao) h(v)m(etor)i Fz(B)5 b FH(.)109 5584 y(A)37 b(diferen\347a)g(\351)g(que) h(s\343o)f(con)m(tabilizadas)e(as)i(seq\374\352ncias)i(cujo)e(v)-5 b(alor)35 b(em)i Fz(A)g FH(\351)g(maior)e(ou)i(igual)e(ao)109 5747 y(n)m(umerador)28 b(da)g(raz\343o)g(da)g(restri\347\343o)g (considerada.)42 b(A)29 b(id\351ia)e(\351)h(con)m(tabilizar)f(as)h (seq\374\352ncias)i(em)e(que)109 5909 y(a)e(en)m(trada)h(de)g(mais)f (um)g(carro)g(asso)s(ciado)g(\340)h(restri\347\343o)f(aumen)m(ta)h(o)f (n)m(\372mero)h(de)g(viola\347\365)s(es.)40 b(P)m(o)s(de-se)p eop %%Page: 21 35 21 34 bop 109 -28 a FB(5.3)60 b(Estruturas)32 b(de)e(dados)2718 b(21)p 109 9 3780 4 v 867 1101 a currentpoint currentpoint translate 0.59677 0.59677 scale neg exch neg exch translate 867 1101 a @beginspecial 2 @llx 349 @lly 457 @urx 539 @ury 4550 @rwi @setspecial %%BeginDocument: ed_vetores.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 2 349 457 539 %%Creator: CorelDRAW 7 %%Title: %%CreationDate: Mon Feb 07 11:28:06 2005 %%DocumentProcessColors: Black %%DocumentSuppliedResources: (atend) %%EndComments %%BeginProlog /AutoFlatness true def /AutoSteps 0 def /CMYKMarks false def /UseLevel2 false def %Color profile: _DEFAULT.CCM - Gen. Profil -Sem %%BeginResource: procset wCorel7Dict 7.0 0 /wCorel7Dict 300 dict def wCorel7Dict begin % Copyright (c)1992-96 Corel Corporation % All rights reserved. v7.0 r1.0 /bd{bind def}bind def/ld{load def}bd/xd{exch def}bd/_ null def/rp{{pop}repeat} bd/@cp/closepath ld/@gs/gsave ld/@gr/grestore ld/@np/newpath ld/Tl/translate ld /$sv 0 def/@sv{/$sv save def}bd/@rs{$sv restore}bd/spg/showpage ld/showpage{} bd currentscreen/@dsp xd/$dsp/@dsp def/$dsa xd/$dsf xd/$sdf false def/$SDF false def/$Scra 0 def/SetScr/setscreen ld/setscreen{pop pop pop}bd/@ss{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if exch $Scra add exch load SetScr}bd /SepMode_5 where{pop}{/SepMode_5 0 def}ifelse/CurrentInkName_5 where{pop} {/CurrentInkName_5(Composite)def}ifelse/$ink_5 where{pop}{/$ink_5 -1 def} ifelse/$c 0 def/$m 0 def/$y 0 def/$k 0 def/$t 1 def/$n _ def/$o 0 def/$fil 0 def/$C 0 def/$M 0 def/$Y 0 def/$K 0 def/$T 1 def/$N _ def/$O 0 def/$PF false def/s1c 0 def/s1m 0 def/s1y 0 def/s1k 0 def/s1t 0 def/s1n _ def/$bkg false def /SK 0 def/SM 0 def/SY 0 def/SC 0 def/$op false def matrix currentmatrix/$ctm xd /$ptm matrix def/$ttm matrix def/$stm matrix def/$ffpnt true def /CorelDrawReencodeVect[16#0/grave 16#5/breve 16#6/dotaccent 16#8/ring 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl 16#88/circumflex/perthousand/Scaron/guilsinglleft/OE 16#91/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash 16#98/tilde/trademark/scaron/guilsinglright/oe 16#9F/Ydieresis 16#A1/exclamdown/cent/sterling/currency/yen/brokenbar/section 16#a8/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/minus/registered/macron 16#b0/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered 16#b8/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown 16#c0/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla 16#c8/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis 16#d0/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply 16#d8/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls 16#e0/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla 16#e8/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis 16#f0/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide 16#f8/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis]def /L2?/languagelevel where{pop languagelevel 2 ge}{false}ifelse def /@BeginSysCorelDict{systemdict/Corel30Dict known{systemdict/Corel30Dict get exec}if}bd/@EndSysCorelDict{systemdict/Corel30Dict known{end}if}bd AutoFlatness {/@ifl{dup currentflat exch sub 10 gt{ ([Error: PathTooComplex; OffendingCommand: AnyPaintingOperator]\n)print flush @np exit}{currentflat 2 add setflat}ifelse}bd/@fill/fill ld/fill{currentflat{ {@fill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@eofill/eofill ld/eofill {currentflat{{@eofill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@clip /clip ld/clip{currentflat{{@clip}stopped{@ifl}{exit}ifelse}bind loop setflat} bd/@eoclip/eoclip ld/eoclip{currentflat{{@eoclip}stopped{@ifl}{exit}ifelse} bind loop setflat}bd/@stroke/stroke ld/stroke{currentflat{{@stroke}stopped {@ifl}{exit}ifelse}bind loop setflat}bd}if L2?{/@ssa{true setstrokeadjust}bd}{ /@ssa{}bd}ifelse/d/setdash ld/j/setlinejoin ld/J/setlinecap ld/M/setmiterlimit ld/w/setlinewidth ld/O{/$o xd}bd/R{/$O xd}bd/W/eoclip ld/c/curveto ld/C/c ld/l /lineto ld/L/l ld/rl/rlineto ld/m/moveto ld/n/newpath ld/N/newpath ld/P{11 rp} bd/u{}bd/U{}bd/A{pop}bd/q/@gs ld/Q/@gr ld/&{}bd/@j{@sv @np}bd/@J{@rs}bd/g{1 exch sub/$k xd/$c 0 def/$m 0 def/$y 0 def/$t 1 def/$n _ def/$fil 0 def}bd/G{1 sub neg/$K xd _ 1 0 0 0/$C xd/$M xd/$Y xd/$T xd/$N xd}bd/k{1 index type /stringtype eq{/$t xd/$n xd}{/$t 0 def/$n _ def}ifelse/$k xd/$y xd/$m xd/$c xd /$fil 0 def}bd/K{1 index type/stringtype eq{/$T xd/$N xd}{/$T 0 def/$N _ def} ifelse/$K xd/$Y xd/$M xd/$C xd}bd/x/k ld/X/K ld/sf{1 index type/stringtype eq{ /s1t xd/s1n xd}{/s1t 0 def/s1n _ def}ifelse/s1k xd/s1y xd/s1m xd/s1c xd}bd/i{ dup 0 ne{setflat}{pop}ifelse}bd/v{4 -2 roll 2 copy 6 -2 roll c}bd/V/v ld/y{2 copy c}bd/Y/y ld/@w{matrix rotate/$ptm xd matrix scale $ptm dup concatmatrix /$ptm xd 1 eq{$ptm exch dup concatmatrix/$ptm xd}if 1 w}bd/@g{1 eq dup/$sdf xd {/$scp xd/$sca xd/$scf xd}if}bd/@G{1 eq dup/$SDF xd{/$SCP xd/$SCA xd/$SCF xd} if}bd/@D{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if 3 copy exch $Scra add exch load SetScr/$dsp xd/$dsa xd/$dsf xd}bd/$ngx{$SDF{$SCF SepMode_5 0 eq{$SCA} {$dsa}ifelse $SCP @ss}if}bd/p{/$pm xd 7 rp/$pyf xd/$pxf xd/$pn xd/$fil 1 def} bd/@MN{2 copy le{pop}{exch pop}ifelse}bd/@MX{2 copy ge{pop}{exch pop}ifelse}bd /InRange{3 -1 roll @MN @MX}bd/@sqr{dup 0 rl dup 0 exch rl neg 0 rl @cp}bd /currentscale{1 0 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt 0 1 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt}bd/@unscale{}bd/wDstChck{2 1 roll dup 3 -1 roll eq{1 add}if}bd /@dot{dup mul exch dup mul add 1 exch sub}bd/@lin{exch pop abs 1 exch sub}bd /cmyk2rgb{3{dup 5 -1 roll add 1 exch sub dup 0 lt{pop 0}if exch}repeat pop}bd /rgb2cmyk{3{1 exch sub 3 1 roll}repeat 3 copy @MN @MN 3{dup 5 -1 roll sub neg exch}repeat}bd/rgb2g{2 index .299 mul 2 index .587 mul add 1 index .114 mul add 4 1 roll pop pop pop}bd/WaldoColor_5 where{pop}{/SetRgb/setrgbcolor ld/GetRgb /currentrgbcolor ld/SetGry/setgray ld/GetGry/currentgray ld/SetRgb2 systemdict /setrgbcolor get def/GetRgb2 systemdict/currentrgbcolor get def/SetHsb systemdict/sethsbcolor get def/GetHsb systemdict/currenthsbcolor get def /rgb2hsb{SetRgb2 GetHsb}bd/hsb2rgb{3 -1 roll dup floor sub 3 1 roll SetHsb GetRgb2}bd/setcmykcolor where{pop/SetCmyk_5/setcmykcolor ld}{/SetCmyk_5{ cmyk2rgb SetRgb}bd}ifelse/currentcmykcolor where{pop/GetCmyk/currentcmykcolor ld}{/GetCmyk{GetRgb rgb2cmyk}bd}ifelse/setoverprint where{pop}{/setoverprint{ /$op xd}bd}ifelse/currentoverprint where{pop}{/currentoverprint{$op}bd}ifelse /@tc_5{5 -1 roll dup 1 ge{pop}{4{dup 6 -1 roll mul exch}repeat pop}ifelse}bd /@trp{exch pop 5 1 roll @tc_5}bd/setprocesscolor_5{SepMode_5 0 eq{SetCmyk_5}{0 4 $ink_5 sub index exch pop 5 1 roll pop pop pop pop SepsColor true eq{$ink_5 3 gt{1 sub neg SetGry}{0 0 0 4 $ink_5 roll SetCmyk_5}ifelse}{1 sub neg SetGry} ifelse}ifelse}bd/findcmykcustomcolor where{pop}{/findcmykcustomcolor{5 array astore}bd}ifelse/setcustomcolor where{pop}{/setcustomcolor{exch aload pop SepMode_5 0 eq{pop @tc_5 setprocesscolor_5}{CurrentInkName_5 eq{4 index}{0} ifelse 6 1 roll 5 rp 1 sub neg SetGry}ifelse}bd}ifelse/@scc_5{dup type /booleantype eq{setoverprint}{1 eq setoverprint}ifelse dup _ eq{pop setprocesscolor_5 pop}{findcmykcustomcolor exch setcustomcolor}ifelse SepMode_5 0 eq{true}{GetGry 1 eq currentoverprint and not}ifelse}bd/colorimage where{pop /ColorImage{colorimage}def}{/ColorImage{/ncolors xd pop/dataaq xd{dataaq ncolors dup 3 eq{/$dat xd 0 1 $dat length 3 div 1 sub{dup 3 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length 3 idiv getinterval pop}{4 eq{/$dat xd 0 1 $dat length 4 div 1 sub{dup 4 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div $dat 4 index 3 add get 255 div cmyk2rgb rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length ncolors idiv getinterval}if}ifelse}image}bd }ifelse/setcmykcolor{1 5 1 roll _ currentoverprint @scc_5/$ffpnt xd}bd /currentcmykcolor{0 0 0 0}bd/setrgbcolor{rgb2cmyk setcmykcolor}bd /currentrgbcolor{currentcmykcolor cmyk2rgb}bd/sethsbcolor{hsb2rgb setrgbcolor} bd/currenthsbcolor{currentrgbcolor rgb2hsb}bd/setgray{dup dup setrgbcolor}bd /currentgray{currentrgbcolor rgb2g}bd}ifelse/WaldoColor_5 true def/@sft{$tllx $pxf add dup $tllx gt{$pwid sub}if/$tx xd $tury $pyf sub dup $tury lt{$phei add}if/$ty xd}bd/@stb{pathbbox/$ury xd/$urx xd/$lly xd/$llx xd}bd/@ep{{cvx exec }forall}bd/@tp{@sv/$in true def 2 copy dup $lly le{/$in false def}if $phei sub $ury ge{/$in false def}if dup $urx ge{/$in false def}if $pwid add $llx le{/$in false def}if $in{@np 2 copy m $pwid 0 rl 0 $phei neg rl $pwid neg 0 rl 0 $phei rl clip @np $pn cvlit load aload pop 7 -1 roll 5 index sub 7 -1 roll 3 index sub Tl matrix currentmatrix/$ctm xd @ep pop pop pop pop}{pop pop}ifelse @rs}bd /@th{@sft 0 1 $tly 1 sub{dup $psx mul $tx add{dup $llx gt{$pwid sub}{exit} ifelse}loop exch $phei mul $ty exch sub 0 1 $tlx 1 sub{$pwid mul 3 copy 3 -1 roll add exch @tp pop}for pop pop}for}bd/@tv{@sft 0 1 $tlx 1 sub{dup $pwid mul $tx add exch $psy mul $ty exch sub{dup $ury lt{$phei add}{exit}ifelse}loop 0 1 $tly 1 sub{$phei mul 3 copy sub @tp pop}for pop pop}for}bd/$fm 0 def/wfill{1 $fm eq{fill}{eofill}ifelse}bd/wclip{1 $fm eq{clip}{eoclip}ifelse}bd/@pf{@gs $ctm setmatrix $pm concat @stb wclip Bburx Bbury $pm 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@endspecial 867 1101 a currentpoint currentpoint translate 1 0.59677 div 1 0.59677 div scale neg exch neg exch translate 867 1101 a 680 1304 a FH(Figura)31 b(5.3:)43 b(V)-8 b(etores)33 b(auxiliares)e(corresp)s(onden)m(tes)k(a)d (uma)g(solu\347\343o.)109 1697 y(observ)-5 b(ar)32 b(que)h(isto)f (inclui)e(seq\374\352ncias)k(que)f(n\343o)f(violam)d(a)j (restri\347\343o,)g(p)s(or\351m)f(cujo)i(v)-5 b(alor)30 b(no)i(v)m(etor)109 1860 y Fz(A)h FH(\351)h(igual)e(ao)h(n)m(umerador)h (da)f(raz\343o,)h(v)-5 b(alor)32 b(m\341ximo)f(p)s(ermitido)g(para)j (resp)s(eitar)f(a)g(restri\347\343o.)47 b(Se)109 2022 y(um)33 b(carro)h(asso)s(ciado)f(a)h(esta)h(restri\347\343o)e(\351)h (adicionado)f(a)g(estas)i(seq\374\352ncias,)i(elas)c(passam)h(en)m (t\343o)g(a)109 2185 y(violar)g(a)i(restri\347\343o.)55 b(A)36 b(Figura)f(5.3)h(con)m(tin)m(ua)g(com)g(o)g(exemplo)f(an)m (terior)h(e)h(apresen)m(ta)g(o)f(v)m(etor)h Fz(C)109 2347 y FH(corresp)s(onden)m(te)d(\340)e(solu\347\343o)g(utilizada.)274 2569 y(P)m(ara)h(mostrar)g(como)f(estes)j(v)m(etores)f(con)m(tribuem)f (para)g(uma)f(implemen)m(ta\347\343o)f(mais)h(e\034cien)m(te)109 2731 y(do)27 b(algoritmo,)e(primeiramen)m(te,)i(ser\341)h(mostrado)e (como)h(eles)g(auxiliam)e(a)i(a)m(v)-5 b(alia\347\343o)25 b(dos)j(mo)m(vimen-)109 2894 y(tos)40 b(duran)m(te)h(a)e(busca)i(lo)s (cal)d(que)j(realiza)d(mo)m(vimen)m(tos)h FE(swap)p FH(.)65 b(A)40 b(aplica\347\343o)e(do)i(mo)m(vimen)m(to)f(de)109 3056 y(tro)s(car)32 b(dois)g(carros)h(que)h(n\343o)f(est\343o)g(asso)s (ciados)g(a)f(uma)h(determinada)e(restri\347\343o)i(certamen)m(te)g (n\343o)109 3219 y(causa)g(v)-5 b(aria\347\343o)31 b(no)i(custo)h(da)e (solu\347\343o,)h(no)f(que)i(se)g(refere)f(ao)g(n)m(\372mero)g(de)g (viola\347\365)s(es)e(desta)j(restri-)109 3381 y(\347\343o.)52 b(O)35 b(mesmo)g(acon)m(tece)h(quando)g(se)h(deseja)f(tro)s(car)f(dois) g(carros)g(que)i(est\343o)f(asso)s(ciados)f(a)g(uma)109 3544 y(mesma)29 b(restri\347\343o.)42 b(P)m(ortan)m(to,)32 b(ser\341)f(analisada)d(a)i(tro)s(ca)g(de)h(dois)f(carros)g(onde)h(um)f (dos)h(carros)g(est\341)109 3706 y(asso)s(ciado)k(a)h(uma)g(dada)g (restri\347\343o)g(e)h(o)f(outro)g(n\343o.)55 b(O)36 b(n)m(\372mero)g(de)h(viola\347\365)s(es)e(de)i(uma)f(restri\347\343o) 109 3869 y(de)g(capacidade)f(de)i(raz\343o)e Fz(N)r(=P)49 b FH(que)37 b(ser\341)f(decrescido)h(no)e(custo)i(da)e(solu\347\343o)g (com)g(a)h(retirada)e(do)109 4031 y(carro)27 b(asso)s(ciado)g(a)h(esta) g(restri\347\343o)g(da)g(p)s(osi\347\343o)e Fz(i)j FH(\351)f(obtido)f (a)g(partir)g(do)h(v)m(etor)g Fz(B)33 b FH(corresp)s(onden)m(te)d(e)109 4194 y(ser\341)f(denotado)f(p)s(or)g FA(\001)977 4209 y Fq(1)1017 4194 y FH(.)42 b(Como)27 b(um)h(carro)g(p)s(o)s(de)h(dimin) m(uir)c(ou)k(aumen)m(tar)f(somen)m(te)h(uma)e(viola\347\343o)109 4356 y(em)k(uma)f(seq\374\352ncia,)j(en)m(t\343o)f(\351)g(su\034cien)m (te)h(calcular)d(quan)m(tas)i(seq\374\352ncias)i(que)e(p)s(ossuem)g (este)g(carro)109 4519 y(est\343o)g(violando)f(a)i(restri\347\343o)f (considerada.)43 b(Desta)34 b(forma,)d(o)h(v)-5 b(alor)31 b(de)i FA(\001)2913 4534 y Fq(1)2985 4519 y FH(\351)g(dado)g(p)s(or:) 1153 4834 y FA(\001)1234 4849 y Fq(1)1301 4834 y FA(=)1405 4663 y Fr(\()1527 4760 y Fz(B)5 b FA([)p Fz(i)p FA(])22 b Fs(\000)h Fz(B)5 b FA([)p Fz(i)23 b Fs(\000)f Fz(P)14 b FA(])p FH(,)32 b(se)i Fz(i)22 b Fs(\000)h Fz(P)41 b(>)28 b FA(0;)1527 4923 y Fz(B)5 b FA([)p Fz(i)p FA(])p FH(,)33 b(caso)g(con)m(tr\341rio.)274 5213 y(O)41 b(v)-5 b(alor)40 b(con)m(tido)g(em)h Fz(B)5 b FA([)p Fz(i)p FA(])41 b FH(corresp)s(onde)i(ao)d(n)m(\372mero)h(de)h(seq\374\352ncias)g (violando)e(a)h(restri\347\343o)109 5376 y(desde)48 b(a)e(primeira)e (seq\374\352ncia)k(at\351)f(a)f(seq\374\352ncia)i(que)f(come\347a)g(na) f(p)s(osi\347\343o)g Fz(i)p FH(,)k(que)e(\351)f(a)f(\372ltima)109 5538 y(seq\374\352ncia)32 b(que)g(con)m(t\351m)g(o)f(carro)g(na)g(p)s (osi\347\343o)f Fz(i)i FH(da)f(solu\347\343o.)42 b(A)32 b(p)s(osi\347\343o)e Fz(i)20 b Fs(\000)g Fz(P)45 b FH(refere-se)32 b(\340)f(\372ltima)109 5701 y(seq\374\352ncia)d(\340)f(qual)g(o)g (carro)h(da)f(p)s(osi\347\343o)f Fz(i)i FH(n\343o)f(p)s(ertence,)j(uma) d(v)m(ez)h(que)h(um)e(carro)g(est\341)h(con)m(tido)f(em)109 5863 y(exatamen)m(te)40 b Fz(P)52 b FH(seq\374\352ncias.)66 b(P)m(ortan)m(to,)42 b(a)d(subtra\347\343o)g(desses)j(dois)d(v)-5 b(alores)39 b(resulta)g(no)g(n)m(\372mero)p eop %%Page: 22 36 22 35 bop 109 -28 a FB(5.3)60 b(Estruturas)32 b(de)e(dados)2718 b(22)p 109 9 3780 4 v 109 256 a FH(de)40 b(seq\374\352ncias)h(que)g (con)m(t\352m)f(o)g(carro)f(da)h(p)s(osi\347\343o)f Fz(i)h FH(e)g(que)h(violam)c(a)j(restri\347\343o.)64 b(Se)41 b(o)e(v)-5 b(alor)39 b(de)109 418 y Fz(i)27 b Fs(\000)g Fz(P)53 b FH(\351)40 b(menor)f(que)h(zero,)i(signi\034ca)c(que)j(o)e (carro)g(aparece)h(no)g(in\355cio)d(da)i(solu\347\343o)g(e,)j(p)s (ortan)m(to,)109 581 y Fz(B)5 b FA([)p Fz(i)p FA(])30 b FH(\351)g(o)g(v)-5 b(alor)28 b(desejado.)43 b(En)m(t\343o,)31 b FA(\001)1517 596 y Fq(1)1586 581 y FH(represen)m(ta)h(o)d(n)m (\372mero)h(de)g(viola\347\365)s(es)f(da)h(restri\347\343o)f(que)i (ser\341)109 743 y(reduzido)h(se)i(a)e(tro)s(ca)g(dos)h(carros)f (considerados)h(for)f(realizada.)274 965 y(De)45 b(maneira)d (an\341loga,)j(o)e(n)m(\372mero)h(de)g(viola\347\365)s(es)f(de)h(uma)f (restri\347\343o)g(que)i(ser\341)g(aumen)m(tado)109 1127 y(decorren)m(te)37 b(da)e(en)m(trada)h(de)g(um)f(carro)g(asso)s(ciado)g (\340)g(restri\347\343o)g(na)g(p)s(osi\347\343o)g Fz(j)6 b FH(,)36 b(que)g(n\343o)f(con)m(tinha)109 1290 y(um)d(carro)g(asso)s (ciado)g(a)g(ela,)g(\351)h(calculado)e(a)h(partir)f(do)i(v)m(etor)g Fz(C)39 b FH(e)33 b(denotado)g(p)s(or)f FA(\001)3329 1305 y Fq(2)3369 1290 y FH(:)1155 1604 y FA(\001)1236 1619 y Fq(2)1304 1604 y FA(=)1407 1434 y Fr(\()1529 1531 y Fz(C)7 b FA([)p Fz(i)p FA(])22 b Fs(\000)h Fz(C)7 b FA([)p Fz(i)23 b Fs(\000)f Fz(P)14 b FA(])p FH(,)32 b(se)i Fz(i)22 b Fs(\000)h Fz(P)41 b(>)27 b FA(0;)1529 1693 y Fz(C)7 b FA([)p Fz(i)p FA(])p FH(,)33 b(caso)g(con)m(tr\341rio.)274 1978 y(Conforme)e(foi)f(dito)g(an)m(teriormen)m(te,)h(este)i(v)m(etor)f (guarda)f(o)g(n)m(\372mero)g(de)h(seq\374\352ncias)h(em)e(que)h(a)109 2140 y(en)m(trada)27 b(de)g(um)f(carro)g(asso)s(ciado)g(\340)h (restri\347\343o)f(corresp)s(onden)m(te)j(aumen)m(ta)d(o)g(n)m (\372mero)h(de)g(viola\347\365)s(es.)109 2303 y(Finalmen)m(te,)39 b(a)g(v)-5 b(aria\347\343o)37 b(no)i(custo)h(causada)g(p)s(ela)e(tro)s (ca)g(desses)k(dois)d(carros)g(\351)g(dada)g(p)s(or)g FA(\001)g(=)109 2465 y(\001)190 2480 y Fq(2)252 2465 y Fs(\000)22 b FA(\001)432 2480 y Fq(1)472 2465 y FH(.)274 2687 y(No)30 b(exemplo)g(da)g(Figura)e(5.3,)i(sup)s(onha)h(que)g(se)g (deseja)g(a)m(v)-5 b(aliar)28 b(a)h(v)-5 b(aria\347\343o)29 b(no)h(custo)h(causada)109 2849 y(p)s(ela)44 b(in)m(v)m(ers\343o)h(dos) h(carros)f(das)g(p)s(osi\347\365)s(es)g(3)g(e)g(7,)j(lem)m(brando)c (que)i(a)f(restri\347\343o)g(de)g(capacidade)109 3012 y(considerada)31 b(tem)h(raz\343o)f(1/4.)43 b(O)31 b(v)-5 b(alor)31 b(que)h(ser\341)h(acrescido)f(decorren)m(te)h(de)f(se)h(colo) s(car)d(um)h(carro)109 3174 y(com)26 b(a)i(restri\347\343o)f(na)g(p)s (osi\347\343o)g(7)g(\351)h(dado)f(p)s(or)g FA(\001)1879 3189 y Fq(2)1946 3174 y FA(=)h Fz(C)7 b FA([7])12 b Fs(\000)g Fz(C)7 b FA([3])28 b(=)f(4)p FH(.)42 b(P)m(or)28 b(outro)f(lado,)g(o)g (v)-5 b(alor)26 b(que)109 3337 y(ser\341)31 b(reduzido)h(decorren)m(te) g(da)g(en)m(trada)f(de)h(um)f(carro)f(sem)i(a)f(restri\347\343o)g(na)g (p)s(osi\347\343o)f(3)h(\351)h(dado)f(p)s(or)109 3499 y FA(\001)190 3514 y Fq(1)265 3499 y FA(=)36 b Fz(B)5 b FA([3])36 b(=)f(3)p FH(.)58 b(Assim,)37 b(a)g(aplica\347\343o)f (deste)i(mo)m(vimen)m(to)e(na)h(solu\347\343o)g(resultar\341)g(no)g (acr\351scimo)109 3662 y(de)c(uma)e(viola\347\343o)g(desta)i (restri\347\343o.)274 3883 y(No)e(en)m(tan)m(to,)h(uma)e(aten\347\343o) h(esp)s(ecial)g(dev)m(e)h(ser)g(dada)f(quando)g(a)g(dist\342ncia)f(en)m (tre)i(as)f(p)s(osi\347\365)s(es)109 4046 y Fz(i)g FH(e)g Fz(j)37 b FH(dos)31 b(carros)g(que)h(se)g(deseja)f(tro)s(car)f(\351)i (menor)e(do)h(que)h(o)e(denominador)g(da)g(raz\343o)h(da)g (restri\347\343o)109 4208 y(que)42 b(se)g(est\341)g(considerando,)i(ou) e(seja,)i(quando)e Fs(j)p Fz(i)28 b Fs(\000)h Fz(j)6 b Fs(j)42 b Fz(<)h(P)14 b FH(.)70 b(Quando)41 b(isto)g(acon)m(tece,)k (os)d(dois)109 4371 y(carros)h(p)s(ertencem)h(a)f(uma)f(ou)i(mais)d (seq\374\352ncias)k(em)e(com)m(um)g(e)g(estas)h(seq\374\352ncias)h (n\343o)e(dev)m(em)109 4533 y(ser)38 b(consideradas)g(na)g(a)m(v)-5 b(alia\347\343o)36 b(do)h(mo)m(vimen)m(to,)h(uma)f(v)m(ez)j(que)e(am)m (b)s(os)g(os)g(carros)g(con)m(tin)m(uar\343o)109 4696 y(nestas)30 b(seq\374\352ncias)i(e,)e(p)s(or)f(conseguin)m(te,)j(o)d(n) m(\372mero)g(de)h(viola\347\365)s(es)f(nelas)g(n\343o)h(sofrer\341)f (altera\347\343o)f(se)109 4858 y(o)k(mo)m(vimen)m(to)g(for)g(aplicado.) 42 b(Dian)m(te)33 b(disto,)g(as)g(viola\347\365)s(es)e(decrescidas)j (decorren)m(tes)h(da)e(tro)s(ca)f(do)109 5021 y(carro)e(da)g(p)s (osi\347\343o)f Fz(i)h FH(asso)s(ciado)g(a)g(uma)f(restri\347\343o)h (de)h(capacidade)f(de)g(raz\343o)g Fz(N)r(=P)44 b FH(com)29 b(o)h(carro)g(da)109 5184 y(p)s(osi\347\343o)h Fz(j)6 b FH(,)33 b(que)g(n\343o)g(est\341)g(asso)s(ciado)e(a)i(esta)g (restri\347\343o,)f(se)h Fz(i)28 b(<)g(j)38 b FH(e)33 b Fz(j)28 b Fs(\000)23 b Fz(i)28 b(<)f(P)14 b FH(,)32 b(\351)h(dado)f(p)s(or:)777 5580 y FA(\001)858 5595 y Fq(1)926 5580 y FA(=)1029 5315 y Fr(8)1029 5405 y(>)1029 5435 y(>)1029 5465 y(<)1029 5644 y(>)1029 5674 y(>)1029 5704 y(:)1159 5425 y Fz(B)5 b FA([)p Fz(j)29 b Fs(\000)22 b Fz(P)14 b FA(])22 b Fs(\000)g Fz(B)5 b FA([)p Fz(i)23 b Fs(\000)g Fz(P)14 b FA(])p FH(,)32 b(se)h Fz(i)23 b Fs(\000)f Fz(P)41 b(>)28 b FA(0)k FH(e)h Fz(j)28 b Fs(\000)23 b Fz(P)41 b(>)27 b FA(0;)1159 5587 y Fz(B)5 b FA([)p Fz(j)29 b Fs(\000)22 b Fz(P)14 b FA(])p FH(,)32 b(se)i Fz(i)22 b Fs(\000)h Fz(P)41 b Fs(\024)28 b FA(0)k FH(e)h Fz(j)28 b Fs(\000)23 b Fz(P)41 b(>)27 b FA(0;)1159 5750 y(0)p FH(,)33 b(caso)f(con)m(tr\341rio.)p eop %%Page: 23 37 23 36 bop 109 -28 a FB(5.3)60 b(Estruturas)32 b(de)e(dados)2718 b(23)p 109 9 3780 4 v 274 256 a FH(P)m(or)33 b(sua)h(v)m(ez,)h(o)e(n)m (\372mero)g(de)g(viola\347\365)s(es)f(que)j(ser\341)e(aumen)m(tado)g (em)g(decorr\352ncia)g(da)g(aplica\347\343o)109 418 y(do)f(mo)m(vimen)m (to,)f(quando)i Fz(i)28 b(<)g(j)38 b FH(e)33 b Fz(j)28 b Fs(\000)23 b Fz(i)28 b(<)f(P)14 b FH(,)33 b(\351)f(dado)h(p)s(or:) 1543 680 y FA(\001)1624 695 y Fq(2)1692 680 y FA(=)27 b Fz(C)7 b FA([)p Fz(j)f FA(])23 b Fs(\000)f Fz(C)7 b FA([)p Fz(j)28 b Fs(\000)23 b Fz(i)p FA(])p Fz(:)274 1001 y FH(Observ)-5 b(a-se)38 b(que)f(a)g(\372ltima)d(seq\374\352ncia)k (considerada)e(no)h(c\341lculo)e(de)j FA(\001)3015 1016 y Fq(1)3091 1001 y FH(come\347a)e(na)h(p)s(osi\347\343o)109 1164 y Fz(j)23 b Fs(\000)18 b Fz(P)c FH(,)31 b(que)g(\351)g(a)f (\372ltima)d(seq\374\352ncia)32 b(que)f(con)m(t\351m)g(o)f(carro)g(em)g Fz(i)g FH(an)m(tes)i(do)e(in)m(terv)-5 b(alo)29 b(de)i (seq\374\352ncias)109 1326 y(em)25 b(com)m(um.)40 b(O)26 b(v)-5 b(alor)24 b(de)j FA(\001)1174 1341 y Fq(1)1239 1326 y FH(p)s(o)s(de)f(ser)g Fz(B)5 b FA([)p Fz(j)14 b Fs(\000)8 b Fz(P)14 b FA(])27 b FH(ou)f(0,)h(quando)f(um)f(ou)h(am)m (b)s(os)f(os)h(carros)g(est\343o)g(na)109 1489 y(primeira)d (seq\374\352ncia)k(do)f(dia)f(de)h(pro)s(du\347\343o,)h(resp)s(ectiv)-5 b(amen)m(te.)42 b(Analogamen)m(te,)26 b(p)s(o)s(de-se)g(observ)-5 b(ar)109 1651 y(que)34 b(o)f(c\341lculo)f(de)i FA(\001)911 1666 y Fq(2)984 1651 y FH(come\347a)f(com)f(a)h(seq\374\352ncia)i(da)e (p)s(osi\347\343o)f Fz(j)d Fs(\000)23 b Fz(i)g FA(+)f(1)p FH(,)34 b(p)s(ois)e(esta)i(\351)g(a)f(primeira)109 1814 y(seq\374\352ncia)i(ap)s(\363s)g(o)f(in)m(terv)-5 b(alo)33 b(de)i(seq\374\352ncias)h(em)e(com)m(um)f(en)m(tre)j(os)e(dois)g (carros.)50 b(Quando)34 b Fz(i)d(>)g(j)6 b FH(,)109 1976 y(a)30 b(forma)g(como)g(os)h(v)m(etores)i(s\343o)e(acessados)h(\351)g (in)m(v)m(ertida:)42 b Fz(B)36 b FH(\351)c(acessado)g(de)f(forma)f (an\341loga)f(a)i Fz(C)7 b FH(,)31 b(e)109 2139 y(vice-v)m(ersa.)274 2361 y(Na)44 b(Figura)f(5.4,)j(con)m(tin)m(ua-se)f(com)e(o)h(exemplo)g (da)g(\034gura)g(an)m(terior.)78 b(Deseja-se)45 b(tro)s(car)f(os)109 2523 y(carros)34 b(da)h(p)s(osi\347\343o)e Fz(i)f FA(=)f(4)p FH(,)j(que)i(est\341)f(asso)s(ciado)f(\340)g(restri\347\343o,)g(e)h(da) g(p)s(osi\347\343o)e Fz(j)k FA(=)31 b(6)p FH(,)k(que)g(n\343o)g (est\341)109 2686 y(asso)s(ciado)f(a)h(ela.)51 b(T)-8 b(em-se,)37 b(p)s(ortan)m(to,)e(as)h(seq\374\352ncias)h(das)e(p)s (osi\347\365)s(es)g(3)g(e)h(4)f(como)g(seq\374\352ncias)i(em)109 2848 y(com)m(um)25 b(en)m(tre)i(os)f(carros.)42 b(Como)25 b(o)h(carro)g(da)g(p)s(osi\347\343o)f(4)h(est\341)h(na)f(primeira)e (seq\374\352ncia)j(mas)f(o)g(outro)109 3011 y(carro)36 b(n\343o)g(est\341,)j FA(\001)865 3026 y Fq(1)939 3011 y FA(=)c Fz(B)5 b FA([6)25 b Fs(\000)g FA(4])35 b(=)f(2)p FH(,)k(enquan)m(to)g(que)f FA(\001)2360 3026 y Fq(2)2435 3011 y FA(=)d Fz(C)7 b FA([6])25 b Fs(\000)h Fz(C)7 b FA([6)25 b Fs(\000)g FA(4])35 b(=)f(2)p FH(.)56 b(P)m(ortan)m(to,)109 3173 y(este)33 b(mo)m(vimen)m(to)e(n\343o)i(causa)g(altera\347\343o)e (no)h(n)m(\372mero)h(de)g(viola\347\365)s(es)e(desta)i(restri\347\343o) f(\()p FA(\001)c(=)g(0)p FH(\).)743 4614 y currentpoint currentpoint translate 0.66231 0.66231 scale neg exch neg exch translate 743 4614 a @beginspecial 2 @llx 325 @lly 457 @urx 539 @ury 4550 @rwi @setspecial %%BeginDocument: ed_vetoresInter.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 2 325 457 539 %%Creator: CorelDRAW 7 %%Title: %%CreationDate: Fri Feb 11 14:20:15 2005 %%DocumentProcessColors: Black %%DocumentSuppliedResources: (atend) %%EndComments %%BeginProlog /AutoFlatness true def /AutoSteps 0 def /CMYKMarks false def /UseLevel2 false def %Color profile: _DEFAULT.CCM - Gen. 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def/$bkg false def /SK 0 def/SM 0 def/SY 0 def/SC 0 def/$op false def matrix currentmatrix/$ctm xd /$ptm matrix def/$ttm matrix def/$stm matrix def/$ffpnt true def /CorelDrawReencodeVect[16#0/grave 16#5/breve 16#6/dotaccent 16#8/ring 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl 16#88/circumflex/perthousand/Scaron/guilsinglleft/OE 16#91/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash 16#98/tilde/trademark/scaron/guilsinglright/oe 16#9F/Ydieresis 16#A1/exclamdown/cent/sterling/currency/yen/brokenbar/section 16#a8/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/minus/registered/macron 16#b0/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered 16#b8/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown 16#c0/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla 16#c8/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis 16#d0/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply 16#d8/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls 16#e0/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla 16#e8/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis 16#f0/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide 16#f8/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis]def /L2?/languagelevel where{pop languagelevel 2 ge}{false}ifelse def /@BeginSysCorelDict{systemdict/Corel30Dict known{systemdict/Corel30Dict get exec}if}bd/@EndSysCorelDict{systemdict/Corel30Dict known{end}if}bd AutoFlatness {/@ifl{dup currentflat exch sub 10 gt{ ([Error: PathTooComplex; OffendingCommand: AnyPaintingOperator]\n)print flush @np exit}{currentflat 2 add setflat}ifelse}bd/@fill/fill ld/fill{currentflat{ {@fill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@eofill/eofill 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def/$N _ def} ifelse/$K xd/$Y xd/$M xd/$C xd}bd/x/k ld/X/K ld/sf{1 index type/stringtype eq{ /s1t xd/s1n xd}{/s1t 0 def/s1n _ def}ifelse/s1k xd/s1y xd/s1m xd/s1c xd}bd/i{ dup 0 ne{setflat}{pop}ifelse}bd/v{4 -2 roll 2 copy 6 -2 roll c}bd/V/v ld/y{2 copy c}bd/Y/y ld/@w{matrix rotate/$ptm xd matrix scale $ptm dup concatmatrix /$ptm xd 1 eq{$ptm exch dup concatmatrix/$ptm xd}if 1 w}bd/@g{1 eq dup/$sdf xd {/$scp xd/$sca xd/$scf xd}if}bd/@G{1 eq dup/$SDF xd{/$SCP xd/$SCA xd/$SCF xd} if}bd/@D{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if 3 copy exch $Scra add exch load SetScr/$dsp xd/$dsa xd/$dsf xd}bd/$ngx{$SDF{$SCF SepMode_5 0 eq{$SCA} {$dsa}ifelse $SCP @ss}if}bd/p{/$pm xd 7 rp/$pyf xd/$pxf xd/$pn xd/$fil 1 def} bd/@MN{2 copy le{pop}{exch pop}ifelse}bd/@MX{2 copy ge{pop}{exch pop}ifelse}bd /InRange{3 -1 roll @MN @MX}bd/@sqr{dup 0 rl dup 0 exch rl neg 0 rl @cp}bd /currentscale{1 0 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt 0 1 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt}bd/@unscale{}bd/wDstChck{2 1 roll dup 3 -1 roll eq{1 add}if}bd /@dot{dup mul exch dup mul add 1 exch sub}bd/@lin{exch pop abs 1 exch sub}bd /cmyk2rgb{3{dup 5 -1 roll add 1 exch sub dup 0 lt{pop 0}if exch}repeat pop}bd /rgb2cmyk{3{1 exch sub 3 1 roll}repeat 3 copy @MN @MN 3{dup 5 -1 roll sub neg exch}repeat}bd/rgb2g{2 index .299 mul 2 index .587 mul add 1 index .114 mul add 4 1 roll pop pop pop}bd/WaldoColor_5 where{pop}{/SetRgb/setrgbcolor ld/GetRgb /currentrgbcolor ld/SetGry/setgray ld/GetGry/currentgray ld/SetRgb2 systemdict /setrgbcolor get def/GetRgb2 systemdict/currentrgbcolor get def/SetHsb systemdict/sethsbcolor get def/GetHsb systemdict/currenthsbcolor get def /rgb2hsb{SetRgb2 GetHsb}bd/hsb2rgb{3 -1 roll dup floor sub 3 1 roll SetHsb GetRgb2}bd/setcmykcolor where{pop/SetCmyk_5/setcmykcolor ld}{/SetCmyk_5{ cmyk2rgb SetRgb}bd}ifelse/currentcmykcolor where{pop/GetCmyk/currentcmykcolor ld}{/GetCmyk{GetRgb rgb2cmyk}bd}ifelse/setoverprint 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lt{$phei add}if/$ty xd}bd/@stb{pathbbox/$ury xd/$urx xd/$lly xd/$llx xd}bd/@ep{{cvx exec }forall}bd/@tp{@sv/$in true def 2 copy dup $lly le{/$in false def}if $phei sub $ury ge{/$in false def}if dup $urx ge{/$in false def}if $pwid add $llx le{/$in false def}if $in{@np 2 copy m $pwid 0 rl 0 $phei neg rl $pwid neg 0 rl 0 $phei rl clip @np $pn cvlit load aload pop 7 -1 roll 5 index sub 7 -1 roll 3 index sub Tl matrix currentmatrix/$ctm xd @ep pop pop pop pop}{pop pop}ifelse @rs}bd /@th{@sft 0 1 $tly 1 sub{dup $psx mul $tx add{dup $llx gt{$pwid sub}{exit} ifelse}loop exch $phei mul $ty exch sub 0 1 $tlx 1 sub{$pwid mul 3 copy 3 -1 roll add exch @tp pop}for pop pop}for}bd/@tv{@sft 0 1 $tlx 1 sub{dup $pwid mul $tx add exch $psy mul $ty exch sub{dup $ury lt{$phei add}{exit}ifelse}loop 0 1 $tly 1 sub{$phei mul 3 copy sub @tp pop}for pop pop}for}bd/$fm 0 def/wfill{1 $fm eq{fill}{eofill}ifelse}bd/wclip{1 $fm eq{clip}{eoclip}ifelse}bd/@pf{@gs $ctm setmatrix $pm concat @stb wclip Bburx Bbury $pm itransform/$tury xd/$turx xd Bbllx Bblly $pm itransform/$tlly xd/$tllx xd/$wid $turx $tllx sub def/$hei $tury $tlly sub def @gs $vectpat{1 0 0 0 0 _ $o @scc_5{wfill}if}{$t $c $m $y $k $n $o @scc_5{SepMode_5 0 eq $pfrg or{$tllx $tlly Tl $wid $hei scale <00> 8 1 false[8 0 0 1 0 0]{}imagemask}{/$bkg true def}ifelse}if}ifelse @gr $wid 0 gt $hei 0 gt and{$pn cvlit load aload pop/$pd xd 3 -1 roll sub/$phei xd exch sub /$pwid xd $wid $pwid div ceiling 1 add/$tlx xd $hei $phei div ceiling 1 add /$tly xd $psx 0 eq{@tv}{@th}ifelse}if @gr @np/$bkg false def}bd/@Pf{@sv SepMode_5 0 eq $Psc 0 ne or $ink_5 3 eq or{0 J 0 j[]0 d $t $c $m $y $k $n $o @scc_5 pop $ctm setmatrix 72 1000 div dup matrix scale dup concat dup Bburx exch Bbury exch itransform ceiling cvi/Bbury xd ceiling cvi/Bburx xd Bbllx exch Bblly exch itransform floor cvi/Bblly xd floor cvi/Bbllx xd $Prm aload pop $Psn load exec}{1 SetGry wfill}ifelse @rs @np}bd/F{matrix currentmatrix $sdf{$scf $sca $scp @ss}if $fil 1 eq{@pf}{$fil 2 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def}ifelse 1 eq{@gs $ctm setmatrix F @gr}if}ifelse @np/$ury xd/$urx xd /$lly xd/$llx xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul 8 div ceiling cvi string def $bkg $frg or{$SDF{$SCF $SCA $SCP @ss}if $llx $lly Tl $urx $llx sub $ury $lly sub scale $bkg{$t $c $m $y $k $n $o @scc_5 pop}if $wid $hei abs $bts 1 eq{$bkg}{$bts}ifelse[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/tcc load $bts 1 eq{imagemask}{image}ifelse $SDF{$dsf $dsa $dsp @ss}if}{$hei abs{tcc pop} repeat}ifelse @gr $ctm setmatrix}bd/@I{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd /$llx xd/$ncl xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def $ngx $llx $lly Tl $urx $llx sub $ury $lly sub scale $wid $hei abs $bts[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/@cc load false $ncl ColorImage $SDF{$dsf $dsa $dsp @ss}if @gr $ctm setmatrix}bd/COMP 0 def L2?{ /@I_2{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd/$llx xd/$ncl xd/$bts xd/$hei xd /$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def $ngx $ncl 1 eq{/DeviceGray}{$ncl 3 eq{/DeviceRGB}{/DeviceCMYK}ifelse}ifelse setcolorspace $llx $lly Tl $urx $llx sub $ury $lly sub scale 8 dict begin/ImageType 1 def /Width $wid def/Height $hei abs def/BitsPerComponent $bts def/Decode $ncl 1 eq {[0 1]}{$ncl 3 eq{[0 1 0 1 0 1]}{[0 1 0 1 0 1 0 1]}ifelse}ifelse def /ImageMatrix[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]def/DataSource currentfile/ASCII85Decode filter COMP 1 eq{/DCTDecode filter}{COMP 2 eq {/RunLengthDecode filter}if}ifelse def currentdict end image $SDF{$dsf $dsa $dsp @ss}if @gr $ctm setmatrix}bd}{/@I_2{}bd}ifelse/@B{@gs S @gr F}bd/@b{@cp @B }bd/@sep{CurrentInkName_5(Composite)eq{/$ink_5 -1 def}{CurrentInkName_5(Cyan) eq{/$ink_5 0 def}{CurrentInkName_5(Magenta)eq{/$ink_5 1 def}{CurrentInkName_5 (Yellow)eq{/$ink_5 2 def}{CurrentInkName_5(Black)eq{/$ink_5 3 def}{/$ink_5 4 def}ifelse}ifelse}ifelse}ifelse}ifelse}bd/@whi{@gs -72000 dup m -72000 72000 l 72000 dup l 72000 -72000 l @cp 1 SetGry fill @gr}bd/@neg{[{1 exch 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y(Ser\341)k(mostrado,)h(agora,)f(como)f(os)h (mo)m(vimen)m(tos)g(do)g(tip)s(o)f FE(shift)45 b FH(s\343o)36 b(a)m(v)-5 b(aliados.)53 b(Conforme)35 b(a)109 5361 y(descri\347\343o)h (geral)g(feita)g(na)g(se\347\343o)h(an)m(terior,)g(a)g(busca)g(lo)s (cal)e(com)h FE(shift)45 b FH(escolhe)38 b(a)e(melhor)f(p)s (osi\347\343o)109 5523 y(para)46 b(reinserir)f(cada)i(carro)f(da)g (solu\347\343o.)84 b(P)m(ara)47 b(facilitar)c(o)j(en)m(tendimen)m(to,)k (assume-se)d(que)g(a)109 5686 y(escolha)f(do)g(mo)m(vimen)m(to)f(\351)h (realizada)e(da)j(seguin)m(te)f(forma:)69 b(remo)m(v)m(e-se)48 b(o)d(carro)h(da)g(solu\347\343o)g(e)109 5848 y(a)m(v)-5 b(alia-se)38 b(qual)h(a)h(melhor)e(p)s(osi\347\343o)h(para)h (reinseri-lo.)63 b(Na)40 b(pr\341tica,)h(a)f(remo)s(\347\343o)f(do)h (carro)f(n\343o)h(\351)p eop %%Page: 24 38 24 37 bop 109 -28 a FB(5.3)60 b(Estruturas)32 b(de)e(dados)2718 b(24)p 109 9 3780 4 v 109 256 a FH(necess\341ria,)42 b(mas)e(isto)f(n\343o)h(altera)e(a)i(complexidade)f(total)f(da)i 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b(O)32 b(v)-5 b(alor)31 b(da)i(p)s(osi\347\343o)e(1)i(p)s(ermanece)f(o)h(mesmo.)p eop %%Page: 25 39 25 38 bop 109 -28 a FB(5.3)60 b(Estruturas)32 b(de)e(dados)2718 b(25)p 109 9 3780 4 v 799 1809 a currentpoint currentpoint translate 0.65704 0.65704 scale neg exch neg exch translate 799 1809 a @beginspecial 2 @llx 237 @lly 440 @urx 539 @ury 4380 @rwi @setspecial %%BeginDocument: shift_A.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 2 237 440 539 %%Creator: CorelDRAW 7 %%Title: %%CreationDate: Sun Mar 27 18:16:25 2005 %%DocumentProcessColors: Black %%DocumentSuppliedResources: (atend) %%EndComments %%BeginProlog /AutoFlatness true def /AutoSteps 0 def /CMYKMarks false def /UseLevel2 false def %Color profile: _DEFAULT.CCM - Gen. 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def/$bkg false def /SK 0 def/SM 0 def/SY 0 def/SC 0 def/$op false def matrix currentmatrix/$ctm xd /$ptm matrix def/$ttm matrix def/$stm matrix def/$ffpnt true def /CorelDrawReencodeVect[16#0/grave 16#5/breve 16#6/dotaccent 16#8/ring 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl 16#88/circumflex/perthousand/Scaron/guilsinglleft/OE 16#91/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash 16#98/tilde/trademark/scaron/guilsinglright/oe 16#9F/Ydieresis 16#A1/exclamdown/cent/sterling/currency/yen/brokenbar/section 16#a8/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/minus/registered/macron 16#b0/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered 16#b8/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown 16#c0/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla 16#c8/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis 16#d0/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply 16#d8/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls 16#e0/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla 16#e8/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis 16#f0/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide 16#f8/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis]def /L2?/languagelevel where{pop languagelevel 2 ge}{false}ifelse def /@BeginSysCorelDict{systemdict/Corel30Dict known{systemdict/Corel30Dict get exec}if}bd/@EndSysCorelDict{systemdict/Corel30Dict known{end}if}bd AutoFlatness {/@ifl{dup currentflat exch sub 10 gt{ ([Error: PathTooComplex; OffendingCommand: AnyPaintingOperator]\n)print flush @np exit}{currentflat 2 add setflat}ifelse}bd/@fill/fill ld/fill{currentflat{ {@fill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@eofill/eofill ld/eofill {currentflat{{@eofill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@clip /clip ld/clip{currentflat{{@clip}stopped{@ifl}{exit}ifelse}bind loop setflat} bd/@eoclip/eoclip ld/eoclip{currentflat{{@eoclip}stopped{@ifl}{exit}ifelse} bind loop setflat}bd/@stroke/stroke ld/stroke{currentflat{{@stroke}stopped {@ifl}{exit}ifelse}bind loop setflat}bd}if L2?{/@ssa{true setstrokeadjust}bd}{ /@ssa{}bd}ifelse/d/setdash ld/j/setlinejoin ld/J/setlinecap ld/M/setmiterlimit ld/w/setlinewidth ld/O{/$o xd}bd/R{/$O xd}bd/W/eoclip ld/c/curveto ld/C/c ld/l /lineto ld/L/l ld/rl/rlineto ld/m/moveto ld/n/newpath ld/N/newpath ld/P{11 rp} bd/u{}bd/U{}bd/A{pop}bd/q/@gs ld/Q/@gr ld/&{}bd/@j{@sv @np}bd/@J{@rs}bd/g{1 exch sub/$k xd/$c 0 def/$m 0 def/$y 0 def/$t 1 def/$n _ def/$fil 0 def}bd/G{1 sub neg/$K xd _ 1 0 0 0/$C xd/$M xd/$Y xd/$T xd/$N xd}bd/k{1 index type /stringtype eq{/$t xd/$n xd}{/$t 0 def/$n _ def}ifelse/$k xd/$y xd/$m xd/$c xd /$fil 0 def}bd/K{1 index type/stringtype eq{/$T xd/$N xd}{/$T 0 def/$N _ def} ifelse/$K xd/$Y xd/$M xd/$C xd}bd/x/k ld/X/K ld/sf{1 index type/stringtype eq{ /s1t xd/s1n xd}{/s1t 0 def/s1n _ def}ifelse/s1k xd/s1y xd/s1m xd/s1c xd}bd/i{ dup 0 ne{setflat}{pop}ifelse}bd/v{4 -2 roll 2 copy 6 -2 roll c}bd/V/v ld/y{2 copy c}bd/Y/y ld/@w{matrix rotate/$ptm xd matrix scale $ptm dup concatmatrix /$ptm xd 1 eq{$ptm exch dup concatmatrix/$ptm xd}if 1 w}bd/@g{1 eq dup/$sdf xd {/$scp xd/$sca xd/$scf xd}if}bd/@G{1 eq dup/$SDF xd{/$SCP xd/$SCA xd/$SCF xd} if}bd/@D{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if 3 copy exch $Scra add exch load SetScr/$dsp xd/$dsa xd/$dsf xd}bd/$ngx{$SDF{$SCF SepMode_5 0 eq{$SCA} {$dsa}ifelse $SCP @ss}if}bd/p{/$pm xd 7 rp/$pyf xd/$pxf xd/$pn xd/$fil 1 def} bd/@MN{2 copy le{pop}{exch pop}ifelse}bd/@MX{2 copy ge{pop}{exch pop}ifelse}bd /InRange{3 -1 roll @MN @MX}bd/@sqr{dup 0 rl dup 0 exch rl neg 0 rl @cp}bd /currentscale{1 0 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt 0 1 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt}bd/@unscale{}bd/wDstChck{2 1 roll dup 3 -1 roll eq{1 add}if}bd /@dot{dup mul exch dup mul add 1 exch sub}bd/@lin{exch pop abs 1 exch sub}bd /cmyk2rgb{3{dup 5 -1 roll add 1 exch sub dup 0 lt{pop 0}if exch}repeat pop}bd /rgb2cmyk{3{1 exch sub 3 1 roll}repeat 3 copy @MN @MN 3{dup 5 -1 roll sub neg exch}repeat}bd/rgb2g{2 index .299 mul 2 index .587 mul add 1 index .114 mul add 4 1 roll pop pop pop}bd/WaldoColor_5 where{pop}{/SetRgb/setrgbcolor ld/GetRgb /currentrgbcolor ld/SetGry/setgray ld/GetGry/currentgray ld/SetRgb2 systemdict /setrgbcolor get def/GetRgb2 systemdict/currentrgbcolor get def/SetHsb systemdict/sethsbcolor get def/GetHsb systemdict/currenthsbcolor get def /rgb2hsb{SetRgb2 GetHsb}bd/hsb2rgb{3 -1 roll dup floor sub 3 1 roll SetHsb GetRgb2}bd/setcmykcolor where{pop/SetCmyk_5/setcmykcolor ld}{/SetCmyk_5{ cmyk2rgb SetRgb}bd}ifelse/currentcmykcolor where{pop/GetCmyk/currentcmykcolor ld}{/GetCmyk{GetRgb rgb2cmyk}bd}ifelse/setoverprint where{pop}{/setoverprint{ /$op xd}bd}ifelse/currentoverprint where{pop}{/currentoverprint{$op}bd}ifelse /@tc_5{5 -1 roll dup 1 ge{pop}{4{dup 6 -1 roll mul exch}repeat pop}ifelse}bd /@trp{exch pop 5 1 roll @tc_5}bd/setprocesscolor_5{SepMode_5 0 eq{SetCmyk_5}{0 4 $ink_5 sub index exch pop 5 1 roll pop pop pop pop SepsColor true eq{$ink_5 3 gt{1 sub neg SetGry}{0 0 0 4 $ink_5 roll SetCmyk_5}ifelse}{1 sub neg SetGry} ifelse}ifelse}bd/findcmykcustomcolor where{pop}{/findcmykcustomcolor{5 array astore}bd}ifelse/setcustomcolor where{pop}{/setcustomcolor{exch aload pop SepMode_5 0 eq{pop @tc_5 setprocesscolor_5}{CurrentInkName_5 eq{4 index}{0} ifelse 6 1 roll 5 rp 1 sub neg SetGry}ifelse}bd}ifelse/@scc_5{dup type /booleantype eq{setoverprint}{1 eq setoverprint}ifelse dup _ eq{pop setprocesscolor_5 pop}{findcmykcustomcolor exch setcustomcolor}ifelse SepMode_5 0 eq{true}{GetGry 1 eq currentoverprint and not}ifelse}bd/colorimage where{pop /ColorImage{colorimage}def}{/ColorImage{/ncolors xd pop/dataaq xd{dataaq ncolors dup 3 eq{/$dat xd 0 1 $dat length 3 div 1 sub{dup 3 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length 3 idiv getinterval pop}{4 eq{/$dat xd 0 1 $dat length 4 div 1 sub{dup 4 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div $dat 4 index 3 add get 255 div cmyk2rgb rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length ncolors idiv getinterval}if}ifelse}image}bd }ifelse/setcmykcolor{1 5 1 roll _ currentoverprint @scc_5/$ffpnt xd}bd /currentcmykcolor{0 0 0 0}bd/setrgbcolor{rgb2cmyk setcmykcolor}bd /currentrgbcolor{currentcmykcolor cmyk2rgb}bd/sethsbcolor{hsb2rgb setrgbcolor} bd/currenthsbcolor{currentrgbcolor rgb2hsb}bd/setgray{dup dup setrgbcolor}bd /currentgray{currentrgbcolor rgb2g}bd}ifelse/WaldoColor_5 true def/@sft{$tllx $pxf add dup $tllx gt{$pwid sub}if/$tx xd $tury $pyf sub dup $tury lt{$phei add}if/$ty xd}bd/@stb{pathbbox/$ury xd/$urx xd/$lly xd/$llx xd}bd/@ep{{cvx exec }forall}bd/@tp{@sv/$in true def 2 copy dup $lly le{/$in false def}if $phei sub $ury ge{/$in false def}if dup $urx ge{/$in false def}if $pwid add $llx le{/$in false def}if $in{@np 2 copy m $pwid 0 rl 0 $phei neg rl $pwid neg 0 rl 0 $phei rl clip @np $pn cvlit load aload pop 7 -1 roll 5 index sub 7 -1 roll 3 index sub Tl matrix currentmatrix/$ctm xd @ep pop pop pop pop}{pop pop}ifelse @rs}bd /@th{@sft 0 1 $tly 1 sub{dup $psx mul $tx add{dup $llx gt{$pwid sub}{exit} ifelse}loop exch $phei mul $ty exch sub 0 1 $tlx 1 sub{$pwid mul 3 copy 3 -1 roll add exch @tp pop}for pop pop}for}bd/@tv{@sft 0 1 $tlx 1 sub{dup $pwid mul $tx add exch $psy mul $ty exch sub{dup $ury lt{$phei add}{exit}ifelse}loop 0 1 $tly 1 sub{$phei mul 3 copy sub @tp pop}for pop pop}for}bd/$fm 0 def/wfill{1 $fm eq{fill}{eofill}ifelse}bd/wclip{1 $fm eq{clip}{eoclip}ifelse}bd/@pf{@gs $ctm setmatrix $pm concat @stb wclip Bburx Bbury $pm itransform/$tury xd/$turx xd Bbllx Bblly $pm itransform/$tlly xd/$tllx xd/$wid $turx $tllx sub def/$hei $tury $tlly sub def @gs $vectpat{1 0 0 0 0 _ $o @scc_5{wfill}if}{$t $c $m $y $k $n $o @scc_5{SepMode_5 0 eq $pfrg or{$tllx $tlly Tl $wid $hei scale <00> 8 1 false[8 0 0 1 0 0]{}imagemask}{/$bkg true def}ifelse}if}ifelse @gr $wid 0 gt $hei 0 gt and{$pn cvlit load aload pop/$pd xd 3 -1 roll sub/$phei xd exch sub /$pwid xd $wid $pwid div ceiling 1 add/$tlx xd $hei $phei div ceiling 1 add /$tly xd $psx 0 eq{@tv}{@th}ifelse}if @gr @np/$bkg false def}bd/@Pf{@sv SepMode_5 0 eq $Psc 0 ne or $ink_5 3 eq or{0 J 0 j[]0 d $t $c $m $y $k $n $o @scc_5 pop $ctm setmatrix 72 1000 div dup matrix scale dup concat dup Bburx exch Bbury exch itransform ceiling cvi/Bbury xd ceiling cvi/Bburx xd Bbllx exch Bblly exch itransform floor cvi/Bblly xd floor cvi/Bbllx xd $Prm aload pop $Psn load exec}{1 SetGry wfill}ifelse @rs @np}bd/F{matrix currentmatrix $sdf{$scf $sca $scp @ss}if $fil 1 eq{@pf}{$fil 2 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def}ifelse 1 eq{@gs $ctm setmatrix F @gr}if}ifelse @np/$ury xd/$urx xd /$lly xd/$llx xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul 8 div ceiling cvi string def $bkg $frg or{$SDF{$SCF $SCA $SCP @ss}if $llx $lly Tl $urx $llx sub $ury $lly sub scale $bkg{$t $c $m $y $k $n $o @scc_5 pop}if $wid $hei abs $bts 1 eq{$bkg}{$bts}ifelse[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/tcc load $bts 1 eq{imagemask}{image}ifelse $SDF{$dsf $dsa $dsp @ss}if}{$hei abs{tcc pop} repeat}ifelse @gr $ctm setmatrix}bd/@I{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd /$llx xd/$ncl xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def $ngx $llx $lly Tl $urx $llx sub $ury $lly sub scale $wid $hei abs $bts[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/@cc load false $ncl ColorImage $SDF{$dsf $dsa $dsp @ss}if @gr $ctm setmatrix}bd/COMP 0 def L2?{ /@I_2{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd/$llx xd/$ncl xd/$bts xd/$hei xd /$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def $ngx $ncl 1 eq{/DeviceGray}{$ncl 3 eq{/DeviceRGB}{/DeviceCMYK}ifelse}ifelse setcolorspace $llx $lly Tl $urx $llx sub $ury $lly sub scale 8 dict begin/ImageType 1 def /Width $wid def/Height $hei abs def/BitsPerComponent $bts def/Decode $ncl 1 eq {[0 1]}{$ncl 3 eq{[0 1 0 1 0 1]}{[0 1 0 1 0 1 0 1]}ifelse}ifelse def /ImageMatrix[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]def/DataSource currentfile/ASCII85Decode filter COMP 1 eq{/DCTDecode filter}{COMP 2 eq {/RunLengthDecode filter}if}ifelse def currentdict end image $SDF{$dsf $dsa $dsp @ss}if @gr $ctm setmatrix}bd}{/@I_2{}bd}ifelse/@B{@gs S @gr F}bd/@b{@cp @B }bd/@sep{CurrentInkName_5(Composite)eq{/$ink_5 -1 def}{CurrentInkName_5(Cyan) eq{/$ink_5 0 def}{CurrentInkName_5(Magenta)eq{/$ink_5 1 def}{CurrentInkName_5 (Yellow)eq{/$ink_5 2 def}{CurrentInkName_5(Black)eq{/$ink_5 3 def}{/$ink_5 4 def}ifelse}ifelse}ifelse}ifelse}ifelse}bd/@whi{@gs -72000 dup m -72000 72000 l 72000 dup l 72000 -72000 l @cp 1 SetGry fill @gr}bd/@neg{[{1 exch 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%%EOF %%EndDocument @endspecial 799 1809 a currentpoint currentpoint translate 1 0.65704 div 1 0.65704 div scale neg exch neg exch translate 799 1809 a 616 2013 a FH(Figura)31 b(5.5:)43 b(A)m(tualiza\347\343o)31 b(do)h(v)m(etor)h(A)g(ap)s(\363s)f (a)h(remo)s(\347\343o)e(de)i(um)f(carro.)274 2406 y(Uma)40 b(v)m(ez)h(que)h(o)e(carro)g Fz(c)h FH(foi)e(remo)m(vido)g(da)i (solu\347\343o)e(e)i(os)g(v)m(etores)h Fz(A)e FH(atualizados,)h(os)g (cus-)109 2568 y(tos)d(dos)g(mo)m(vimen)m(tos)f(p)s(o)s(dem)g(ser)i(a)m (v)-5 b(aliados.)58 b(Seja)38 b Fz(shif)11 b(t)p FA(\()p Fz(\031)t(;)17 b(i;)g(j)6 b FA(\))38 b FH(o)g(mo)m(vimen)m(to)e(de)j (remo)m(v)m(er)f(o)109 2731 y(carro)f(da)h(p)s(osi\347\343o)f Fz(i)h FH(e)g(reinseri-lo)d(na)j(p)s(osi\347\343o)f Fz(j)44 b FH(da)37 b(solu\347\343o)g Fz(\031)t FH(.)60 b(A)37 b(a)m(v)-5 b(alia\347\343o)36 b(dos)i(mo)m(vimen)m(tos)109 2893 y(\351)f(baseada)g(na)g(seguin)m(te)g(id\351ia:)51 b(a)37 b(v)-5 b(aria\347\343o)35 b(no)i(custo)g(decorren)m(te)i(da)e (aplica\347\343o)e(do)i(mo)m(vimen)m(to)109 3056 y Fz(shif)11 b(t)p FA(\()p Fz(\031)t(;)17 b(i;)g(j)6 b FA(\))31 b FH(\351)h(calculada)e(apro)m(v)m(eitando-se)i(o)f(custo)h(do)g(mo)m (vimen)m(to)e Fz(shif)11 b(t)p FA(\()p Fz(\031)t(;)17 b(i;)g(j)26 b Fs(\000)20 b FA(1\))p FH(.)43 b(Dian)m(te)109 3218 y(disto,)37 b(os)h(mo)m(vimen)m(tos)e(p)s(o)s(dem)g(ser)i (rapidamen)m(te)e(a)m(v)-5 b(aliados,)36 b(com)h(exce\347\343o)h(do)f (primeiro)e(mo)m(vi-)109 3381 y(men)m(to)40 b Fz(shif)11 b(t)p FA(\()p Fz(\031)t(;)17 b(i;)g FA(1\))p FH(,)43 b(que)f(precisa)f(ser)h(calculado)d(indep)s(enden)m(temen)m(te)k(dos)f (demais.)68 b(Sab)s(e-se)109 3543 y(que)41 b(existem)g(exatamen)m(te)h Fz(n)f FH(p)s(osi\347\365)s(es)f(para)h(reinserir)f(o)h(carro)f Fz(c)p FH(,)j(uma)d(v)m(ez)i(que)g Fs(j)p Fz(\031)t Fs(j)f FA(=)h Fz(n)28 b Fs(\000)g FA(1)p FH(.)109 3706 y(Al\351m)35 b(disso,)k(em)d(rela\347\343o)g(a)h(uma)f(restri\347\343o)h(de)g (capacidade)g(de)g(raz\343o)g Fz(N)r(=P)14 b FH(,)38 b(a)e(inser\347\343o)h(de)h(um)109 3868 y(carro)g(na)g(p)s (osi\347\343o)g Fz(j)44 b FH(in)m(terfere)39 b(em)f Fz(P)51 b FH(seq\374\352ncias:)57 b Fz(P)40 b Fs(\000)26 b FA(1)39 b FH(seq\374\352ncias)h(s\343o)e(mo)s(di\034cadas)f(e)i(uma)109 4031 y(no)m(v)-5 b(a)32 b(seq\374\352ncia)i(\351)f(inserida)e(na)i(p)s (osi\347\343o)e Fz(j)6 b FH(.)274 4253 y(P)m(ara)44 b(uma)f (restri\347\343o)g(de)h(capacidade)f(de)i(raz\343o)e Fz(N)r(=P)14 b FH(,)46 b(a)d(v)-5 b(aria\347\343o)42 b(no)i(custo)g(\(n)m(\372mero)g(de)109 4415 y(viola\347\365)s(es)d (acrescen)m(tadas)j(ou)f(subtra\355das\))f(da)h(solu\347\343o)e (causada)i(p)s(ela)f(inser\347\343o)g(do)h(carro)f Fz(c)g FH(na)109 4578 y(primeira)c(p)s(osi\347\343o)i Fz(i)893 4593 y Fq(0)974 4578 y FH(do)h(dia)f(D)h(\351)h(dada)f(p)s(elo)f(n)m (\372mero)h(de)g(viola\347\365)s(es)f(desta)i(restri\347\343o)e(con)m (tidas)109 4740 y(na)e(no)m(v)-5 b(a)39 b(seq\374\352ncia)h(inserida)e 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b(o)p FA(\))22 b Fs(\000)g Fz(r)s FA(\()p Fz(c)2357 5484 y Ft(k)2394 5495 y Fn(i)2416 5510 y Fo(0)2450 5495 y(+)p Fn(P)8 b Fm(\000)p Fo(1)2631 5469 y Fz(;)17 b(o)p FA(\))27 b Fz(>)g(N)10 b FA(;)1321 5631 y(0)p FH(,)33 b(caso)g(con)m(tr\341rio.)109 5857 y(Ou)j(seja,)j(o)d(n)m(\372mero)h(de)g(carros)g(asso)s(ciados)f (\340)h(restri\347\343o)f(na)h(no)m(v)-5 b(a)36 b(seq\374\352ncia,)j (que)f(ser\341)f(inserida)p eop %%Page: 26 40 26 39 bop 109 -28 a FB(5.3)60 b(Estruturas)32 b(de)e(dados)2718 b(26)p 109 9 3780 4 v 109 256 a FH(na)31 b(p)s(osi\347\343o)f Fz(i)619 271 y Fq(0)659 256 y FH(,)h(\351)g(o)g(v)-5 b(alor)30 b(corresp)s(onden)m(te)j(\340)e(seq\374\352ncia)h(que)g (come\347a)f(atualmen)m(te)f(nesta)i(p)s(osi\347\343o)109 418 y(acrescido)h(de)h(1,)f(se)i(o)e(no)m(v)m(o)h(carro)f(est\341)h (asso)s(ciado)e(\340)h(restri\347\343o,)g(e)h(subtra\355do)f(de)h(1,)f (se)h(o)f(carro)g(da)109 581 y(p)s(osi\347\343o)i Fz(i)490 596 y Fq(0)554 581 y FA(+)25 b Fz(P)38 b Fs(\000)25 b FA(1)p FH(,)37 b(que)g(n\343o)f(far\341)f(parte)i(da)f(no)m(v)-5 b(a)36 b(seq\374\352ncia,)i(est\341)f(asso)s(ciado)e(\340)h (restri\347\343o.)54 b(O)109 743 y(n)m(\372mero)38 b(de)g (viola\347\365)s(es)f(desta)i(restri\347\343o)e(na)h(no)m(v)-5 b(a)38 b(seq\374\352ncia)h(\351)g(calculado)d(como)i(an)m(teriormen)m (te:)109 906 y(ele)h(\351)h(dado)f(p)s(ela)g(diferen\347a)g(do)g(n)m (\372mero)h(de)g(carros)g(asso)s(ciados)f(\340)g(restri\347\343o)g(na)g (seq\374\352ncia)i(p)s(elo)109 1068 y(n)m(umerador)32 b(da)g(restri\347\343o,)h(se)g(a)f(diferen\347a)h(for)f(p)s(ositiv)-5 b(a;)30 b(e)j(zero,)g(caso)g(con)m(tr\341rio.)274 1290 y(A)g(v)-5 b(aria\347\343o)31 b(no)h(custo)h(decorren)m(te)h(das)f (seq\374\352ncias)h(mo)s(di\034cadas)e(\351)h(dada)f(p)s(or:)703 1686 y FA(\001)784 1701 y Fq(2)851 1686 y FA(=)1077 1561 y Ft(i)1101 1570 y Fo(0)1135 1561 y Fl(\000)p Fq(1)1079 1591 y Fr(X)955 1807 y Ft(i)p Fq(=)p Ft(i)1058 1816 y Fo(0)1092 1807 y Fl(\000)p Fq(\()p Ft(P)10 b Fl(\000)p Fq(1\))1364 1422 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Fs(\000)34 b FA(\()p Fz(P)46 b Fs(\000)34 b FA(1\))p Fz(;)17 b(:)g(:)g(:)e(;)i(i)3172 2259 y Fq(0)3245 2244 y Fs(\000)33 b FA(1)p FH(,)53 b(o)48 b(carro)g Fz(c)109 2406 y FH(en)m(tra)37 b(e)h(o)f(carro)f(da)h(p)s(osi\347\343o)g Fz(i)25 b FA(+)g Fz(P)39 b Fs(\000)26 b FA(1)37 b FH(\351)g(deslo)s (cado)g(uma)f(p)s(osi\347\343o)g(para)h(a)g(direita,)g(saindo)f(da)109 2569 y(seq\374\352ncia.)51 b(Com)34 b(isto,)h(o)g(mo)m(vimen)m(to)e (causa)i(uma)f(viola\347\343o)f(a)i(mais)e(da)i(restri\347\343o,)g(se)h (o)e(n)m(\372mero)109 2731 y(de)i(carros)f(asso)s(ciados)h(\340)f (restri\347\343o)g(na)h(seq\374\352ncia)h(aumen)m(ta)e(e)h(este)g(n)m (\372mero)g(era)f(maior)f(ou)h(igual)109 2894 y(ao)40 b(n)m(umerador)g(da)h(restri\347\343o;)j(uma)c(viola\347\343o)e(a)i (menos,)j(se)e(o)g(n)m(\372mero)f(de)h(carros)g(asso)s(ciados)f(\340) 109 3056 y(restri\347\343o)30 b(dimin)m(ui)e(e)k(esta)f (seq\374\352ncia)h(viola)m(v)-5 b(a)30 b(a)g(restri\347\343o;)h(e)h (n\343o)e(altera)g(o)h(n)m(\372mero)g(de)g(viola\347\365)s(es,)109 3219 y(caso)i(con)m(tr\341rio.)45 b(A)33 b(v)-5 b(aria\347\343o)32 b(total)g(no)h(custo)h(da)f(solu\347\343o)g(causada)g(p)s(ela)g (inser\347\343o)g(do)g(carro)g Fz(c)g FH(na)109 3381 y(primeira)d(p)s(osi\347\343o)h Fz(i)876 3396 y Fq(0)949 3381 y FH(da)h(solu\347\343o)g(\351)h(dada)f(p)s(or)g FA(\001)c(=)g(\001)2210 3396 y Fq(1)2272 3381 y FA(+)22 b(\001)2451 3396 y Fq(2)2490 3381 y FH(.)274 3603 y(A)30 b(partir)e(do)i(custo)g(da)g(inser\347\343o)g(na)f(primeira)f(p)s (osi\347\343o,)h(p)s(o)s(de-se,)i(en)m(t\343o,)f(calcular)e(o)i(custo)g (da)109 3765 y(inser\347\343o)37 b(nas)g(demais)g(p)s(osi\347\365)s (es,)h(que)g(tam)m(b)s(\351m)e(\351)h(dado)g(p)s(or)g FA(\001)f(=)g(\001)2794 3780 y Fq(1)2859 3765 y FA(+)25 b(\001)3041 3780 y Fq(2)3080 3765 y FH(,)39 b(onde)f FA(\001)3465 3780 y Fq(1)3541 3765 y FH(tam)m(b)s(\351m)109 3928 y(corresp)s(onde)k(ao)f(custo)g(do)g(no)m(v)-5 b(a)41 b(seq\374\352ncia)i(inserida)d(e)h(\351)h(calculado)d(como)i(an)m (teriormen)m(te.)68 b(O)109 4090 y(v)-5 b(alor)27 b(de)j FA(\001)554 4105 y Fq(2)623 4090 y FH(\(v)-5 b(aria\347\343o)27 b(de)j(custo)g(nas)f(seq\374\352ncias)i(mo)s(di\034cadas\))d(para)h(a)g (inser\347\343o)g(na)g(p)s(osi\347\343o)f Fz(j)35 b FH(\351)109 4253 y(calculado)c(a)h(partir)g(do)g(v)-5 b(alor)31 b(de)j FA(\001)1483 4268 y Fq(2)1555 4253 y FH(obtido)d(para)i(a)f (inser\347\343o)h(na)f(p)s(osi\347\343o)g Fz(j)c Fs(\000)23 b FA(1)p FH(.)43 b(F)-8 b(ormalmen)m(te,)109 4415 y(o)32 b(v)-5 b(alor)31 b(de)i FA(\001)642 4430 y Fq(2)714 4415 y FH(para)f(inser\347\343o)h(do)f(carro)h Fz(c)f FH(na)g(p)s (osi\347\343o)g Fz(j)6 b FH(,)33 b Fz(j)g FA(=)28 b Fz(i)2566 4430 y Fq(0)2628 4415 y FA(+)22 b(1)p Fz(;)17 b(:)g(:)g(:)e(;)i(n)p FH(,)33 b(\351)g(dado)f(p)s(or:)1498 4677 y FA(\001)1579 4692 y Fq(2)1646 4677 y FA(=)c(\001)1831 4692 y Fq(2)1893 4677 y Fs(\000)22 b Fz(\016)2035 4692 y Ft(j)t Fl(\000)p Ft(P)2204 4677 y FA(+)g Fz(\016)2345 4692 y Ft(j)t Fl(\000)p Fq(1)2472 4677 y Fz(;)695 5082 y FH(onde)33 b Fz(\016)971 5097 y Ft(j)t Fl(\000)p Ft(P)1145 5082 y FA(=)1248 4818 y Fr(8)1248 4908 y(>)1248 4938 y(>)1248 4967 y(<)1248 5147 y(>)1248 5177 y(>)1248 5206 y(:)1378 4927 y Fs(\000)p FA(1)p Fz(;)84 b FH(se)33 b Fz(r)s FA(\()p Fz(c;)17 b(o)p FA(\))27 b Fz(<)g(r)s FA(\()p Fz(c)2242 4942 y Ft(k)2279 4952 y Fn(j)s Fm(\000)p Fo(1)2394 4927 y Fz(;)17 b(o)p FA(\))32 b FH(e)h Fz(A)p FA([)p Fz(j)28 b Fs(\000)23 b Fz(P)14 b FA(])27 b Fz(>)g(N)10 b FA(;)1379 5090 y(+1)p Fz(;)84 b FH(se)33 b Fz(r)s FA(\()p Fz(c;)17 b(o)p FA(\))27 b Fz(>)g(r)s FA(\()p Fz(c)2242 5105 y Ft(k)2279 5115 y Fn(j)s Fm(\000)p Fo(1)2394 5090 y Fz(;)17 b(o)p FA(\))32 b FH(e)h Fz(A)p FA([)p Fz(j)28 b Fs(\000)23 b Fz(P)14 b FA(])27 b Fs(\025)h Fz(N)10 b FA(;)1417 5252 y(0)p Fz(;)122 b FH(caso)32 b(con)m(tr\341rio.)750 5632 y(e)h Fz(\016)869 5647 y Ft(j)t Fl(\000)p Fq(1)1024 5632 y FA(=)1127 5368 y Fr(8)1127 5457 y(>)1127 5487 y(>)1127 5517 y(<)1127 5697 y(>)1127 5726 y(>)1127 5756 y(:)1257 5477 y Fs(\000)p FA(1)p Fz(;)84 b FH(se)33 b Fz(r)s FA(\()p Fz(c;)17 b(o)p FA(\))27 b Fz(<)g(r)s FA(\()p Fz(c)2121 5492 y Ft(k)2158 5503 y Fn(j)s Fo(+)p Fn(P)8 b Fm(\000)p Fo(2)2366 5477 y Fz(;)17 b(o)p FA(\))32 b FH(e)h Fz(A)p FA([)p Fz(j)28 b Fs(\000)23 b FA(1])28 b Fz(>)f(N)10 b FA(;)1258 5639 y(+1)p Fz(;)84 b FH(se)33 b Fz(r)s FA(\()p Fz(c;)17 b(o)p FA(\))27 b Fz(>)g(r)s FA(\()p Fz(c)2121 5654 y Ft(k)2158 5665 y Fn(j)s Fo(+)p Fn(P)8 b Fm(\000)p Fo(2)2366 5639 y Fz(;)17 b(o)p FA(\))32 b FH(e)h Fz(A)p FA([)p Fz(j)28 b Fs(\000)23 b FA(1])28 b Fs(\025)g Fz(N)10 b FA(;)1296 5802 y(0)p Fz(;)122 b FH(caso)32 b(con)m(tr\341rio.)p eop %%Page: 27 41 27 40 bop 109 -28 a FB(5.4)60 b(Complexidade)33 b(assin)m(t\363tica) 2509 b(27)p 109 9 3780 4 v 274 256 a FH(Em)m(b)s(ora)32 b(o)g(v)-5 b(alor)31 b(de)i FA(\001)1177 271 y Fq(2)1249 256 y FH(para)f(as)g(p)s(osi\347\365)s(es)h Fz(j)g FA(=)28 b Fz(i)2181 271 y Fq(0)2242 256 y FA(+)22 b(1)p Fz(;)17 b(:)g(:)g(:)f(;)h(n)32 b FH(p)s(ossa)h(ser)g(obtido)e(de)i(maneira)109 418 y(igual)25 b(ao)j(da)f(p)s(osi\347\343o)g Fz(i)971 433 y Fq(0)1011 418 y FH(,)i(ele)e(\351)h(calculado)f(realizando)f (menos)i(op)s(era\347\365)s(es.)42 b(A)m(o)28 b(in)m(v)m(\351s)h(de)f (se)h(calcular)109 581 y(a)24 b(v)-5 b(aria\347\343o)24 b(em)h(cada)g(uma)f(das)h Fz(P)20 b Fs(\000)7 b FA(1)25 b FH(seq\374\352ncias)i(mo)s(di\034cadas,)e(atualiza-se)f(o)g(v)-5 b(alor)24 b(de)i FA(\001)3553 596 y Fq(2)3617 581 y FH(obtido)109 743 y(para)34 b(a)g(p)s(osi\347\343o)f Fz(j)c Fs(\000)24 b FA(1)p FH(.)49 b(Retira-se)34 b(de)g FA(\001)1685 758 y Fq(2)1759 743 y FH(o)h(v)-5 b(alor)32 b Fz(\016)2128 758 y Ft(j)t Fl(\000)p Ft(P)2275 743 y FH(,)j(que)g(corresp)s(onde)g (\340)f(v)-5 b(aria\347\343o)33 b(no)i(custo)109 906 y(da)30 b(primeira)e(seq\374\352ncia)k(mo)s(di\034cada)c(\(p)s (osi\347\343o)i Fz(j)23 b Fs(\000)c Fz(P)14 b FH(\))30 b(em)g(rela\347\343o)f(\340)h(inser\347\343o)g(na)h(p)s(osi\347\343o)e Fz(j)24 b Fs(\000)18 b FA(1)p FH(,)109 1068 y(que)40 b(n\343o)g(mais)e(ser\341)i(afetada)f(quando)h Fz(c)g FH(for)f(inserido)g(em)g Fz(j)6 b FH(.)65 b(Al\351m)38 b(disso,)k(adiciona-se)c(a)h FA(\001)3760 1083 y Fq(2)3839 1068 y FH(o)109 1231 y(v)-5 b(alor)31 b Fz(\016)393 1246 y Ft(j)t Fl(\000)p Fq(1)520 1231 y FH(,)j(que)g(corresp)s(onde)g(\340)f (v)-5 b(aria\347\343o)31 b(no)i(custo)h(da)f(\372ltima)e (seq\374\352ncia)j(mo)s(di\034cada)d(\(p)s(osi\347\343o)109 1393 y Fz(j)g Fs(\000)26 b FA(1)p FH(\))38 b(em)f(rela\347\343o)g(\340) g(inser\347\343o)h(na)f(p)s(osi\347\343o)g Fz(j)6 b FH(,)39 b(que)g(n\343o)e(foi)f(con)m(tabilizada)g(para)h(a)h(inser\347\343o)f (na)109 1556 y(p)s(osi\347\343o)31 b Fz(j)d Fs(\000)23 b FA(1)p FH(.)109 1947 y Fx(5.4)155 b(Complexidade)53 b(assin)l(t\363tica)274 2268 y FH(Com)46 b(base)h(nas)g(estruturas)h (de)f(dados)f(descritas)h(na)g(se\347\343o)g(an)m(terior,)i(p)s(o)s (de-se)e(analisar)d(a)109 2430 y(complexidade)26 b(assin)m(t\363tica)g (das)h(busca)h(lo)s(cais)d(desen)m(v)m(olvidas,)30 b(ou)c(seja,)j(como) d(elas)h(se)g(comp)s(ortam)109 2593 y(em)32 b(rela\347\343o)f(ao)h (temp)s(o)g(computacional)e(exigido)h(em)i(fun\347\343o)f(do)h(tamanho) e(da)h(en)m(trada.)274 2814 y(Primeiramen)m(te,)d(analisa-se)g(a)h (busca)h(lo)s(cal)d(com)i(mo)m(vimen)m(tos)f FE(swap)p FH(.)42 b(Sejam)30 b Fz(n)g FH(o)g(n)m(\372mero)h(de)109 2977 y(carros)36 b(na)h(solu\347\343o,)g Fz(m)g FH(o)f(n)m(\372mero)h (de)g(restri\347\365)s(es)g(de)g(capacidade)g(e)p 2762 2897 77 4 v 37 w Fz(P)50 b FH(o)36 b(denominador)g(m\341ximo)109 3139 y(den)m(tre)47 b(to)s(das)f(as)g(restri\347\365)s(es.)84 b(A)46 b(complexidade)f(da)g(a)m(v)-5 b(alia\347\343o)44 b(de)j(um)e(mo)m(vimen)m(to)f(demanda)109 3302 y(temp)s(o)h Fz(O)s FA(\()p Fz(m)p FA(\))p FH(,)j(uma)d(v)m(ez)i(que)g(ela)e(\351)h (feita)e(atra)m(v)m(\351s)j(das)f(f\363rm)m(ulas)e(dadas)i(an)m (teriormen)m(te)g(para)109 3464 y(cada)38 b(uma)f(das)h(restri\347\365) s(es.)59 b(A)38 b(aplica\347\343o)e(do)i(mo)m(vimen)m(to)e(na)i (solu\347\343o)f(demanda)h(a)f(atualiza\347\343o)109 3627 y(das)47 b(estruturas)h(de)g(dados)f(corresp)s(onden)m(tes.)90 b(P)m(ara)47 b(atualizar)e(o)i(v)m(etor)h Fz(A)f FH(de)g(uma)g (restri\347\343o)109 3789 y(de)g(capacidade)f(de)h(raz\343o)f Fz(N)r(=P)14 b FH(,)49 b(dev)m(e-se)f(atualizar)c(exatamen)m(te)j Fz(P)60 b FH(p)s(osi\347\365)s(es)46 b(do)h(v)m(etor)g(para)109 3952 y(cada)h(um)h(dos)g(carros)g(tro)s(cados,)k(corresp)s(ondendo)d(a) e(cada)h(uma)f(das)h(seq\374\352ncias)i(a)d(que)i(eles)109 4114 y(p)s(ertencem.)72 b(Assim,)43 b(a)f(atualiza\347\343o)d(dos)k(v)m (etores)g Fz(A)f FH(de)g(to)s(das)g(as)g(restri\347\365)s(es)g(resulta) g(em)f(uma)109 4277 y(complexidade)36 b Fz(O)s FA(\()p 839 4197 V Fz(P)12 b(:m)p FA(\))p FH(,)39 b(p)s(ois)d Fz(P)48 b Fs(\024)p 1562 4197 V 36 w Fz(P)13 b FH(.)57 b(A)37 b(atualiza\347\343o)d(dos)k(v)m(etores)g Fz(B)k FH(e)37 b Fz(C)44 b FH(de)38 b(uma)e(restri\347\343o)109 4439 y(de)30 b(capacidade)g(de)g(raz\343o)g Fz(N)r(=P)44 b FH(decorren)m(te)31 b(da)f(tro)s(ca)f(dos)i(carros)f(das)g(p)s (osi\347\365)s(es)g Fz(i)g FH(e)g Fz(j)36 b FH(implica,)28 b(de)109 4602 y(forma)35 b(geral,)i(na)g(altera\347\343o)e(de)j(to)s (das)e(as)h(p)s(osi\347\365)s(es)g(dos)g(v)m(etores)i(a)e(partir)e(da)i (p)s(osi\347\343o)f Fz(i)25 b Fs(\000)h Fz(P)14 b FH(,)37 b(se)109 4764 y Fz(i)28 b(<)f(j)6 b FH(,)30 b(ou)f Fz(j)21 b Fs(\000)15 b Fz(P)f FH(,)29 b(caso)g(con)m(tr\341rio.)42 b(Esta)29 b(atualiza\347\343o)e(\351)i(necess\341ria)h(p)s(ois)e(os)h (v)-5 b(alores)28 b(armazenados)109 4927 y(nestes)37 b(v)m(etores)h(corresp)s(ondem)e(a)g(v)-5 b(alores)35 b(que)i(s\343o)f(acum)m(ulados)f(desde)i(o)f(in\355cio)d(da)j (solu\347\343o)f(e)h(a)109 5089 y(altera\347\343o)28 b(de)i(qualquer)f(p)s(osi\347\343o)g(deste)i(v)m(etor)f (in\035uenciar\341)e(em)h(to)s(das)g(as)h(p)s(osi\347\365)s(es)f (subseq\374en)m(tes.)109 5252 y(Desta)45 b(forma,)i(a)d (atualiza\347\343o)f(dos)i(v)m(etores)i Fz(B)j FH(e)45 b Fz(C)51 b FH(de)46 b(to)s(das)e(as)h(restri\347\365)s(es)h(demanda)e (temp)s(o)109 5415 y(computacional)29 b Fz(O)s FA(\()p Fz(n:m)p FA(\))p FH(,)j(o)g(que)g(implica)d(que)k(to)s(da)e(a)h (atualiza\347\343o)d(necess\341ria)k(ap)s(\363s)e(a)h(aplica\347\343o) 109 5577 y(de)d(um)g(mo)m(vimen)m(to)f(\351)h Fz(O)s FA(\()p 1086 5497 V Fz(P)13 b(:m)p FA(\))i(+)g Fz(O)s FA(\()p Fz(n:m)p FA(\))28 b(=)g Fz(O)s FA(\()p Fz(n:m)p FA(\))p FH(,)h(p)s(ois)p 2455 5497 V 29 w Fz(P)41 b Fs(\024)28 b Fz(n)p FH(.)43 b(P)m(ara)29 b(\034nalizar)e(a)i(an\341lise)f(da)109 5740 y(complexidade)36 b(de)i(temp)s(o)f(da)h(busca)g(lo)s(cal,)f(\351) h(necess\341rio)g(sab)s(er)h(a)e(quan)m(tidade)h(de)g(mo)m(vimen)m(tos) 109 5902 y(da)27 b(vizinhan\347a)g FE(swap)33 b FH(de)28 b(uma)f(solu\347\343o.)41 b(T)-8 b(ro)s(cando-se)28 b(cada)g(carro)f (com)g(os)h(demais)f(e)h(eliminando-)p eop %%Page: 28 42 28 41 bop 109 -28 a FB(5.4)60 b(Complexidade)33 b(assin)m(t\363tica) 2509 b(28)p 109 9 3780 4 v 109 256 a FH(se)48 b(os)h(mo)m(vimen)m(tos)e (rep)s(etidos,)52 b(o)47 b(n)m(\372mero)h(de)h(mo)m(vimen)m(tos)e(ou)h (solu\347\365)s(es)g(vizinhas)f(\351)i(igual)c(a)109 418 y Fz(n)p FA(\()p Fz(n)6 b Fs(\000)g FA(1\))p Fz(=)p FA(2)p FH(,)26 b(o)f(que)g(\351)h Fz(O)s FA(\()p Fz(n)1080 382 y Fq(2)1118 418 y FA(\))p FH(.)41 b(En)m(t\343o,)27 b(realizam-se)22 b Fz(O)s FA(\()p Fz(n)2201 382 y Fq(2)2240 418 y FA(\))j FH(a)m(v)-5 b(alia\347\365)s(es,)25 b(uma)e(para)i(cada)g (mo)m(vimen)m(to)109 581 y(da)34 b(vizinhan\347a,)h(enquan)m(to)h(que)g (s\343o)f(executadas)h Fz(O)s FA(\()p Fz(n)p FA(\))e FH(atualiza\347\365)s(es,)g(uma)g(para)h(cada)g(carro)f(da)109 743 y(solu\347\343o.)44 b(Dian)m(te)33 b(disto,)g(tem-se)g(que)h(a)f (complexidade)f(de)h(temp)s(o)g(exigida)e(p)s(or)i(uma)f (itera\347\343o)g(da)109 906 y(busca)h(lo)s(cal)d(\351)j Fz(O)s FA(\()p Fz(n)860 869 y Fq(2)899 906 y FA(\))p Fz(:O)s FA(\()p Fz(m)p FA(\))22 b(+)g Fz(O)s FA(\()p Fz(n)p FA(\))p Fz(:O)s FA(\()p Fz(n:m)p FA(\))27 b(=)g Fz(O)s FA(\()p Fz(n)2190 869 y Fq(2)2229 906 y Fz(:m)p FA(\))p FH(.)274 1127 y(Uma)j(implemen)m(ta\347\343o)f(mais)g(ing\352n) m(ua)i(desta)g(busca)h(lo)s(cal)d(lev)-5 b(aria)29 b(a)i(um)f(temp)s(o) g(computacio-)109 1290 y(nal)23 b(maior,)h(decorren)m(te)i(da)f (aus\352ncia)g(das)g(estruturas)g(de)g(dados)g(auxiliares.)39 b(Os)25 b(v)m(etores)h(utilizados)109 1452 y(guardam)35 b(informa\347\365)s(es)f(referen)m(tes)k(a)e(seq\374\352ncias)h(de)g (carros)f(e)g(a)g(in)m(terv)-5 b(alos)35 b(de)i(seq\374\352ncias)g (con-)109 1615 y(secutiv)-5 b(as.)71 b(No)42 b(en)m(tan)m(to,)i(tais)d (informa\347\365)s(es)f(lev)-5 b(am)41 b(temp)s(o)f(prop)s(orcional)g (ao)h(denominador)f(da)109 1777 y(restri\347\343o)28 b(considerada)g(para)g(serem)g(calculadas.)41 b(P)m(ortan)m(to,)30 b(o)e(temp)s(o)f(necess\341rio)i(para)f(se)h(a)m(v)-5 b(aliar)109 1940 y(cada)32 b(mo)m(vimen)m(to,)f(sem)i(a)f (utiliza\347\343o)e(de)j(tais)f(v)m(etores,)i(teria)e(adicionalmen)m (te)e(um)i(fator)p 3554 1860 77 4 v 32 w Fz(P)13 b FH(.)274 2161 y(Em)45 b(rela\347\343o)g(\340)g(busca)i(com)e(mo)m(vimen)m(tos)g FE(shift)p FH(,)j(observ)-5 b(a-se,)50 b(a)c(partir)e(da)i(se\347\343o) g(an)m(terior,)109 2324 y(que)c(o)g(temp)s(o)f(para)g(inserir)g(um)g (carro)g(na)h(primeira)d(p)s(osi\347\343o)i(\351)h Fz(O)s FA(\()p 2773 2244 V Fz(P)13 b FA(\))41 b FH(para)h(uma)e (restri\347\343o)i(de)109 2486 y(capacidade,)37 b(p)s(ois)e(precisa-se) i(a)m(v)-5 b(aliar)34 b(exatamen)m(te)j Fz(P)50 b FH(seq\374\352ncias) 38 b(em)e(rela\347\343o)f(a)h(uma)g(restri\347\343o)109 2649 y(de)44 b(capacidade)f(de)h(raz\343o)f Fz(N)r(=P)58 b FH(e)44 b Fz(P)59 b Fs(\024)p 1754 2569 V 47 w Fz(P)14 b FH(.)76 b(No)44 b(en)m(tan)m(to,)j(para)c(se)i(a)m(v)-5 b(aliar)41 b(as)j(demais)e Fz(n)30 b Fs(\000)g FA(1)109 2811 y FH(p)s(osi\347\365)s(es,)38 b(o)g(temp)s(o)e(computacional)g (exigido)g(\351)i(constan)m(te,)i(ou)d(seja,)i Fz(O)s FA(\(1\))e FH(para)g(cada)h(restri\347\343o)109 2974 y(de)d(capacidade.)51 b(Logo,)35 b(a)g(a)m(v)-5 b(alia\347\343o)33 b(dos)i Fz(n)g FH(mo)m(vimen)m(tos)f(p)s(oss\355v)m(eis)i(para)e(um)h (carro)g(lev)-5 b(a)34 b(temp)s(o)109 3136 y Fz(O)s FA(\()p 225 3056 V Fz(P)12 b FA(\))c(+)g(\()p Fz(n)g Fs(\000)g FA(1\))p Fz(:O)s FA(\(1\))27 b(=)g Fz(O)s FA(\()p Fz(n)p FA(\))p FH(,)g(p)s(ois)p 1528 3056 V 24 w Fz(P)42 b Fs(\024)28 b Fz(n)p FH(.)41 b(P)m(o)s(de-se)27 b(observ)-5 b(ar)26 b(que,)i(em)m(b)s(ora)c(esta)i(op)s(era\347\343o)f(n\343o)109 3299 y(precise)33 b(ser)g(feita)f(na)g(pr\341tica,)g(a)h(remo)s (\347\343o)e(de)i(um)f(carro)h(an)m(tes)g(da)g(a)m(v)-5 b(alia\347\343o)30 b(dos)j Fz(n)g FH(mo)m(vimen)m(tos)109 3461 y(n\343o)27 b(altera)f(a)h(complexidade)f(de)i(temp)s(o)f(da)g (busca,)i(uma)e(v)m(ez)i(que)f(isto)f(tam)m(b)s(\351m)f(lev)-5 b(a)26 b(temp)s(o)h Fz(O)s FA(\()p Fz(n)p FA(\))109 3624 y FH(e)41 b Fz(O)s FA(\()p Fz(n)p FA(\))28 b(+)g Fz(O)s FA(\()p Fz(n)p FA(\))42 b(=)h Fz(O)s FA(\()p Fz(n)p FA(\))p FH(.)70 b(Como)41 b(o)g(n)m(\372mero)g(de)h(restri\347\365)s(es)g(de)g (capacidade)g(\351)f Fz(m)h FH(e)g(o)f(n)m(\372mero)109 3786 y(de)36 b(carros)h(na)f(solu\347\343o)g(\351)g Fz(n)p FH(,)i(o)e(temp)s(o)g(total)e(necess\341rio)j(para)f(a)m(v)-5 b(aliar)34 b(to)s(dos)i(os)h(mo)m(vimen)m(tos)e(na)109 3949 y(busca)d(\351)g Fz(O)s FA(\()p Fz(n)628 3913 y Fq(2)667 3949 y Fz(:m)p FA(\))p FH(.)44 b(A)m(o)32 b(se)g(aplicar)e(um) h(mo)m(vimen)m(to)g(na)g(solu\347\343o,)g(precisa-se)i(atualizar)c(o)j (v)m(etor)g Fz(A)109 4112 y FH(de)d(cada)f(restri\347\343o)g(de)h (capacidade.)42 b(P)m(ara)29 b(atualizar)d(o)j(v)m(etor)g Fz(A)f FH(de)h(uma)f(restri\347\343o)g(de)h(capacidade)109 4274 y(de)e(raz\343o)g Fz(N)r(=P)41 b FH(quando)27 b(aplica-se)f(um)g (mo)m(vimen)m(to)g Fz(shif)11 b(t)p FA(\()p Fz(\031)t(;)17 b(i;)g(j)6 b FA(\))p FH(,)28 b(dev)m(e-se)h(atualizar)c(as)i(p)s (osi\347\365)s(es)109 4437 y(corresp)s(onden)m(tes)k(\340s)e (seq\374\352ncias)i(que)f(sofreram)e(altera\347\343o,)g(o)h(que)h(\351) f Fz(O)s FA(\()p 2862 4357 V Fz(P)13 b FA(\))p FH(.)42 b(Al\351m)28 b(disso,)i(precisa-)109 4599 y(se)44 b(deslo)s(car)g(uma)f (p)s(osi\347\343o)g(para)g(a)h(esquerda)h(to)s(das)f(os)g(v)-5 b(alores)43 b(nas)h(p)s(osi\347\365)s(es)g(en)m(tre)g Fz(i)h FH(e)f Fz(j)6 b FH(,)46 b(se)109 4762 y Fz(i)f(<)g(j)6 b FH(,)45 b(ou)e(uma)f(p)s(osi\347\343o)g(para)g(a)h(direita,)h(se)f Fz(i)j(>)f(j)6 b FH(,)45 b(o)d(que)i(lev)-5 b(a)42 b(temp)s(o)g Fz(O)s FA(\()p Fz(n)p FA(\))g FH(no)h(pior)f(caso.)109 4924 y(P)m(ortan)m(to,)g(o)e(temp)s(o)g(necess\341rio)h(para)f (atualizar)e(os)j Fz(m)f FH(v)m(etores)i(A)f(\351)f Fz(m:O)s FA(\()p 3076 4844 V Fz(P)h FA(+)27 b Fz(n)p FA(\))41 b(=)g Fz(O)s FA(\()p Fz(n:m)p FA(\))p FH(.)109 5087 y(Como)i(s\343o)i (realizadas)e(exatamen)m(te)i Fz(n)f FH(atualiza\347\365)s(es,)i(uma)e (para)g(cada)h(carro,)i(o)d(temp)s(o)g(gasto)109 5249 y(com)33 b(atualiza\347\365)s(es)g(\351)h Fz(n:O)s FA(\()p Fz(n:m)p FA(\))d(=)f Fz(O)s FA(\()p Fz(n)1660 5213 y Fq(2)1699 5249 y Fz(:m)p FA(\))p FH(.)48 b(Finalizando)31 b(a)j(an\341lise,)f(o)h(temp)s(o)f(total)g(gasto)h(em)109 5412 y(cada)41 b(itera\347\343o)f(da)h(busca)i(\351)e(o)g(temp)s(o)g (necess\341rio)h(para)f(realizar)e(a)i(a)m(v)-5 b(alia\347\343o)39 b(dos)j(mo)m(vimen)m(tos)109 5574 y(mais)47 b(o)h(temp)s(o)g (necess\341rio)h(para)f(aplicar)f(os)h(mo)m(vimen)m(tos)g(\340)g (solu\347\343o,)k(o)c(que)i(d\341)e(um)g(temp)s(o)109 5737 y Fz(O)s FA(\()p Fz(n)283 5701 y Fq(2)322 5737 y Fz(:m)p FA(\))22 b(+)g Fz(O)s FA(\()p Fz(n)766 5701 y Fq(2)805 5737 y Fz(:m)p FA(\))28 b(=)f Fz(O)s FA(\()p Fz(n)1260 5701 y Fq(2)1299 5737 y Fz(:m)p FA(\))p FH(.)p eop %%Page: 29 43 29 42 bop 109 726 a FD(Cap\355tulo)64 b(6)109 1390 y(Otimiza\347\343o)g (do)g(Primeiro)g(Ob)10 b(jetiv)-5 b(o)274 2092 y FH(Neste)35 b(cap\355tulo,)e(apresen)m(ta-se)i(a)f(estrat\351gia)f(desen)m(v)m (olvida)i(para)e(a)h(otimiza\347\343o)d(do)j(primeiro)109 2255 y(ob)5 b(jetiv)m(o)40 b(do)g(PSC:)h(minimizar)c(o)j(n)m(\372mero)g (de)h(viola\347\365)s(es)e(de)h(restri\347\365)s(es)h(de)g(capacidade)f (de)h(alta)109 2417 y(prioridade.)h(Sab)s(e-se)33 b(que)g(a)g (heur\355stica)e(construtiv)-5 b(a)33 b(obt\351m)f(uma)f(solu\347\343o) h(inicial)d(somen)m(te)34 b(para)109 2580 y(este)j(subproblema,)g (desprezando)i(os)d(demais)g(ob)5 b(jetiv)m(os,)38 b(o)f(que)g (signi\034ca)f(que)h(\351)g(p)s(oss\355v)m(el)g(que)g(a)109 2742 y(solu\347\343o)g(inicial)d(seja)k(uma)f(seq\374\352ncia)i(que)g (n\343o)e(resp)s(eita)h(a)f(limita\347\343o)d(do)k(tamanho)e(dos)i (grup)s(os)109 2905 y(de)e(carros)g(de)g(mesma)f(cor.)54 b(Da)36 b(mesma)f(forma,)g(o)h(algoritmo)c(que)37 b(otimiza)c(o)j (primeiro)d(ob)5 b(jetiv)m(o)109 3067 y(tam)m(b)s(\351m)32 b(p)s(o)s(de)i(visitar)f(solu\347\365)s(es)h(in)m(vi\341)m(v)m(eis,)g (deixando)g(a)f(restaura\347\343o)h(da)g(viabilidade,)e(caso)i(seja)109 3230 y(necess\341ria,)f(para)f(ser)h(realizada)e(somen)m(te)i(no)g (momen)m(to)e(da)i(minimiza\347\343o)28 b(do)33 b(n)m(\372mero)f(de)h (tro)s(cas)109 3392 y(de)g(cor.)109 3784 y Fx(6.1)155 b(Algoritmo)54 b(desen)l(v)l(olvido)274 4104 y FH(O)28 b(algoritmo)c(desen)m(v)m(olvido)29 b(\351)f(baseado)g(na)g (metaheur\355stica)e(ILS)j(\()p FE(Iter)-5 b(ate)g(d)30 b(L)-5 b(o)g(c)g(al)30 b(Se)-5 b(ar)g(ch)7 b FH(\))27 b([9],)109 4267 y(cuja)j(descri\347\343o)g(\351)g(apresen)m(tada)h(na)e (pr\363)m(xima)g(se\347\343o.)43 b(Nas)30 b(se\347\365)s(es)h(seguin)m (tes,)h(s\343o)e(apresen)m(tados)h(os)109 4429 y(passos)i(que)h(comp)s (\365)s(em)d(o)h(algoritmo)d(implemen)m(tado.)109 4777 y FJ(6.1.1)129 b Fg(Iter)-7 b(ate)g(d)48 b(L)-7 b(o)g(c)g(al)47 b(Se)-7 b(ar)g(ch)274 5063 y FH(A)24 b(metaheur\355stica)e(ILS)i (consiste)g(basicamen)m(te)g(em)f(construir)g(iterativ)-5 b(amen)m(te)22 b(uma)h(seq\374\352ncia)109 5226 y(de)32 b(solu\347\365)s(es)f(atra)m(v)m(\351s)i(da)e(aplica\347\343o)f (consecutiv)-5 b(a)32 b(de)g(uma)e(mo)s(di\034ca\347\343o)g(ou)i(de)f (uma)g(p)s(erturba\347\343o)109 5388 y(na)h(solu\347\343o)g(atual,)f (seguida)i(p)s(ela)e(aplica\347\343o)g(de)i(um)f(pro)s(cedimen)m(to)g (de)h(busca)g(lo)s(cal.)274 5610 y(A)f(Figura)f(6.1)h(apresen)m(ta)h(o) f(pseudo-c\363)s(digo)g(da)g(estrat\351gia)g(ILS.)g(De)h(forma)e(mais)g (detalhada,)109 5772 y(ILS)45 b(inicia)e(o)h(pro)s(cesso)i(de)g(busca)g (a)f(partir)e(de)j(uma)e(solu\347\343o)h(gerada)f(p)s(or)h(alguma)e (heur\355stica)109 5935 y(construtiv)-5 b(a)27 b(e,)i(em)e(seguida,)i (aprimorada)c(p)s(or)i(um)g(m\351to)s(do)g(de)h(busca)g(lo)s(cal)e (\(linhas)g(1)i(e)g(2\).)41 b(Dada)p eop %%Page: 30 44 30 43 bop 109 -28 a FB(6.1)60 b(Algoritmo)32 b(desen)m(v)m(olvido)2588 b(30)p 109 9 3780 4 v 109 256 a FH(a)26 b(solu\347\343o)g(atual,)g (aplica-se)g(uma)f(p)s(erturba\347\343o)i(que)h(lev)-5 b(a)25 b(a)i(uma)e(solu\347\343o)h(in)m(termedi\341ria,)f(tam)m(b)s (\351m)109 418 y(c)m(hamada)e(solu\347\343o)h(vizinha)f(\(linha)f(4\).) 41 b(Uma)23 b(busca)i(lo)s(cal)d(\351)i(aplicada)f(a)g(esta)i (solu\347\343o,)g(alcan\347ando-)109 581 y(se,)k(assim,)f(uma)f(no)m(v) -5 b(a)27 b(solu\347\343o)g(\(linha)f(5\).)42 b(Se)28 b(esta)g(solu\347\343o)f(passar)h(p)s(or)f(um)g(determinado)g (crit\351rio)109 743 y(de)47 b(aceita\347\343o,)j(ela)c(torna-se)h(a)g (no)m(v)-5 b(a)47 b(solu\347\343o)g(atual)f(no)h(pro)s(cesso)h(de)f (busca;)56 b(caso)47 b(con)m(tr\341rio,)109 906 y(retorna-se)g(para)g (aquela)g(\340)g(qual)f(foi)g(aplicada)f(a)i(p)s(erturba\347\343o)h (\(linha)d(6\).)87 b(Estes)49 b(passos)f(s\343o)109 1068 y(realizados)31 b(iterativ)-5 b(amen)m(te)31 b(at\351)h(que)i(a)e (condi\347\343o)g(de)h(parada)f(seja)h(encon)m(trada)g(\(linha)e(3\).)p 886 1331 2225 4 v 886 2667 4 1337 v 947 1523 a Fw(pro)s(cedure)i Fk(ILS)p FH(\(\);)947 1643 y(1)105 b Fz(s)1147 1658 y Fq(0)1214 1643 y Fs( )32 b Fk(GeraSolucaoInicial)p FH(\(\))947 1764 y(2)105 b Fz(s)1147 1727 y Fl(\003)1214 1764 y Fs( )32 b Fk(BuscaLocal)p FH(\()p Fz(s)1940 1779 y Fq(0)1982 1764 y FH(\))947 1884 y(3)105 b Fw(while)31 b FH(condi\347\343o)h(de)h (parada)f(n\343o)h(encon)m(trada)g Fw(do)947 2004 y FH(4)260 b Fz(s)1302 1968 y Fl(0)1353 2004 y Fs( )32 b Fk(Perturbacao)p FH(\()p Fz(s)2130 1968 y Fl(\003)2172 2004 y FH(\))947 2125 y(5)260 b Fz(s)1302 2089 y Fl(0)1353 2125 y Fs( )32 b Fk(BuscaLocal)p FH(\()p Fz(s)2079 2089 y Fl(0)2104 2125 y FH(\))947 2245 y(6)260 b Fz(s)1302 2209 y Fl(\003)1369 2245 y Fs( )32 b Fk(CriterioAceitacao)p FH(\()p Fz(s)2452 2209 y Fl(\003)2495 2245 y Fz(;)17 b(s)2585 2209 y Fl(0)2608 2245 y FH(\))947 2366 y(7)105 b Fw(end-while)947 2486 y FH(8)g Fw(return)37 b Fv(s)1502 2450 y Fh(\003)947 2606 y Fw(end)c Fk(ILS)p FH(;)p 3107 2667 V 886 2670 2225 4 v 938 2939 a(Figura)e(6.1:)43 b(Pseudo-c\363)s(digo)32 b(da)g(metaheur\355stica)f(ILS.)109 3338 y FJ(6.1.2)129 b(P)l(erturba\347\343o)274 3624 y FH(Esta)27 b(fase)f(tem)g(p)s(or)g (ob)5 b(jetiv)m(o)26 b(obter)g(uma)g(no)m(v)-5 b(a)26 b(solu\347\343o)f(a)h(partir)f(de)i(uma)e(p)s(erturba\347\343o)h(na)g (so-)109 3786 y(lu\347\343o)k(atual.)42 b(A)32 b(p)s(erturba\347\343o)f (que)h(foi)e(utilizada)f(consiste)j(em)f(destruir)h(parcialmen)m(te)e (a)h(solu\347\343o,)109 3949 y(ou)e(seja,)i(retirar)e(alguns)g(carros)h (da)f(seq\374\352ncia)i(escalonada)f(e,)g(em)g(seguida,)g(reinserir)f (estes)i(carros)109 4111 y(em)36 b(uma)h(ordem)g(aleat\363ria)d(na)j (solu\347\343o.)57 b(Esta)38 b(p)s(erturba\347\343o)f(p)s(o)s(de)g(ser) h(vista)f(como)f(a)h(aplica\347\343o)109 4274 y(consecutiv)-5 b(a)39 b(de)g(um)g(determinado)f(n)m(\372mero)g(de)i(mo)m(vimen)m(tos)e (do)h(tip)s(o)e FE(shift)p FH(,)k(descrito)d(an)m(terior-)109 4437 y(men)m(te.)43 b(O)32 b(n)m(\372mero)f(de)i(mo)m(vimen)m(tos)e (aplicados)f(\351)i(um)f(par\342metro)g(de)h(en)m(trada)g(do)g(pro)s (cedimen)m(to)109 4599 y(de)h(p)s(erturba\347\343o.)274 4821 y(Os)43 b(carros)f(remo)m(vidos)g(da)g(seq\374\352ncia)i(duran)m (te)f(a)f(p)s(erturba\347\343o)g(s\343o)g(carros)h(en)m(v)m(olvidos)g (em)109 4983 y(viola\347\365)s(es)27 b(de)h(restri\347\365)s(es.)43 b(Estes,)30 b(p)s(or)e(sua)h(v)m(ez,)h(s\343o)e(aqueles)h(que)g(p)s (ertencem)g(a)f(alguma)e(seq\374\352ncia)109 5146 y(que)37 b(est\341)g(violando)e(alguma)g(restri\347\343o)h(asso)s(ciada)g(a)g (uma)g(op)s(\347\343o)g(que)i(eles)f(p)s(ossuem.)56 b(A)37 b(melhor)109 5308 y(p)s(osi\347\343o)g(para)i(in)m(tro)s(duzir)e(estes) k(carros)d(no)m(v)-5 b(amen)m(te)40 b(na)e(solu\347\343o)g(\351)i (escolhida)e(de)h(acordo)f(com)g(a)109 5471 y(v)-5 b(aria\347\343o)26 b(no)h(custo)h(causada)g(p)s(elo)e(mo)m(vimen)m(to.)41 b(\311)28 b(imp)s(ortan)m(te)d(lem)m(brar)i(que)h(o)f(custo)h(da)g (solu\347\343o,)109 5633 y(neste)39 b(momen)m(to,)e(refere-se)i(ap)s (enas)f(ao)f(n)m(\372mero)h(de)g(viola\347\365)s(es)e(de)i (restri\347\365)s(es)g(de)g(capacidade)g(de)109 5796 y(alta)31 b(prioridade.)p eop %%Page: 31 45 31 44 bop 109 -28 a FB(6.1)60 b(Algoritmo)32 b(desen)m(v)m(olvido)2588 b(31)p 109 9 3780 4 v 274 256 a FH(A)45 b(Figura)e(6.2)h(ilustra)f(um)h (exemplo)h(de)g(funcionamen)m(to)f(da)g(p)s(erturba\347\343o)h (utilizada.)77 b(Na)109 418 y(Figura)22 b(6.2\(a\),)j(tem-se)f(a)g (seq\374\352ncia)h(original)20 b(com)k(to)s(dos)f(os)i(carros)f (escalonados,)i(onde)e(cada)g(letra)109 581 y(represen)m(ta)j(um)f (carro)f(da)h(seq\374\352ncia.)42 b(Na)26 b(Figura)e(6.2\(b\),)j(p)s(o) s(de-se)f(observ)-5 b(ar)27 b(que)f(foram)f(retirados)109 743 y(tr\352s)40 b(carros,)i(C,)e(E)g(e)g(H,)g(deixando)g(a)f (solu\347\343o)g(parcialmen)m(te)f(destru\355da.)65 b(As)41 b(setas)f(indicam)e(as)109 906 y(p)s(osi\347\365)s(es)32 b(escolhidas)g(para)h(reinserir)f(cada)g(um)g(dos)h(tr\352s)h(carros.) 44 b(A)32 b(seguir,)h(na)f(Figura)f(6.2\(c\),)i(os)109 1068 y(carros)f(s\343o)h(inseridos)f(em)g(suas)h(resp)s(ectiv)-5 b(as)34 b(p)s(osi\347\365)s(es,)e(formando-se)f(uma)h(no)m(v)-5 b(a)33 b(seq\374\352ncia.)863 3093 y currentpoint currentpoint translate 0.55363 0.55363 scale neg exch neg exch translate 863 3093 a @beginspecial 18 @llx 227 @lly 510 @urx 611 @ury 4920 @rwi @setspecial %%BeginDocument: perturb.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 18 227 510 611 %%Creator: CorelDRAW 7 %%Title: %%CreationDate: Thu Jan 20 15:19:21 2005 %%DocumentProcessColors: Black %%DocumentSuppliedResources: (atend) %%EndComments %%BeginProlog /AutoFlatness true def /AutoSteps 0 def /CMYKMarks false def /UseLevel2 false def %Color profile: _DEFAULT.CCM - Gen. Profil -Sem %%BeginResource: procset wCorel7Dict 7.0 0 /wCorel7Dict 300 dict def wCorel7Dict begin % Copyright (c)1992-96 Corel Corporation % All rights reserved. v7.0 r1.0 /bd{bind def}bind def/ld{load def}bd/xd{exch def}bd/_ null def/rp{{pop}repeat} bd/@cp/closepath ld/@gs/gsave ld/@gr/grestore ld/@np/newpath ld/Tl/translate ld /$sv 0 def/@sv{/$sv save def}bd/@rs{$sv restore}bd/spg/showpage ld/showpage{} bd currentscreen/@dsp xd/$dsp/@dsp def/$dsa xd/$dsf xd/$sdf false def/$SDF false def/$Scra 0 def/SetScr/setscreen ld/setscreen{pop pop pop}bd/@ss{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if exch $Scra add exch load SetScr}bd /SepMode_5 where{pop}{/SepMode_5 0 def}ifelse/CurrentInkName_5 where{pop} {/CurrentInkName_5(Composite)def}ifelse/$ink_5 where{pop}{/$ink_5 -1 def} ifelse/$c 0 def/$m 0 def/$y 0 def/$k 0 def/$t 1 def/$n _ def/$o 0 def/$fil 0 def/$C 0 def/$M 0 def/$Y 0 def/$K 0 def/$T 1 def/$N _ def/$O 0 def/$PF false def/s1c 0 def/s1m 0 def/s1y 0 def/s1k 0 def/s1t 0 def/s1n _ def/$bkg false def /SK 0 def/SM 0 def/SY 0 def/SC 0 def/$op false def matrix currentmatrix/$ctm xd /$ptm matrix def/$ttm matrix def/$stm matrix def/$ffpnt true def /CorelDrawReencodeVect[16#0/grave 16#5/breve 16#6/dotaccent 16#8/ring 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl 16#88/circumflex/perthousand/Scaron/guilsinglleft/OE 16#91/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash 16#98/tilde/trademark/scaron/guilsinglright/oe 16#9F/Ydieresis 16#A1/exclamdown/cent/sterling/currency/yen/brokenbar/section 16#a8/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/minus/registered/macron 16#b0/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered 16#b8/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown 16#c0/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla 16#c8/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis 16#d0/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply 16#d8/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls 16#e0/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla 16#e8/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis 16#f0/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide 16#f8/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis]def /L2?/languagelevel where{pop languagelevel 2 ge}{false}ifelse def /@BeginSysCorelDict{systemdict/Corel30Dict known{systemdict/Corel30Dict get exec}if}bd/@EndSysCorelDict{systemdict/Corel30Dict known{end}if}bd AutoFlatness {/@ifl{dup currentflat exch sub 10 gt{ ([Error: PathTooComplex; OffendingCommand: AnyPaintingOperator]\n)print flush @np exit}{currentflat 2 add setflat}ifelse}bd/@fill/fill ld/fill{currentflat{ {@fill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@eofill/eofill ld/eofill {currentflat{{@eofill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@clip /clip ld/clip{currentflat{{@clip}stopped{@ifl}{exit}ifelse}bind loop setflat} bd/@eoclip/eoclip ld/eoclip{currentflat{{@eoclip}stopped{@ifl}{exit}ifelse} bind loop setflat}bd/@stroke/stroke ld/stroke{currentflat{{@stroke}stopped {@ifl}{exit}ifelse}bind loop setflat}bd}if L2?{/@ssa{true setstrokeadjust}bd}{ /@ssa{}bd}ifelse/d/setdash ld/j/setlinejoin ld/J/setlinecap ld/M/setmiterlimit ld/w/setlinewidth ld/O{/$o xd}bd/R{/$O xd}bd/W/eoclip ld/c/curveto ld/C/c ld/l /lineto ld/L/l ld/rl/rlineto ld/m/moveto ld/n/newpath ld/N/newpath ld/P{11 rp} bd/u{}bd/U{}bd/A{pop}bd/q/@gs ld/Q/@gr ld/&{}bd/@j{@sv @np}bd/@J{@rs}bd/g{1 exch sub/$k xd/$c 0 def/$m 0 def/$y 0 def/$t 1 def/$n _ def/$fil 0 def}bd/G{1 sub neg/$K xd _ 1 0 0 0/$C xd/$M xd/$Y xd/$T xd/$N xd}bd/k{1 index type /stringtype eq{/$t xd/$n xd}{/$t 0 def/$n _ def}ifelse/$k xd/$y xd/$m xd/$c xd /$fil 0 def}bd/K{1 index type/stringtype eq{/$T xd/$N xd}{/$T 0 def/$N _ def} ifelse/$K xd/$Y xd/$M xd/$C xd}bd/x/k ld/X/K ld/sf{1 index type/stringtype eq{ /s1t xd/s1n xd}{/s1t 0 def/s1n _ def}ifelse/s1k xd/s1y xd/s1m xd/s1c xd}bd/i{ dup 0 ne{setflat}{pop}ifelse}bd/v{4 -2 roll 2 copy 6 -2 roll c}bd/V/v ld/y{2 copy c}bd/Y/y ld/@w{matrix rotate/$ptm xd matrix scale $ptm dup concatmatrix /$ptm xd 1 eq{$ptm exch dup concatmatrix/$ptm xd}if 1 w}bd/@g{1 eq dup/$sdf xd {/$scp xd/$sca xd/$scf xd}if}bd/@G{1 eq dup/$SDF xd{/$SCP xd/$SCA xd/$SCF xd} if}bd/@D{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if 3 copy exch $Scra add exch load SetScr/$dsp xd/$dsa xd/$dsf xd}bd/$ngx{$SDF{$SCF SepMode_5 0 eq{$SCA} {$dsa}ifelse $SCP @ss}if}bd/p{/$pm xd 7 rp/$pyf xd/$pxf xd/$pn xd/$fil 1 def} bd/@MN{2 copy le{pop}{exch pop}ifelse}bd/@MX{2 copy ge{pop}{exch pop}ifelse}bd /InRange{3 -1 roll @MN @MX}bd/@sqr{dup 0 rl dup 0 exch rl neg 0 rl @cp}bd /currentscale{1 0 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt 0 1 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt}bd/@unscale{}bd/wDstChck{2 1 roll dup 3 -1 roll eq{1 add}if}bd /@dot{dup mul exch dup mul add 1 exch sub}bd/@lin{exch pop abs 1 exch sub}bd /cmyk2rgb{3{dup 5 -1 roll add 1 exch sub dup 0 lt{pop 0}if exch}repeat pop}bd /rgb2cmyk{3{1 exch sub 3 1 roll}repeat 3 copy @MN @MN 3{dup 5 -1 roll sub neg exch}repeat}bd/rgb2g{2 index .299 mul 2 index .587 mul add 1 index .114 mul add 4 1 roll pop pop pop}bd/WaldoColor_5 where{pop}{/SetRgb/setrgbcolor ld/GetRgb /currentrgbcolor ld/SetGry/setgray ld/GetGry/currentgray ld/SetRgb2 systemdict /setrgbcolor get def/GetRgb2 systemdict/currentrgbcolor get def/SetHsb systemdict/sethsbcolor get def/GetHsb systemdict/currenthsbcolor get def /rgb2hsb{SetRgb2 GetHsb}bd/hsb2rgb{3 -1 roll dup floor sub 3 1 roll SetHsb GetRgb2}bd/setcmykcolor where{pop/SetCmyk_5/setcmykcolor ld}{/SetCmyk_5{ cmyk2rgb SetRgb}bd}ifelse/currentcmykcolor where{pop/GetCmyk/currentcmykcolor ld}{/GetCmyk{GetRgb rgb2cmyk}bd}ifelse/setoverprint where{pop}{/setoverprint{ /$op xd}bd}ifelse/currentoverprint where{pop}{/currentoverprint{$op}bd}ifelse /@tc_5{5 -1 roll dup 1 ge{pop}{4{dup 6 -1 roll mul exch}repeat pop}ifelse}bd /@trp{exch pop 5 1 roll @tc_5}bd/setprocesscolor_5{SepMode_5 0 eq{SetCmyk_5}{0 4 $ink_5 sub index exch pop 5 1 roll pop pop pop pop SepsColor true eq{$ink_5 3 gt{1 sub neg SetGry}{0 0 0 4 $ink_5 roll SetCmyk_5}ifelse}{1 sub neg SetGry} ifelse}ifelse}bd/findcmykcustomcolor where{pop}{/findcmykcustomcolor{5 array astore}bd}ifelse/setcustomcolor where{pop}{/setcustomcolor{exch aload pop SepMode_5 0 eq{pop @tc_5 setprocesscolor_5}{CurrentInkName_5 eq{4 index}{0} ifelse 6 1 roll 5 rp 1 sub neg SetGry}ifelse}bd}ifelse/@scc_5{dup type /booleantype eq{setoverprint}{1 eq setoverprint}ifelse dup _ eq{pop setprocesscolor_5 pop}{findcmykcustomcolor exch setcustomcolor}ifelse SepMode_5 0 eq{true}{GetGry 1 eq currentoverprint and not}ifelse}bd/colorimage where{pop /ColorImage{colorimage}def}{/ColorImage{/ncolors xd pop/dataaq xd{dataaq ncolors dup 3 eq{/$dat xd 0 1 $dat length 3 div 1 sub{dup 3 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length 3 idiv getinterval pop}{4 eq{/$dat xd 0 1 $dat length 4 div 1 sub{dup 4 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div $dat 4 index 3 add get 255 div cmyk2rgb rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length ncolors idiv getinterval}if}ifelse}image}bd }ifelse/setcmykcolor{1 5 1 roll _ currentoverprint @scc_5/$ffpnt xd}bd /currentcmykcolor{0 0 0 0}bd/setrgbcolor{rgb2cmyk setcmykcolor}bd /currentrgbcolor{currentcmykcolor cmyk2rgb}bd/sethsbcolor{hsb2rgb setrgbcolor} bd/currenthsbcolor{currentrgbcolor rgb2hsb}bd/setgray{dup dup setrgbcolor}bd /currentgray{currentrgbcolor rgb2g}bd}ifelse/WaldoColor_5 true def/@sft{$tllx $pxf add dup $tllx gt{$pwid sub}if/$tx xd $tury $pyf sub dup $tury lt{$phei add}if/$ty xd}bd/@stb{pathbbox/$ury xd/$urx xd/$lly xd/$llx xd}bd/@ep{{cvx exec }forall}bd/@tp{@sv/$in true def 2 copy dup $lly le{/$in false def}if $phei sub $ury ge{/$in false def}if dup $urx ge{/$in false def}if $pwid add $llx le{/$in false def}if $in{@np 2 copy m $pwid 0 rl 0 $phei neg rl $pwid neg 0 rl 0 $phei rl clip @np $pn cvlit load aload pop 7 -1 roll 5 index sub 7 -1 roll 3 index sub Tl matrix currentmatrix/$ctm xd @ep pop pop pop pop}{pop pop}ifelse @rs}bd /@th{@sft 0 1 $tly 1 sub{dup $psx mul $tx add{dup $llx gt{$pwid sub}{exit} ifelse}loop exch $phei mul $ty exch sub 0 1 $tlx 1 sub{$pwid mul 3 copy 3 -1 roll add exch @tp pop}for pop pop}for}bd/@tv{@sft 0 1 $tlx 1 sub{dup $pwid mul $tx add exch $psy mul $ty exch sub{dup $ury lt{$phei add}{exit}ifelse}loop 0 1 $tly 1 sub{$phei mul 3 copy sub @tp pop}for pop pop}for}bd/$fm 0 def/wfill{1 $fm eq{fill}{eofill}ifelse}bd/wclip{1 $fm eq{clip}{eoclip}ifelse}bd/@pf{@gs $ctm setmatrix $pm concat @stb wclip Bburx Bbury $pm itransform/$tury xd/$turx xd Bbllx Bblly $pm itransform/$tlly xd/$tllx xd/$wid $turx $tllx sub def/$hei $tury $tlly sub def @gs $vectpat{1 0 0 0 0 _ $o @scc_5{wfill}if}{$t $c $m $y $k $n $o @scc_5{SepMode_5 0 eq $pfrg or{$tllx $tlly Tl $wid $hei scale <00> 8 1 false[8 0 0 1 0 0]{}imagemask}{/$bkg true def}ifelse}if}ifelse @gr $wid 0 gt $hei 0 gt and{$pn cvlit load aload pop/$pd xd 3 -1 roll sub/$phei xd exch sub /$pwid xd $wid $pwid div ceiling 1 add/$tlx xd $hei $phei div ceiling 1 add /$tly xd $psx 0 eq{@tv}{@th}ifelse}if @gr @np/$bkg false def}bd/@Pf{@sv SepMode_5 0 eq $Psc 0 ne or $ink_5 3 eq or{0 J 0 j[]0 d $t $c $m $y $k $n $o @scc_5 pop $ctm setmatrix 72 1000 div dup matrix scale dup concat dup Bburx exch Bbury exch itransform ceiling cvi/Bbury xd ceiling cvi/Bburx xd Bbllx exch Bblly exch itransform floor cvi/Bblly xd floor cvi/Bbllx xd $Prm aload pop $Psn load exec}{1 SetGry wfill}ifelse @rs @np}bd/F{matrix currentmatrix $sdf{$scf $sca $scp @ss}if $fil 1 eq{@pf}{$fil 2 eq{@ff}{$fil 3 eq{@Pf}{$t $c $m $y $k $n $o @scc_5{wfill}{@np}ifelse}ifelse}ifelse}ifelse $sdf{$dsf $dsa $dsp @ss}if setmatrix}bd/f{@cp F}bd/S{matrix currentmatrix $ctm setmatrix $SDF{$SCF $SCA $SCP @ss}if $T $C $M $Y $K $N $O @scc_5{matrix currentmatrix $ptm concat stroke setmatrix}{@np}ifelse $SDF{$dsf $dsa $dsp @ss}if setmatrix}bd/s{@cp S}bd/B{@gs F @gr S}bd/b{@cp B}bd/_E{5 array astore exch cvlit xd}bd/@cc{currentfile $dat readhexstring pop}bd/@sm{/$ctm $ctm currentmatrix def}bd/@E{/Bbury xd/Bburx xd /Bblly xd/Bbllx xd}bd/@c{@cp}bd/@p{/$fil 1 def 1 eq dup/$vectpat xd{/$pfrg true def}{@gs $t $c $m $y $k $n $o @scc_5/$pfrg xd @gr}ifelse/$pm xd/$psy xd/$psx xd /$pyf xd/$pxf xd/$pn xd}bd/@P{/$fil 3 def/$Psn xd/$Psc xd array astore/$Prm xd }bd/@ii{concat 3 index 3 index m 3 index 1 index l 2 copy l 1 index 3 index l 3 index 3 index l clip pop pop pop pop}bd/tcc{@cc}def/@i{@sm @gs @ii 6 index 1 ne {/$frg true def pop pop}{1 eq{s1t s1c s1m s1y s1k s1n $O @scc_5/$frg xd}{/$frg false def}ifelse 1 eq{@gs $ctm setmatrix F @gr}if}ifelse @np/$ury xd/$urx xd /$lly xd/$llx xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul 8 div ceiling cvi string def $bkg $frg or{$SDF{$SCF $SCA $SCP @ss}if $llx $lly Tl $urx $llx sub $ury $lly sub scale $bkg{$t $c $m $y $k $n $o @scc_5 pop}if $wid $hei abs $bts 1 eq{$bkg}{$bts}ifelse[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/tcc load $bts 1 eq{imagemask}{image}ifelse $SDF{$dsf $dsa $dsp @ss}if}{$hei abs{tcc pop} repeat}ifelse @gr $ctm setmatrix}bd/@I{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd /$llx xd/$ncl xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def $ngx $llx $lly Tl $urx $llx sub $ury $lly sub scale $wid $hei abs $bts[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/@cc load false $ncl ColorImage $SDF{$dsf $dsa $dsp @ss}if @gr $ctm setmatrix}bd/COMP 0 def L2?{ /@I_2{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd/$llx xd/$ncl xd/$bts xd/$hei xd /$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def 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b(jet\363ria)39 b(atual)g(da)h(busca)h(n\343o)f (consegue)i(mais)d(obter)h(solu\347\365)s(es)p eop %%Page: 33 47 33 46 bop 109 -28 a FB(6.1)60 b(Algoritmo)32 b(desen)m(v)m(olvido)2588 b(33)p 109 9 3780 4 v 109 256 a FH(aprimoran)m(tes.)42 b(O)32 b(no)m(v)m(o)i(p)s(on)m(to)e(de)h(partida)e(para)h(a)h(busca)g (\351)g(obtido)e(de)j(duas)f(formas:)255 544 y(\025)49 b(atra)m(v)m(\351s)26 b(de)f(uma)f(p)s(erturba\347\343o)g(forte)h(na)g (solu\347\343o)f(atual.)39 b(Isto)25 b(\351)g(realizado)e(com)h (aplica\347\343o)f(da)353 706 y(mesma)37 b(p)s(erturba\347\343o)h (utilizada)e(an)m(teriormen)m(te,)j(retirando-se,)h(no)e(en)m(tan)m (to,)i(um)e(n)m(\372mero)353 869 y(b)s(em)32 b(maior)e(de)j(carros)g (para)f(escalonar)g(no)m(v)-5 b(amen)m(te.)255 1109 y(\025)49 b(atra)m(v)m(\351s)33 b(de)g(uma)f(no)m(v)-5 b(a)33 b(solu\347\343o)f (obtida)f(p)s(ela)h(heur\355stica)f(construtiv)-5 b(a.)274 1397 y(Inicialmen)m(te,)40 b(utiliza-se)e(a)i(primeira)d(forma)i(de)h 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2535 y(par\342metro)31 b(do)h(algoritmo,)d(discutido)j(no)h (Cap\355tulo)e(8.)274 2756 y(Se)49 b(ap)s(\363s)f(uma)f (reinicializa\347\343o)d(seguida)k(p)s(or)g(um)g(determinado)f(n)m (\372mero)h(de)g(itera\347\365)s(es)g(do)109 2919 y(algoritmo)42 b(n\343o)k(se)h(consegue)h(obter)e(uma)f(solu\347\343o)h(de)h (qualidade)e(melhor)g(ou)h(igual)e(\340)i(melhor)109 3082 y(solu\347\343o)32 b(conhecida,)g(a)h(solu\347\343o)f(atual)f (passa)i(a)f(ser)h(a)g(melhor)e(solu\347\343o)h(conhecida.)274 3303 y(A)f(reinicializa\347\343o)26 b(tam)m(b)s(\351m)k(a)5 b(juda)31 b(a)f(de\034nir)h(o)f(crit\351rio)f(de)i(estagna\347\343o)g (do)g(algoritmo,)c(como)109 3466 y(\351)33 b(p)s(oss\355v)m(el)f (observ)-5 b(ar)33 b(na)f(pr\363)m(xima)g(se\347\343o.)109 3811 y FJ(6.1.6)129 b(Crit\351rio)46 b(de)d(estagna\347\343o)274 4097 y FH(O)d(crit\351rio)f(de)i(estagna\347\343o)g(do)g(algoritmo)36 b(\351)41 b(um)f(p)s(on)m(to)h(cr\355tico)e(e)i(dev)m(e)h(ser)f (escolhido)f(com)109 4259 y(bastan)m(te)h(cautela)f(devido)h(\340)g (estrat\351gia)f(que)h(foi)f(utilizada)e(para)i(resolv)m(er)i(o)e (problema.)67 b(Como)109 4422 y(foram)32 b(desen)m(v)m(olvidos)j (tr\352s)f(algoritmos)d(indep)s(enden)m(tes,)k(um)e(para)h(cada)f(ob)5 b(jetiv)m(o)34 b(do)g(problema,)109 4584 y(\351)23 b(m)m(uito)e(imp)s (ortan)m(te)g(sab)s(er)i(em)f(que)i(momen)m(to)d(dev)m(e-se)k(passar)e (a)g(explorar)f(o)g(ob)5 b(jetiv)m(o)23 b(seguin)m(te)g(na)109 4747 y(escala)33 b(de)h(prioridade.)44 b(Precisa-se)34 b(sab)s(er)f(quando)h(o)f(subproblema)g(que)h(est\341)g(sendo)g (resolvido)f(j\341)109 4909 y(foi)23 b(satisfatoriamen)m(te)g (solucionado)h(e)h(quando)h(dev)m(e-se)h(passar)e(a)g(resolv)m(er,)i (en)m(t\343o,)g(o)e(subproblema)109 5072 y(seguin)m(te.)274 5293 y(O)i(m\351to)s(do)f(de)h(reinicializa\347\343o)c(utilizado)i (serviu)i(como)g(base)g(para)g(a)g(de\034ni\347\343o)g(de)g(um)g (crit\351rio)109 5456 y(de)41 b(estagna\347\343o.)68 b(Quando,)43 b(p)s(or)d(um)h(determinado)e(n)m(\372mero)i(de)g(v)m (ezes,)k(c)m(hega-se)d(a)f(solu\347\365)s(es)g(de)109 5618 y(custo)28 b(igual)d(ao)i(da)g(melhor)f(solu\347\343o)h(conhecida) g(no)h(momen)m(to)e(da)h(reinicializa\347\343o,)e(o)i(algoritmo)d(de) 109 5781 y(otimiza\347\343o)31 b(do)k(primeiro)d(ob)5 b(jetiv)m(o)34 b(termina)g(e)g(o)h(algoritmo)c(para)j(otimizar)d(o)k (segundo)g(ob)5 b(jetiv)m(o)109 5943 y(\351)33 b(executado.)p eop %%Page: 34 48 34 47 bop 109 -28 a FB(6.1)60 b(Algoritmo)32 b(desen)m(v)m(olvido)2588 b(34)p 109 9 3780 4 v 274 256 a FH(Jun)m(tamen)m(te)46 b(com)f(o)h(crit\351rio)d(de)j(estagna\347\343o)g(descrito)g(acima,)h (utiliza-se)c(uma)i(fra\347\343o)g(de)109 418 y(temp)s(o)29 b(de)i(execu\347\343o)h(do)f(algoritmo)26 b(como)k(crit\351rio)f(da)h (parada,)h(j\341)f(que)h(uma)f(determinada)f(quan-)109 581 y(tidade)40 b(de)i(temp)s(o)e(de)h(execu\347\343o)i(\351)e (estipulada)f(para)h(a)f(solu\347\343o)h(do)g(problema)e(como)h(um)h (to)s(do.)109 743 y(Desta)j(forma,)h(mesmo)e(o)h(primeiro)d(ob)5 b(jetiv)m(o)44 b(p)s(ossuindo)f(um)g(p)s(eso)i(b)s(em)e(maior)e(na)j (fun\347\343o)g(de)109 906 y(custo,)31 b(uma)e(fra\347\343o)g(de)h (temp)s(o)f(menor)g(\351)h(dedicada)g(aos)f(outros)h(ob)5 b(jetiv)m(os,)31 b(se)g(o)e(crit\351rio)f(de)i(estag-)109 1068 y(na\347\343o)i(n\343o)g(tiv)m(er)h(sido)f(atingido.)274 1290 y(Um)26 b(terceiro)f(crit\351rio)g(de)i(estagna\347\343o)f(bastan) m(te)h(in)m(tuitiv)m(o)d(tam)m(b)s(\351m)h(\351)i(utilizado.)39 b(Ele)26 b(consiste)109 1452 y(em)f(terminar)g(a)g(execu\347\343o)j(do) e(algoritmo)c(quando)27 b(se)g(tem)e(certeza)i(de)g(que)g(a)e (solu\347\343o)h(n\343o)g(p)s(o)s(de)f(ser)109 1615 y(melhorada,)k(ou)g (seja,)i(quando)g(encon)m(tra-se)g(uma)e(solu\347\343o)h(com)f(nenh)m (uma)h(viola\347\343o)e(de)j(restri\347\365)s(es)109 1777 y(de)i(capacidade.)109 2125 y FJ(6.1.7)129 b(Estrutura)45 b(geral)f(do)g(algoritmo)274 2411 y FH(P)m(ara)26 b(melhor)e(mostrar)g (a)h(in)m(tera\347\343o)g(en)m(tre)h(cada)g(uma)f(partes)h(do)f (algoritmo)d(apresen)m(tadas)27 b(nas)109 2574 y(se\347\365)s(es)i(an)m (teriores,)f(uma)f(vis\343o)g(geral)f(da)i(estrutura)g(do)f(algoritmo)d (\351)k(apresen)m(tada)h(nesta)f(se\347\343o.)42 b(O)109 2736 y(algoritmo)29 b(considera)j(somen)m(te)i(o)e(primeiro)e(ob)5 b(jetiv)m(o)33 b(do)f(problema)g(e)h(tem)f(como)g(solu\347\343o)g (inicial)109 2899 y(aquela)k(constru\355da)g(p)s(ela)f(heur\355stica)h (construtiv)-5 b(a)36 b(\(v)m(er)h(Cap\355tulo)e(4\).)54 b(A)37 b(cada)f(itera\347\343o,)g(obt\351m-)109 3061 y(se)42 b(uma)g(solu\347\343o)f(atra)m(v)m(\351s)i(de)g(uma)e(p)s (erturba\347\343o)h(na)g(solu\347\343o)f(atual)g(e)h(aplica-se)f(a)h (busca)g(lo)s(cal)109 3224 y(com)31 b(mo)m(vimen)m(tos)g Fz(sw)s(ap)g FH(nesta)h(solu\347\343o)f("p)s(erturbada",)h(obtendo-se)g (uma)f(solu\347\343o)g(aprimorada.)109 3386 y(Utiliza-se)26 b(a)i(busca)i(lo)s(cal)c(r\341pida)h(ou)i(a)f(busca)h(lo)s(cal)e (completa,)h(dep)s(endendo)i(do)e(n)m(\372mero)h(total)e(de)109 3549 y(carros)37 b(en)m(v)m(olvidos)h(em)f(viola\347\365)s(es)f(na)h (solu\347\343o.)58 b(Com)37 b(esta)h(solu\347\343o)e(aprimorada,)h (utiliza-se)e(um)109 3711 y(crit\351rio)30 b(de)i(aceita\347\343o)f (que)h(decide)g(se)h(a)e(solu\347\343o)g(\351)h(aceita)f(ou)h(n\343o)f (como)g(solu\347\343o)g(atual,)g(baseado)109 3874 y(no)36 b(custo)h(da)f(solu\347\343o.)54 b(Sempre)37 b(que)g(se)g(consegue)h (melhoria)c(na)i(solu\347\343o)g(atual,)g(v)m(eri\034ca-se)h(se)g(\351) 109 4036 y(necess\341rio)i(atualizar)e(a)i(melhor)f(solu\347\343o)g (encon)m(trada)i(p)s(elo)e(algoritmo.)60 b(Quando)39 b(o)g(n)m(\372mero)g(de)109 4199 y(itera\347\365)s(es)i(desde)h(o)f (\372ltimo)e(melhoramen)m(to)g(na)j(solu\347\343o)e(atual)g(atinge)h (um)f(determinado)g(v)-5 b(alor,)109 4361 y(aplica-se)36 b(a)h(in)m(tensi\034ca\347\343o/div)m(ersi\034ca\347\343o)g(nesta)i (solu\347\343o)e(e)h(a)f(solu\347\343o)g(obtida)g(p)s(or)g(este)h(pro)s (ce-)109 4524 y(dimen)m(to)43 b(\351)h(tam)m(b)s(\351m)f(submetida)g (ao)g(crit\351rio)g(de)h(aceita\347\343o.)77 b(Quando)44 b(um)f(n)m(\372mero)h(maior)e(de)109 4686 y(itera\347\365)s(es)34 b(sem)g(melhoria)e(na)j(solu\347\343o)f(atual)f(for)h(atingido)e(e)j(o) f(custo)h(desta)g(solu\347\343o)f(for)g(igual)f(ao)109 4849 y(da)28 b(melhor)e(solu\347\343o)h(conhecida,)j(aplica-se)c(o)i (pro)s(cedimen)m(to)f(de)i(reinicializa\347\343o)24 b(a)j(\034m)h(de)g (se)h(obter)109 5011 y(um)36 b(no)m(v)m(o)i(p)s(on)m(to)f(de)h(partida) e(para)h(o)g(algoritmo.)54 b(Se,)39 b(caso)e(con)m(tr\341rio,)h(n\343o) f(se)h(conseguiu)f(obter)109 5174 y(uma)d(solu\347\343o)g(de)h(mesmo)f (custo)h(que)h(a)f(melhor)e(solu\347\343o)h(conhecida,)i(esta)f(v)m (olta)f(a)h(ser)g(a)g(solu\347\343o)109 5336 y(atual.)47 b(O)34 b(algoritmo)c(p\341ra)k(quando)h(um)f(dos)g(crit\351rios)f(de)i (estagna\347\343o)f(de\034nidos)h(na)f(Se\347\343o)h(6.1.6)109 5499 y(\351)e(encon)m(trado.)274 5720 y(Uma)25 b(vis\343o)g(mais)g (detalhada)g(da)h(estrutura)g(geral)f(do)h(algoritmo)c(\351)k(dada)g (atra)m(v)m(\351s)h(da)f(descri\347\343o)109 5883 y(do)35 b(pseudo-c\363)s(digo)g(apresen)m(tado)i(na)e(Figura)f(6.3.)52 b(Algumas)34 b(v)-5 b(ari\341)m(v)m(eis)36 b(e)f(par\342metros)g (utilizados)p eop %%Page: 35 49 35 48 bop 109 -28 a FB(6.1)60 b(Algoritmo)32 b(desen)m(v)m(olvido)2588 b(35)p 109 9 3780 4 v 109 256 a FH(no)39 b(algoritmo)c(s\343o)k (descritos)g(a)g(seguir.)63 b(Sejam)38 b Fz(\031)2062 219 y Fl(\003)2141 256 y FH(a)g(melhor)g(solu\347\343o)g(conhecida,)j Fz(\031)i FH(a)c(solu\347\343o)109 418 y(atual)24 b(e)h Fz(\031)478 382 y Fl(0)527 418 y FH(uma)f(v)-5 b(ari\341)m(v)m(el)25 b(auxiliar)d(para)j(armazenar)g(o)g(resultado)g(da)g(aplica\347\343o)f (de)h(pro)s(cedimen)m(tos)109 581 y(tais)35 b(como)g(p)s (erturba\347\343o.)53 b(Sejam)35 b Fz(i)h FH(a)g(v)-5 b(ari\341)m(v)m(el)34 b(usada)j(para)e(armazenar)g(o)h(n)m(\372mero)f (de)i(v)m(ezes)h(em)109 743 y(que)33 b(o)f(custo)h(de)g Fz(\031)j FH(\351)d(igual)d(ao)i(custo)h(de)g Fz(\031)1735 707 y Fl(\003)1807 743 y FH(desde)h(o)e(\372ltimo)e(melhoramen)m(to)g (de)j Fz(\031)3288 707 y Fl(\003)3360 743 y FH(no)f(momen)m(to)109 906 y(da)41 b(reinicializa\347\343o)c(e)42 b Fz(i)1008 921 y Ft(max)1193 906 y FH(o)f(par\342metro)g(que)h(estab)s(elece)g(o)f (v)-5 b(alor)40 b(m\341ximo)f(p)s(ermitido)g(para)i Fz(i)p FH(.)109 1068 y(Sejam)e Fz(\013)h FH(o)f(par\342metro)g(que)i(guarda)e (o)g(n)m(\372mero)h(de)g(itera\347\365)s(es)f(sem)h(melhoramen)m(to)e (em)h Fz(\031)44 b FH(para)109 1231 y(aplicar)35 b(a)i(in)m (tensi\034ca\347\343o)g(e)h Fz(\014)43 b FH(para)37 b(aplicar)e(a)i (reinicializa\347\343o.)54 b(Na)37 b(primeira)e(linha)g(do)j(pseudo-) 109 1393 y(c\363)s(digo,)33 b(as)h(v)-5 b(ari\341)m(v)m(eis)34 b(s\343o)g(inicializadas:)43 b(a)34 b(melhor)f(solu\347\343o)g Fz(\031)2534 1357 y Fl(\003)2608 1393 y FH(e)h(a)g(solu\347\343o)g (atual)f Fz(\031)38 b FH(receb)s(em)c(a)109 1556 y(solu\347\343o)27 b(inicial)e(vinda)i(da)h(heur\355stica)f(construtiv)-5 b(a)28 b(e)g Fz(i)h FH(receb)s(e)g(zero.)42 b(Cada)28 b(itera\347\343o)f(do)h(algoritmo)109 1718 y(ILS)42 b(inicia-se)d(com)j (uma)f(p)s(erturba\347\343o)g(na)h(solu\347\343o)f(atual)g Fz(\031)k FH(\(linha)40 b(3\),)k(conforme)d(descrito)h(na)109 1881 y(Se\347\343o)35 b(6.1.2,)h(gerando)f(uma)g(solu\347\343o)g(in)m (termedi\341ria)d Fz(\031)2242 1845 y Fl(0)2266 1881 y FH(.)52 b(Em)35 b(seguida,)h(aplica-se)e(a)h(busca)h(lo)s(cal,)109 2043 y(descrita)28 b(na)h(Se\347\343o)g(6.1.3,)f(\340)h(solu\347\343o)f (vinda)g(da)g(p)s(erturba\347\343o)h(e)g(o)f(resultado)g(\351)h (armazenado)f(em)g Fz(\031)3865 2007 y Fl(0)109 2206 y FH(\(linha)j(4\).)46 b(Na)34 b(linha)e(5,)h(tem-se)h(o)f(crit\351rio) f(de)i(aceita\347\343o)e(da)i(solu\347\343o)f(obtida)f(na)i (itera\347\343o,)e(que)j(\351)109 2368 y(aceita)28 b(se)i(o)g(seu)g (custo)g(for)f(menor)g(ou)g(igual)e(ao)i(custo)h(da)g(solu\347\343o)e (atual)g Fz(\031)t FH(.)43 b(A)29 b(melhor)f(solu\347\343o)h Fz(\031)3849 2332 y Fl(\003)109 2531 y FH(\351)38 b(atualizada)e(se)j (a)f(no)m(v)-5 b(a)38 b(solu\347\343o)g(atual)f(encon)m(trada)i(p)s (ossui)f(custo)h(melhor)d(\(blo)s(co)h(condicional)109 2693 y(da)f(linha)e(6\).)55 b(Al\351m)35 b(disso,)i(a)f(v)-5 b(ari\341)m(v)m(el)36 b Fz(i)g FH(\(que)i(represen)m(ta)g(o)e(n)m (\372mero)g(de)h(v)m(ezes)h(em)e(que)h(o)g(custo)109 2856 y(da)29 b(solu\347\343o)g(atual)f(\351)i(igual)d(ao)i(da)g(melhor) f(conhecida)i(no)f(momen)m(to)f(da)i(reinicializa\347\343o\))25 b(\351)30 b(zerada,)109 3018 y(p)s(ois)e(a)g(melhor)g(solu\347\343o)g (foi)f(aprimorada)g(\(linha)g(8\).)42 b(O)28 b(blo)s(co)g Fw(if)g FH(da)h(linha)e(11)h(v)m(eri\034ca)h(se)h(a)e(fase)i(de)109 3181 y(in)m(tensi\034ca\347\343o)g(e)h(div)m(ersi\034ca\347\343o)g(dev) m(e)i(ser)e(aplicada,)e(ou)i(seja,)h(se)f(um)g(determinado)e(n)m (\372mero)i Fz(\013)h FH(de)109 3343 y(itera\347\365)s(es)27 b(desde)j(o)d(\372ltimo)f(melhoramen)m(to)g(na)i(solu\347\343o)f(atual) g(foi)f(atingido.)40 b(Em)27 b(caso)i(a\034rmativ)m(o,)109 3506 y(a)41 b(fase)h(\351)h(executada)g(e)f(as)g(solu\347\365)s(es)g (nas)g(v)-5 b(ari\341)m(v)m(eis)42 b Fz(\031)j FH(e)d Fz(\031)2388 3470 y Fl(\003)2470 3506 y FH(s\343o)f(atualizadas)g(se)h (necess\341rio.)72 b(O)109 3668 y(blo)s(co)26 b Fw(if)i FH(seguin)m(te)g(\(linha)e(20\))h(implemen)m(ta)f(a)i(fase)g(de)g (reinicializa\347\343o,)d(segundo)k(a)e(Se\347\343o)i(6.1.5.)41 b(A)109 3831 y(reinicializa\347\343o)26 b(\351)k(executada)h(ap)s (\363s)f(um)g(dado)g(n)m(\372mero)g Fz(\014)35 b FH(de)c(itera\347\365) s(es)e(sem)h(melhoria)e(na)i(solu\347\343o)109 3993 y(atual,)e (similarmen)m(te)e(\340)i(in)m(tensi\034ca\347\343o/div)m (ersi\034ca\347\343o.)42 b(V)-8 b(ale)28 b(salien)m(tar)f(que)j(o)f (par\342metro)e Fz(\013)j FH(dev)m(e)109 4156 y(ter)g(v)-5 b(alor)30 b(b)s(em)g(menor)g(que)h(o)g(par\342metro)e Fz(\014)6 b FH(,)31 b(p)s(ois)f(precisa-se)h(explorar)f(su\034cien)m (temen)m(te)i(a)f(regi\343o)109 4318 y(pr\363)m(xima)e(\340)i (solu\347\343o)g(atual)e(para)i(que)h(um)e(no)m(v)m(o)i(p)s(on)m(to)f (de)h(partida)d(seja)j(utilizado.)40 b(Se)32 b(o)f(custo)g(da)109 4481 y(solu\347\343o)e(atual,)g(obtida)g(ap)s(\363s)g(v)-5 b(\341rias)29 b(itera\347\365)s(es)g(do)h(algoritmo,)d(n\343o)i(for)h (igual)d(ao)i(custo)i(da)f(melhor)109 4643 y(solu\347\343o,)d(a)g (solu\347\343o)f(atual)g(v)m(olta)g(a)h(ser)h(a)e(melhor)g (solu\347\343o)g(conhecida)h(\(linha)f(24\).)41 b(Caso)27 b(con)m(tr\341rio,)109 4806 y(a)34 b(reinicializa\347\343o)d(\351)k (aplicada)e(e)i(o)g(n)m(\372mero)g(de)g(v)m(ezes)i(em)e(que)h(o)e (custo)i(da)e(solu\347\343o)h(atual)e(\351)i(igual)109 4969 y(ao)j(da)i(melhor)e(conhecida)h(\351)h(incremen)m(tado.)63 b(O)39 b(algoritmo)d(termina)h(quando)j(\351)g(transcorrida)e(a)109 5131 y(fra\347\343o)28 b(de)h(temp)s(o)g(execu\347\343o)h(determinada)e (ou)h(quando)g(obt\351m-se)g(solu\347\365)s(es)g(de)h(mesmo)e(custo)h (que)109 5294 y(a)i(melhor)g(conhecida)h(no)g(momen)m(to)f(da)h (reinicializa\347\343o)c(p)s(or)k(um)f(determinado)g(n)m(\372mero)h(de) h(v)m(ezes)109 5456 y Fz(i)142 5471 y Ft(max)318 5456 y FH(\(la\347o)f(da)g(linha)f(2\).)p eop %%Page: 36 50 36 49 bop 109 -28 a FB(6.1)60 b(Algoritmo)32 b(desen)m(v)m(olvido)2588 b(36)p 109 9 3780 4 v 248 1214 3501 4 v 248 4598 4 3384 v 309 1407 a Fw(pro)s(cedure)33 b Fk(ILS_HPRC)p FH(\(Solu\347\343o)g (inicial)d Fz(\031)1979 1422 y Fq(0)2018 1407 y FH(\);)309 1527 y(1)105 b Fz(\031)32 b Fs( )27 b Fz(\031)732 1542 y Fq(0)772 1527 y FH(,)33 b Fz(\031)891 1491 y Fl(\003)958 1527 y Fs( )27 b Fz(\031)1140 1542 y Fq(0)1180 1527 y FH(,)32 b Fz(i)c Fs( )f FA(0)309 1647 y FH(2)105 b Fw(while)31 b Fz(i)d(<)g(i)950 1662 y Ft(max)1126 1647 y Fw(and)34 b FH(fra\347\343o)e(de)h(temp)s(o)f(n\343o)g(excedida)h Fw(do)309 1768 y FH(3)260 b Fz(\031)677 1732 y Fl(0)728 1768 y Fs( )32 b Fk(Perturbacao)p FH(\()p Fz(\031)t FH(\))309 1888 y(4)260 b Fz(\031)677 1852 y Fl(0)728 1888 y Fs( )32 b Fk(BuscaLocal)p FH(\()p Fz(\031)1467 1852 y Fl(0)1492 1888 y FH(\))309 2009 y(5)260 b Fz(\031)31 b Fs( )h Fk (CriterioAceitacao)p FH(\()p Fz(\031)t(;)17 b(\031)1903 1972 y Fl(0)1930 2009 y FH(\))309 2129 y(6)260 b Fw(if)32 b Fz(custo)p FA(\()p Fz(\031)t FA(\))27 b Fz(<)g(custo)p FA(\()p Fz(\031)1530 2093 y Fl(\003)1569 2129 y FA(\))32 b Fw(then)309 2249 y FH(7)414 b Fz(\031)831 2213 y Fl(\003)898 2249 y Fs( )27 b Fz(\031)309 2370 y FH(8)414 b Fz(i)28 b Fs( )f FA(0)309 2490 y FH(10)211 b Fw(end-if)309 2610 y FH(11)g Fw(if)32 b FH(n)m(\372mero)g(de)h(itera\347\365)s(es)f(desde) i(a)f(\372ltima)c(melhoria)h(em)i Fz(\031)37 b FH(for)32 b(igual)e(a)j Fz(\013)g Fw(then)309 2731 y FH(12)365 b Fz(\031)831 2695 y Fl(0)882 2731 y Fs( )32 b Fk (IntensificacaoDiversificac)q(ao)p FH(\()p Fz(\031)t FH(\))309 2851 y(13)365 b Fz(\031)32 b Fs( )g Fk(CriterioAceitacao)p FH(\()p Fz(\031)t(;)17 b(\031)2058 2815 y Fl(0)2085 2851 y FH(\))309 2972 y(14)365 b Fw(if)32 b Fz(custo)p FA(\()p Fz(\031)t FA(\))27 b Fz(<)h(custo)p FA(\()p Fz(\031)1685 2935 y Fl(\003)1723 2972 y FA(\))33 b Fw(then)309 3092 y FH(15)520 b Fz(\031)986 3056 y Fl(\003)1053 3092 y Fs( )27 b Fz(\031)309 3212 y FH(16)520 b Fz(i)27 b Fs( )h FA(0)309 3333 y FH(17)365 b Fw(end-if)309 3453 y FH(19)211 b Fw(end-if)309 3573 y FH(20)g Fw(if)32 b FH(n)m(\372mero)g(de)h (itera\347\365)s(es)f(desde)i(a)f(\372ltima)c(melhoria)h(em)i Fz(\031)37 b FH(for)32 b(igual)e(a)j Fz(\014)38 b Fw(then)309 3694 y FH(21)365 b Fw(if)32 b Fz(custo)p FA(\()p Fz(\031)t FA(\))27 b(=)h Fz(custo)p FA(\()p Fz(\031)1685 3658 y Fl(\003)1723 3694 y FA(\))33 b Fw(then)309 3814 y FH(22)520 b Fz(\031)31 b Fs( )h Fk(Reinicializacao)p FH(\()p Fz(\031)t FH(\))309 3935 y(23)520 b Fz(i)27 b Fs( )h Fz(i)22 b FA(+)g(1)309 4055 y FH(24)365 b Fw(else)32 b Fz(\031)g Fs( )27 b Fz(\031)1255 4019 y Fl(\003)309 4175 y FH(25)211 b Fw(end-if)309 4296 y FH(26)56 b Fw(end-while)309 4416 y FH(27)g Fw(return)33 b Fz(\031)866 4380 y Fl(\003)309 4537 y Fw(end)g Fk(ILS_HPRC)p FH(;)p 3745 4598 V 248 4601 3501 4 v 411 4869 a(Figura)e(6.3:)43 b(Pseudo-c\363)s(digo)32 b(do)g(algoritmo)d(para)j(otimizar)e(o)i(primeiro)e(ob)5 b(jetiv)m(o.)p eop %%Page: 37 51 37 50 bop 109 726 a FD(Cap\355tulo)64 b(7)109 1390 y(Otimiza\347\343o) 78 b(do)f(Segundo)f(e)g(T)-16 b(erceiro)77 b(Ob)10 b(je-)109 1639 y(tiv)-5 b(os)274 2301 y FH(Neste)40 b(cap\355tulo,)e(apresen)m (tam-se)h(as)g(estrat\351gias)f(desen)m(v)m(olvidas)i(para)e(a)g (otimiza\347\343o)e(do)i(se-)109 2464 y(gundo)33 b(e)g(terceiro)g(ob)5 b(jetiv)m(os)34 b(do)f(PSC:)h(minimizar)29 b(o)k(n)m(\372mero)g(de)g (viola\347\365)s(es)f(de)i(restri\347\365)s(es)f(de)h(ca-)109 2626 y(pacidade)f(de)i(baixa)e(prioridade)g(e)h(minimizar)c(o)k(n)m (\372mero)g(de)g(tro)s(cas)g(de)g(cores,)i(resp)s(ectiv)-5 b(amen)m(te.)109 2789 y(As)40 b(duas)h(estrat\351gias)e(t\352m)h (algumas)e(similaridades,)g(como)h(p)s(or)h(exemplo)f(a)h (metaheur\355stica)e(na)109 2951 y(qual)e(s\343o)h(baseadas.)57 b(Na)36 b(pr\363)m(xima)g(se\347\343o,)i(apresen)m(ta-se)g(uma)e(brev)m (e)j(descri\347\343o)e(da)f(metaheur\355s-)109 3114 y(tica)k(VNS)h(\()p FE(V)-7 b(ariable)41 b(Neighb)-5 b(orho)g(o)g(d)41 b(Se)-5 b(ar)g(ch)7 b FH(\))41 b([6])g(utilizada)d(nos)j(dois)f(algoritmos.)66 b(Nas)41 b(se\347\365)s(es)109 3276 y(seguin)m(tes,)34 b(os)g(algoritmos)c(desen)m(v)m(olvidos)k(para)f(otimizar)e(o)i (segundo)h(e)f(o)h(terceiro)e(ob)5 b(jetiv)m(os)34 b(s\343o)109 3439 y(descritos.)109 3830 y Fx(7.1)155 b Ff(V)-13 b(ariable)61 b(Neighb)-9 b(orho)g(o)g(d)61 b(Se)-9 b(ar)g(ch)274 4151 y FH(A)34 b(metaheur\355stica)e(VNS)i(\351)g(baseada)h(na)e(id\351ia)f (de)j(tro)s(car)e(sistematicamen)m(te)f(as)i(vizinhan\347as)109 4313 y(utilizadas)e(na)j(busca.)51 b(Cada)35 b(itera\347\343o)f (consiste)i(em)e(aplicar)f(uma)h(fase)h(de)h(p)s(erturba\347\343o)e (seguida)109 4476 y(p)s(or)27 b(uma)g(busca)i(lo)s(cal.)39 b(As)28 b(vizinhan\347as)g(utilizadas)e(na)h(p)s(erturba\347\343o)h (crescem)h(\340)e(medida)g(que)h(n\343o)109 4638 y(se)34 b(conseguem)g(melhoramen)m(tos)d(na)i(solu\347\343o)g(atual.)44 b(O)33 b(princ\355pio)e(\351)j(iniciar)c(o)j(pro)s(cesso)i(de)e(busca) 109 4801 y(explorando)27 b(vizinhan\347as)h(menores,)h(com)e (solu\347\365)s(es)h(mais)e(\020pr\363)m(ximas\021)34 b(da)28 b(solu\347\343o)f(atual,)h(e)g(passar)109 4963 y(a)d(explorar)g(solu\347\365)s(es)h(mais)e(\020distan)m(tes\021)34 b(quando)26 b(n\343o)f(se)i(conseguir)f(melhoria)d(na)i(vizinhan\347a)g (atual)109 5126 y(da)32 b(solu\347\343o.)274 5347 y(A)i(Figura)e(6.1)i (apresen)m(ta)h(o)e(pseudo-c\363)s(digo)h(da)f(metaheur\355stica)g (VNS.)h(O)g(conjun)m(to)g(de)h(vizi-)109 5510 y(nhan\347as)e(que)h (ser\343o)f(utilizadas)d(na)j(fase)g(de)g(p)s(erturba\347\343o)g(\351)g (denotado)g(p)s(or)f Fz(N)3111 5525 y Ft(k)3154 5510 y FH(,)g Fz(k)f FA(=)d(1)p Fz(;)17 b(:)g(:)g(:)f(;)h(k)3718 5525 y Ft(max)3861 5510 y FH(.)109 5672 y(O)43 b(pro)s(cesso)h(de)g (busca)g(\351)g(iniciado)d(a)i(partir)f(de)i(uma)f(solu\347\343o)g (gerada)g(p)s(or)g(alguma)e(heur\355stica)109 5835 y(construtiv)-5 b(a)41 b(\(linha)g(1\).)72 b(Inicia-se)41 b(a)h(busca)h(a)f(partir)f (da)h(vizinhan\347a)g(de)h(menor)e(ordem)h(\(linha)p eop %%Page: 38 52 38 51 bop 109 -28 a FB(7.2)60 b(Algoritmo)32 b(para)f(o)f(segundo)h(ob) 5 b(jetiv)m(o)2138 b(38)p 109 9 3780 4 v 109 256 a FH(3\).)42 b(Em)29 b(cada)g(itera\347\343o,)g(aplica-se)e(uma)i(p)s (erturba\347\343o)g(den)m(tro)h(da)f(vizinhan\347a)g(corren)m(te)h (\(linha)d(5\),)109 418 y(aplica-se)i(uma)g(busca)j(lo)s(cal)c(na)i (solu\347\343o)g(obtida)f(\(linha)g(6\))h(e)h(utiliza-se)d(um)i (crit\351rio)f(de)i(aceita\347\343o)109 581 y(para)j(atualizar)e(a)j (solu\347\343o)f(atual)f(\(linha)g(7\).)49 b(Nas)35 b(linhas)e(8)i(e)g (9,)f(de\034ne-se)j(qual)d(vizinhan\347a)g(ser\341)109 743 y(utilizada)29 b(na)j(pr\363)m(xima)e(itera\347\343o.)43 b(Se)32 b(a)g(solu\347\343o)f(obtida)g(ap)s(\363s)g(a)h(busca)h(lo)s (cal)d(for)h(aceita,)g(passa-se)109 906 y(a)39 b(explorar)g(a)g(menor)h (vizinhan\347a)f(desta)h(no)m(v)-5 b(a)39 b(solu\347\343o;)k(caso)d (con)m(tr\341rio,)g(explora-se)g(uma)f(vizi-)109 1068 y(nhan\347a)c(de)g(mais)e(alta)g(ordem)h(com)g(solu\347\365)s(es)h (mais)e(distan)m(tes)i(da)g(solu\347\343o)f(atual.)49 b(Este)35 b(pro)s(cesso)109 1231 y(p\341ra)44 b(quando)h(a)f (vizinhan\347a)g(de)h(maior)e(ordem)h(de\034nida)g(for)g(atingida)f (\(linha)f(4\).)80 b(A)m(t\351)45 b(que)g(a)109 1393 y(condi\347\343o)32 b(de)h(parada)f(seja)h(encon)m(trada,)g(iniciam-se) d(no)m(v)-5 b(as)33 b(itera\347\365)s(es)f(do)g(algoritmo)d(\(linha)i (2\).)p 886 1656 2225 4 v 886 3474 4 1819 v 947 1848 a Fw(pro)s(cedure)i Fk(VNS)p FH(\(\);)947 1968 y(1)105 b Fz(s)1147 1932 y Fl(\003)1214 1968 y Fs( )32 b Fk(GeraSolucaoInicial) p FH(\(\))947 2089 y(2)105 b Fw(while)31 b FH(condi\347\343o)h(de)h (parada)f(n\343o)h(encon)m(trada)g Fw(do)947 2209 y FH(3)260 b Fz(k)30 b Fs( )e FA(1)947 2329 y FH(4)260 b Fw(while)31 b Fz(k)f Fs(\024)f Fz(k)1783 2344 y Ft(max)1959 2329 y Fw(do)947 2450 y FH(5)414 b Fz(s)1456 2414 y Fl(0)1507 2450 y Fs( )32 b Fk(Perturbacao)p FH(\()p Fz(s)2284 2414 y Fl(\003)2326 2450 y Fz(;)17 b(N)2448 2465 y Ft(k)2491 2450 y FH(\))947 2570 y(6)414 b Fz(s)1456 2534 y Fl(0)1507 2570 y Fs( )32 b Fk(BuscaLocal)p FH(\()p Fz(s)2233 2534 y Fl(0)2259 2570 y FH(\))947 2691 y(7)414 b Fz(s)1456 2654 y Fl(\003)1523 2691 y Fs( )32 b Fk(CriterioAceitacao)p FH(\()p Fz(s)2606 2654 y Fl(\003)2650 2691 y Fz(;)17 b(s)2740 2654 y Fl(0)2763 2691 y FH(\))947 2811 y(8)414 b Fw(if)32 b Fz(s)1554 2775 y Fl(\003)1621 2811 y FA(=)c Fz(s)1771 2775 y Fl(0)1826 2811 y Fw(then)33 b Fz(k)e Fs( )c FA(1)947 2931 y FH(9)414 b Fw(else)32 b Fz(k)f Fs( )c Fz(k)e FA(+)d(1)947 3052 y FH(10)211 b Fw(end-while)947 3172 y FH(11)56 b Fw(end-while)947 3292 y FH(12)g Fw(return)37 b Fv(s)1502 3256 y Fh(\003)947 3413 y Fw(end)c Fk(VNS)p FH(;)p 3107 3474 V 886 3477 2225 4 v 913 3745 a(Figura)e(7.1:)43 b(Pseudo-c\363)s(digo)32 b(da)g(metaheur\355stica)f(VNS.)109 4189 y Fx(7.2)155 b(Algoritmo)54 b(para)f(o)f(segundo)h(ob)9 b(jetiv)l(o)274 4509 y FH(Este)36 b(algoritmo)31 b(tem)k(como)f (solu\347\343o)h(inicial)c(a)k(melhor)e(solu\347\343o)i(obtida)f(p)s (elo)g(algoritmo)d(que)109 4671 y(otimiza)36 b(o)i(primeiro)f(ob)5 b(jetiv)m(o.)62 b(Agora,)40 b(os)f(dois)f(primeiros)f(ob)5 b(jetiv)m(os)39 b(do)g(problema)e(s\343o)i(consi-)109 4834 y(derados.)59 b(A)37 b(id\351ia)f(\351)i(otimizar)c(o)k(segundo)g (ob)5 b(jetiv)m(o)37 b(sem)h(deteriorar)f(o)g(primeiro,)f(cujo)i(v)-5 b(alor)36 b(j\341)109 4996 y(foi)k(otimizado)e(an)m(teriormen)m(te.)70 b(Em)m(b)s(ora)40 b(n\343o)h(o)s(corra)g(com)f(freq\374\352ncia,)k (\351)e(p)s(oss\355v)m(el)f(que)h(o)f(pri-)109 5159 y(meiro)29 b(ob)5 b(jetiv)m(o)31 b(ainda)f(seja)h(reduzido)g(p)s(or)g(este)h (algoritmo.)39 b(Nas)32 b(se\347\365)s(es)g(seguin)m(tes,)h(apresen)m (ta-se)109 5321 y(cada)38 b(etapa)f(que)i(in)m(tegra)e(o)h(algoritmo)c (desen)m(v)m(olvido)39 b(para)f(minimizar)c(o)j(n)m(\372mero)h(de)g (viola\347\365)s(es)109 5484 y(de)33 b(restri\347\365)s(es)g(de)g (capacidade)f(de)h(baixa)f(prioridade,)f(conforme)h(foi)f(feito)g(no)i (Cap\355tulo)e(6.)p eop %%Page: 39 53 39 52 bop 109 -28 a FB(7.2)60 b(Algoritmo)32 b(para)f(o)f(segundo)h(ob) 5 b(jetiv)m(o)2138 b(39)p 109 9 3780 4 v 109 256 a FJ(7.2.1)129 b(P)l(erturba\347\343o)274 541 y FH(Diferen)m(temen)m(te)33 b(da)g(fase)g(de)f(p)s(erturba\347\343o)h(do)f(algoritmo)d(an)m (terior,)i(que)j(otimiza)29 b(o)k(primeiro)109 704 y(ob)5 b(jetiv)m(o,)43 b(observ)m(ou-se,)i(a)40 b(partir)g(de)i(testes)g (preliminares,)f(que)h(a)e(utiliza\347\343o)f(de)i(dois)g(tip)s(os)f (de)109 866 y(p)s(erturba\347\343o)29 b(diferen)m(tes)h(no)f(algoritmo) d(resulta)j(em)f(solu\347\365)s(es)i(de)f(melhor)f(qualidade.)42 b(O)29 b(primeiro)109 1029 y(tip)s(o)45 b(de)h(p)s(erturba\347\343o)g (utilizado)e(\351)j(semelhan)m(te)f(\340quele)g(utilizado)e(no)i (Cap\355tulo)f(6:)70 b(destr\363i-se)109 1191 y(parcialmen)m(te)35 b(a)h(solu\347\343o,)h(retirando-se)g(alguns)f(carros)h(en)m(v)m (olvidos)g(em)f(viola\347\365)s(es)f(da)i(seq\374\352ncia)109 1354 y(escalonada,)j(e)g(estes)h(s\343o)e(inseridos)g(no)m(v)-5 b(amen)m(te)40 b(na)f(solu\347\343o)f(em)h(uma)g(ordem)g(aleat\363ria,) f(o)h(que)109 1517 y(equiv)-5 b(ale)32 b(\340)g(aplica\347\343o)e (consecutiv)-5 b(a)33 b(de)g(mo)m(vimen)m(tos)f FE(shift)p FH(.)274 1738 y(O)c(segundo)h(tip)s(o)e(de)i(p)s(erturba\347\343o)f (utilizado)e(\351)i(baseado)h(na)f(aplica\347\343o)f(de)i(mo)m(vimen)m (tos)e FE(swap)p FH(.)109 1901 y(Esta)45 b(p)s(erturba\347\343o)f (aplica)e(sucessiv)-5 b(amen)m(te)46 b(um)e(determinado)f(n)m(\372mero) i(de)g(mo)m(vimen)m(tos)e FE(swap)109 2063 y FH(aleat\363rios)32 b(na)i(solu\347\343o)g(atual,)g(sem)g(considerar)h(o)f(custo)h(dos)g (mo)m(vimen)m(tos.)48 b(V)-8 b(ale)34 b(lem)m(brar)f(que)i(o)109 2226 y(custo)i(considerado)g(neste)h(algoritmo)33 b(refere-se)38 b(ap)s(enas)f(ao)g(n)m(\372mero)g(de)g(viola\347\365)s(es)f(de)h (restri\347\365)s(es)109 2388 y(de)48 b(capacidade)g(de)h(alta)d(e)i (de)h(baixa)e(prioridade.)88 b(A)48 b(Figura)f(7.2)g(ilustra)g(a)g (aplica\347\343o)g(desta)109 2551 y(p)s(erturba\347\343o,)31 b(atra)m(v)m(\351s)i(de)e(tr\352s)h(mo)m(vimen)m(tos)e(aleat\363rios.) 41 b(A)32 b(Figura)d(7.2\(a\))i(mostra)f(a)h(solu\347\343o)f(na)109 2713 y(qual)38 b(a)i(p)s(erturba\347\343o)f(\351)h(aplicada,)f(as)g (letras)g(represen)m(tam)i(os)e(carros)h(da)f(solu\347\343o.)63 b(As)40 b(solu\347\365)s(es)109 2876 y(das)d(Figuras)f(7.2)h(\(b\),)i (\(c\))e(e)h(\(d\))f(s\343o)h(as)f(solu\347\365)s(es)h(obtidas)e(p)s (ela)h(aplica\347\343o)e(consecutiv)-5 b(a)38 b(de)g(tr\352s)109 3038 y(mo)m(vimen)m(tos)28 b FE(swap)35 b FH(aleat\363rios.)40 b(No)30 b(primeiro)d(mo)m(vimen)m(to,)h(tro)s(cam-se)h(as)g(p)s (osi\347\365)s(es)h(dos)g(carros)f(B)109 3201 y(e)h(F;)g(no)h(segundo,) h(os)e(carros)h(E)f(e)h(M)g(s\343o)f(tro)s(cados)g(e,)i(p)s(or)e (\034m,)g(os)h(carros)f(M)h(e)g(I)f(s\343o)h(tro)s(cados.)42 b(A)109 3363 y(solu\347\343o)32 b(da)g(Figura)f(7.2\(d\))h(\351)h(a)f (solu\347\343o)g(obtida)f(ap)s(\363s)i(a)f(p)s(erturba\347\343o.)863 5376 y currentpoint currentpoint translate 0.55363 0.55363 scale neg exch neg exch translate 863 5376 a @beginspecial 18 @llx 227 @lly 510 @urx 611 @ury 4920 @rwi @setspecial %%BeginDocument: perturb2.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 18 227 510 611 %%Creator: CorelDRAW 7 %%Title: %%CreationDate: Fri Feb 11 14:27:57 2005 %%DocumentProcessColors: Black %%DocumentSuppliedResources: (atend) %%EndComments %%BeginProlog /AutoFlatness true def /AutoSteps 0 def /CMYKMarks false def /UseLevel2 false def %Color profile: _DEFAULT.CCM - Gen. Profil -Sem %%BeginResource: procset wCorel7Dict 7.0 0 /wCorel7Dict 300 dict def wCorel7Dict begin % Copyright (c)1992-96 Corel Corporation % All rights reserved. v7.0 r1.0 /bd{bind def}bind def/ld{load def}bd/xd{exch def}bd/_ null def/rp{{pop}repeat} bd/@cp/closepath ld/@gs/gsave ld/@gr/grestore ld/@np/newpath ld/Tl/translate ld /$sv 0 def/@sv{/$sv save def}bd/@rs{$sv restore}bd/spg/showpage ld/showpage{} bd currentscreen/@dsp xd/$dsp/@dsp def/$dsa xd/$dsf xd/$sdf false def/$SDF false def/$Scra 0 def/SetScr/setscreen ld/setscreen{pop pop pop}bd/@ss{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if exch $Scra add exch load SetScr}bd /SepMode_5 where{pop}{/SepMode_5 0 def}ifelse/CurrentInkName_5 where{pop} {/CurrentInkName_5(Composite)def}ifelse/$ink_5 where{pop}{/$ink_5 -1 def} ifelse/$c 0 def/$m 0 def/$y 0 def/$k 0 def/$t 1 def/$n _ def/$o 0 def/$fil 0 def/$C 0 def/$M 0 def/$Y 0 def/$K 0 def/$T 1 def/$N _ def/$O 0 def/$PF false def/s1c 0 def/s1m 0 def/s1y 0 def/s1k 0 def/s1t 0 def/s1n _ def/$bkg false def /SK 0 def/SM 0 def/SY 0 def/SC 0 def/$op false def matrix currentmatrix/$ctm xd /$ptm matrix def/$ttm matrix def/$stm matrix def/$ffpnt true def /CorelDrawReencodeVect[16#0/grave 16#5/breve 16#6/dotaccent 16#8/ring 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl 16#88/circumflex/perthousand/Scaron/guilsinglleft/OE 16#91/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash 16#98/tilde/trademark/scaron/guilsinglright/oe 16#9F/Ydieresis 16#A1/exclamdown/cent/sterling/currency/yen/brokenbar/section 16#a8/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/minus/registered/macron 16#b0/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered 16#b8/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown 16#c0/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla 16#c8/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis 16#d0/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply 16#d8/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls 16#e0/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla 16#e8/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis 16#f0/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide 16#f8/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis]def /L2?/languagelevel where{pop languagelevel 2 ge}{false}ifelse def /@BeginSysCorelDict{systemdict/Corel30Dict known{systemdict/Corel30Dict get exec}if}bd/@EndSysCorelDict{systemdict/Corel30Dict known{end}if}bd AutoFlatness {/@ifl{dup currentflat exch sub 10 gt{ ([Error: PathTooComplex; OffendingCommand: AnyPaintingOperator]\n)print flush @np exit}{currentflat 2 add setflat}ifelse}bd/@fill/fill ld/fill{currentflat{ {@fill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@eofill/eofill ld/eofill {currentflat{{@eofill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@clip /clip ld/clip{currentflat{{@clip}stopped{@ifl}{exit}ifelse}bind loop setflat} bd/@eoclip/eoclip ld/eoclip{currentflat{{@eoclip}stopped{@ifl}{exit}ifelse} bind loop setflat}bd/@stroke/stroke ld/stroke{currentflat{{@stroke}stopped {@ifl}{exit}ifelse}bind loop setflat}bd}if L2?{/@ssa{true setstrokeadjust}bd}{ /@ssa{}bd}ifelse/d/setdash ld/j/setlinejoin ld/J/setlinecap ld/M/setmiterlimit ld/w/setlinewidth ld/O{/$o xd}bd/R{/$O xd}bd/W/eoclip ld/c/curveto ld/C/c ld/l /lineto ld/L/l ld/rl/rlineto ld/m/moveto ld/n/newpath ld/N/newpath ld/P{11 rp} bd/u{}bd/U{}bd/A{pop}bd/q/@gs ld/Q/@gr ld/&{}bd/@j{@sv @np}bd/@J{@rs}bd/g{1 exch sub/$k xd/$c 0 def/$m 0 def/$y 0 def/$t 1 def/$n _ def/$fil 0 def}bd/G{1 sub neg/$K xd _ 1 0 0 0/$C xd/$M xd/$Y xd/$T xd/$N xd}bd/k{1 index type /stringtype eq{/$t xd/$n xd}{/$t 0 def/$n _ def}ifelse/$k xd/$y xd/$m xd/$c xd /$fil 0 def}bd/K{1 index type/stringtype eq{/$T xd/$N xd}{/$T 0 def/$N _ def} ifelse/$K xd/$Y xd/$M xd/$C xd}bd/x/k ld/X/K ld/sf{1 index type/stringtype eq{ /s1t xd/s1n xd}{/s1t 0 def/s1n _ def}ifelse/s1k xd/s1y xd/s1m xd/s1c xd}bd/i{ dup 0 ne{setflat}{pop}ifelse}bd/v{4 -2 roll 2 copy 6 -2 roll c}bd/V/v ld/y{2 copy c}bd/Y/y ld/@w{matrix rotate/$ptm xd matrix scale $ptm dup concatmatrix /$ptm xd 1 eq{$ptm exch dup concatmatrix/$ptm xd}if 1 w}bd/@g{1 eq dup/$sdf xd {/$scp xd/$sca xd/$scf xd}if}bd/@G{1 eq dup/$SDF xd{/$SCP xd/$SCA xd/$SCF xd} if}bd/@D{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if 3 copy exch $Scra add exch load SetScr/$dsp xd/$dsa xd/$dsf xd}bd/$ngx{$SDF{$SCF SepMode_5 0 eq{$SCA} {$dsa}ifelse $SCP @ss}if}bd/p{/$pm xd 7 rp/$pyf xd/$pxf xd/$pn xd/$fil 1 def} bd/@MN{2 copy le{pop}{exch pop}ifelse}bd/@MX{2 copy ge{pop}{exch pop}ifelse}bd /InRange{3 -1 roll @MN @MX}bd/@sqr{dup 0 rl dup 0 exch rl neg 0 rl @cp}bd /currentscale{1 0 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt 0 1 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt}bd/@unscale{}bd/wDstChck{2 1 roll dup 3 -1 roll eq{1 add}if}bd /@dot{dup mul exch dup mul add 1 exch sub}bd/@lin{exch pop abs 1 exch sub}bd /cmyk2rgb{3{dup 5 -1 roll add 1 exch sub dup 0 lt{pop 0}if exch}repeat pop}bd /rgb2cmyk{3{1 exch sub 3 1 roll}repeat 3 copy @MN @MN 3{dup 5 -1 roll sub neg exch}repeat}bd/rgb2g{2 index .299 mul 2 index .587 mul add 1 index .114 mul add 4 1 roll pop pop pop}bd/WaldoColor_5 where{pop}{/SetRgb/setrgbcolor ld/GetRgb /currentrgbcolor ld/SetGry/setgray ld/GetGry/currentgray ld/SetRgb2 systemdict /setrgbcolor get def/GetRgb2 systemdict/currentrgbcolor get def/SetHsb systemdict/sethsbcolor get def/GetHsb systemdict/currenthsbcolor get def /rgb2hsb{SetRgb2 GetHsb}bd/hsb2rgb{3 -1 roll dup floor sub 3 1 roll SetHsb GetRgb2}bd/setcmykcolor where{pop/SetCmyk_5/setcmykcolor ld}{/SetCmyk_5{ cmyk2rgb SetRgb}bd}ifelse/currentcmykcolor where{pop/GetCmyk/currentcmykcolor ld}{/GetCmyk{GetRgb rgb2cmyk}bd}ifelse/setoverprint where{pop}{/setoverprint{ /$op xd}bd}ifelse/currentoverprint where{pop}{/currentoverprint{$op}bd}ifelse /@tc_5{5 -1 roll dup 1 ge{pop}{4{dup 6 -1 roll mul exch}repeat pop}ifelse}bd /@trp{exch pop 5 1 roll @tc_5}bd/setprocesscolor_5{SepMode_5 0 eq{SetCmyk_5}{0 4 $ink_5 sub index exch pop 5 1 roll pop pop pop pop SepsColor true eq{$ink_5 3 gt{1 sub neg SetGry}{0 0 0 4 $ink_5 roll SetCmyk_5}ifelse}{1 sub neg SetGry} ifelse}ifelse}bd/findcmykcustomcolor where{pop}{/findcmykcustomcolor{5 array astore}bd}ifelse/setcustomcolor where{pop}{/setcustomcolor{exch aload pop SepMode_5 0 eq{pop @tc_5 setprocesscolor_5}{CurrentInkName_5 eq{4 index}{0} ifelse 6 1 roll 5 rp 1 sub neg SetGry}ifelse}bd}ifelse/@scc_5{dup type /booleantype eq{setoverprint}{1 eq setoverprint}ifelse dup _ eq{pop setprocesscolor_5 pop}{findcmykcustomcolor exch setcustomcolor}ifelse SepMode_5 0 eq{true}{GetGry 1 eq currentoverprint and not}ifelse}bd/colorimage where{pop /ColorImage{colorimage}def}{/ColorImage{/ncolors xd pop/dataaq xd{dataaq ncolors dup 3 eq{/$dat xd 0 1 $dat length 3 div 1 sub{dup 3 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length 3 idiv getinterval pop}{4 eq{/$dat xd 0 1 $dat length 4 div 1 sub{dup 4 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div $dat 4 index 3 add get 255 div cmyk2rgb rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length ncolors idiv getinterval}if}ifelse}image}bd }ifelse/setcmykcolor{1 5 1 roll _ currentoverprint @scc_5/$ffpnt xd}bd /currentcmykcolor{0 0 0 0}bd/setrgbcolor{rgb2cmyk setcmykcolor}bd /currentrgbcolor{currentcmykcolor cmyk2rgb}bd/sethsbcolor{hsb2rgb setrgbcolor} bd/currenthsbcolor{currentrgbcolor rgb2hsb}bd/setgray{dup dup setrgbcolor}bd /currentgray{currentrgbcolor rgb2g}bd}ifelse/WaldoColor_5 true def/@sft{$tllx $pxf add dup $tllx gt{$pwid sub}if/$tx xd $tury $pyf sub dup $tury lt{$phei add}if/$ty xd}bd/@stb{pathbbox/$ury xd/$urx xd/$lly xd/$llx xd}bd/@ep{{cvx exec }forall}bd/@tp{@sv/$in true def 2 copy dup $lly le{/$in false def}if $phei sub $ury ge{/$in false def}if dup $urx ge{/$in false def}if $pwid add $llx le{/$in false def}if $in{@np 2 copy m $pwid 0 rl 0 $phei neg rl $pwid neg 0 rl 0 $phei rl clip @np $pn cvlit load aload pop 7 -1 roll 5 index sub 7 -1 roll 3 index sub Tl matrix currentmatrix/$ctm xd @ep pop pop pop pop}{pop pop}ifelse @rs}bd /@th{@sft 0 1 $tly 1 sub{dup $psx mul $tx add{dup $llx gt{$pwid sub}{exit} ifelse}loop exch $phei mul $ty exch sub 0 1 $tlx 1 sub{$pwid mul 3 copy 3 -1 roll add exch @tp pop}for pop pop}for}bd/@tv{@sft 0 1 $tlx 1 sub{dup $pwid mul $tx add exch $psy mul $ty exch sub{dup $ury lt{$phei add}{exit}ifelse}loop 0 1 $tly 1 sub{$phei mul 3 copy sub @tp pop}for pop pop}for}bd/$fm 0 def/wfill{1 $fm eq{fill}{eofill}ifelse}bd/wclip{1 $fm eq{clip}{eoclip}ifelse}bd/@pf{@gs $ctm setmatrix $pm concat @stb wclip Bburx Bbury $pm itransform/$tury xd/$turx xd Bbllx Bblly $pm itransform/$tlly xd/$tllx xd/$wid $turx $tllx sub def/$hei $tury $tlly sub def @gs $vectpat{1 0 0 0 0 _ $o @scc_5{wfill}if}{$t $c $m $y $k $n $o @scc_5{SepMode_5 0 eq $pfrg or{$tllx $tlly Tl $wid $hei scale <00> 8 1 false[8 0 0 1 0 0]{}imagemask}{/$bkg true def}ifelse}if}ifelse @gr $wid 0 gt $hei 0 gt and{$pn cvlit load aload pop/$pd xd 3 -1 roll sub/$phei xd exch sub /$pwid xd $wid $pwid div ceiling 1 add/$tlx xd $hei $phei div ceiling 1 add /$tly xd $psx 0 eq{@tv}{@th}ifelse}if @gr @np/$bkg false def}bd/@Pf{@sv SepMode_5 0 eq $Psc 0 ne or $ink_5 3 eq or{0 J 0 j[]0 d $t $c $m $y $k $n $o @scc_5 pop $ctm setmatrix 72 1000 div dup matrix scale dup concat dup Bburx exch Bbury exch itransform ceiling cvi/Bbury xd ceiling cvi/Bburx xd Bbllx exch Bblly exch itransform floor cvi/Bblly xd floor cvi/Bbllx xd $Prm aload pop $Psn load exec}{1 SetGry wfill}ifelse @rs @np}bd/F{matrix currentmatrix $sdf{$scf $sca $scp @ss}if $fil 1 eq{@pf}{$fil 2 eq{@ff}{$fil 3 eq{@Pf}{$t $c $m $y $k $n $o @scc_5{wfill}{@np}ifelse}ifelse}ifelse}ifelse $sdf{$dsf $dsa $dsp @ss}if setmatrix}bd/f{@cp F}bd/S{matrix currentmatrix $ctm setmatrix $SDF{$SCF $SCA $SCP @ss}if $T $C $M $Y $K $N $O @scc_5{matrix currentmatrix $ptm concat stroke setmatrix}{@np}ifelse $SDF{$dsf $dsa $dsp @ss}if setmatrix}bd/s{@cp S}bd/B{@gs F @gr S}bd/b{@cp B}bd/_E{5 array astore exch cvlit xd}bd/@cc{currentfile $dat readhexstring pop}bd/@sm{/$ctm $ctm currentmatrix def}bd/@E{/Bbury xd/Bburx xd /Bblly xd/Bbllx xd}bd/@c{@cp}bd/@p{/$fil 1 def 1 eq dup/$vectpat xd{/$pfrg true def}{@gs $t $c $m $y $k $n $o @scc_5/$pfrg xd @gr}ifelse/$pm xd/$psy xd/$psx xd /$pyf xd/$pxf xd/$pn xd}bd/@P{/$fil 3 def/$Psn xd/$Psc xd array astore/$Prm xd }bd/@ii{concat 3 index 3 index m 3 index 1 index l 2 copy l 1 index 3 index l 3 index 3 index l clip pop pop pop pop}bd/tcc{@cc}def/@i{@sm @gs @ii 6 index 1 ne {/$frg true def pop pop}{1 eq{s1t s1c s1m s1y s1k s1n $O @scc_5/$frg xd}{/$frg false 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-28 a FB(7.2)60 b(Algoritmo)32 b(para)f(o)f(segundo)h(ob) 5 b(jetiv)m(o)2138 b(42)p 109 9 3780 4 v 109 256 a FJ(7.2.5)129 b(Estrutura)45 b(geral)f(do)g(algoritmo)274 541 y FH(O)22 b(algoritmo)c(considera)23 b(o)e(primeiro)f(e)j(segundo)g(ob)5 b(jetiv)m(os)22 b(dos)h(problema)d(e)j(tem)f(como)f(solu\347\343o)109 704 y(inicial)27 b(aquela)j(obtida)g(p)s(elo)g(algoritmo)d(que)32 b(otimiza)c(o)i(primeiro)f(ob)5 b(jetiv)m(o.)43 b(Em)m(b)s(ora)30 b(com)g(menor)109 866 y(freq\374\352ncia,)j(o)f(primeiro)e(ob)5 b(jetiv)m(o)33 b(ainda)e(p)s(o)s(de)i(ser)g(minimizado)28 b(p)s(or)k(este)i(algoritmo.)274 1088 y(Cada)i(itera\347\343o)e(do)i (algoritmo)c(\351)k(comp)s(osta)f(p)s(or)g(duas)i(etapas:)50 b(p)s(erturba\347\343o)36 b(e)g(busca)g(lo)s(cal,)109 1251 y(que)30 b(s\343o)g(aplicadas)e(conforme)h(descrito)g(a)h(seguir.) 42 b(Inicialmen)m(te,)28 b(obt\351m-se)h(uma)g(solu\347\343o)g(atra)m (v)m(\351s)109 1413 y(de)45 b(uma)f(p)s(erturba\347\343o)h(na)f (solu\347\343o)h(atual.)78 b(A)45 b(p)s(erturba\347\343o)g(aplica)e(mo) m(vimen)m(tos)h(na)h(primeira)109 1576 y(vizinhan\347a)24 b(e)i(passa)g(a)f(utilizar)e(vizinhan\347as)i(maiores)f(\340)i(medida)e (que)i(a)f(solu\347\343o)g(n\343o)g(\351)h(melhorada.)109 1738 y(Ap)s(\363s)45 b(a)g(p)s(erturba\347\343o,)j(aplica-se)43 b(a)i(busca)h(lo)s(cal)d(r\341pida)h(com)g(mo)m(vimen)m(tos)g Fz(sw)s(ap)h FH(na)g(solu\347\343o)109 1901 y("p)s(erturbada",)30 b(obtendo-se)h(uma)f(solu\347\343o)g(aprimorada.)41 b(O)30 b(crit\351rio)f(de)i(aceita\347\343o)f(desta)h(solu\347\343o)109 2063 y(\351)i(igual)e(ao)i(do)g(algoritmo)c(an)m(terior:)44 b(a)33 b(solu\347\343o)g(\351)g(aceita)f(se)i(o)f(seu)h(custo)g(for)f (melhor)f(ou)h(igual)e(ao)109 2226 y(da)h(solu\347\343o)h(atual.)43 b(Se)33 b(esta)h(solu\347\343o)e(obtida)g(p)s(ela)g(busca)h(lo)s(cal)e (for)h(melhor)g(que)i(a)e(solu\347\343o)g(atual,)109 2388 y(utiliza-se)22 b(a)j(menor)f(vizinhan\347a)g(da)h(p)s (erturba\347\343o)g(corren)m(te)h(na)e(itera\347\343o)g(seguin)m(te;)k (caso)d(con)m(tr\341rio,)109 2551 y(utiliza-se)h(uma)i(vizinhan\347a)g (maior.)40 b(Quando)28 b(a)g(p)s(erturba\347\343o)h(corren)m(te)g (atingir)e(a)h(sua)h(vizinhan\347a)109 2713 y(m\341xima,)21 b(passa-se)i(a)f(aplicar)e(o)i(outro)f(tip)s(o)g(de)h(p)s (erturba\347\343o.)40 b(Neste)23 b(momen)m(to,)g(aplica-se)d(tam)m(b)s (\351m)109 2876 y(o)39 b(pro)s(cedimen)m(to)g(de)i(in)m (tensi\034ca\347\343o/div)m(ersi\034ca\347\343o)e(na)h(solu\347\343o)f (atual.)64 b(Quando)40 b(o)g(n)m(\372mero)g(de)109 3038 y(aplica\347\365)s(es)35 b(deste)j(pro)s(cedimen)m(to)e(atingir)e(um)i (v)-5 b(alor)36 b(m\341ximo)e(ou)j(quando)g(uma)f(fra\347\343o)g (m\341xima)109 3201 y(de)d(temp)s(o)g(de)h(execu\347\343o)h(for)d (excedida,)j(o)e(algoritmo)c(termina.)44 b(P)m(o)s(de-se)35 b(observ)-5 b(ar)33 b(que)i(a)e(melhor)109 3363 y(solu\347\343o)j (conhecida)h(p)s(elo)f(algoritmo)e(\351)j(a)g(sua)h(solu\347\343o)e (atual,)h(diferen)m(temen)m(te)h(do)f(algoritmo)c(do)109 3526 y(primeiro)d(ob)5 b(jetiv)m(o,)32 b(que)i(utiliza)c (reinicializa\347\343o.)274 3747 y(O)j(pseudo-c\363)s(digo)f(apresen)m (tado)i(na)f(Figura)e(7.3)i(p)s(ermite)f(obter)h(uma)f(vis\343o)g(mais) g(detalhada)109 3910 y(da)g(estrutura)i(geral)d(do)i(algoritmo.)41 b(Algumas)31 b(v)-5 b(ari\341)m(v)m(eis)32 b(e)h(par\342metros)f (utilizados)f(no)i(algoritmo)109 4072 y(s\343o)44 b(descritos)h(a)f (seguir.)79 b(Sejam)43 b Fz(\031)1512 4036 y Fl(\003)1596 4072 y FH(a)h(v)-5 b(ari\341)m(v)m(el)44 b(que)h(armazena)f(a)g (solu\347\343o)f(atual)g(\(tam)m(b)s(\351m)g(a)109 4235 y(melhor)35 b(solu\347\343o\))h(e)g Fz(\031)960 4199 y Fl(0)1020 4235 y FH(uma)g(v)-5 b(ari\341)m(v)m(el)35 b(auxiliar)f(para)i(armazenar)g(o)h(resultado)f(da)g(aplica\347\343o)f (dos)109 4397 y(pro)s(cedimen)m(tos)f(de)h(p)s(erturba\347\343o)g(e)g (busca)g(lo)s(cal.)48 b(A)34 b(v)-5 b(ari\341)m(v)m(el)34 b Fz(\036)2586 4361 y Fl(\003)2660 4397 y FH(armazena)g(o)g(custo)h(da) g(solu\347\343o)109 4560 y(atual)43 b(e)j Fz(\036)e FH(guarda)h(o)f (custo)i(da)f(solu\347\343o)f(obtida)g(ap)s(\363s)h(a)g(\372ltima)d (aplica\347\343o)h(do)i(pro)s(cedimen)m(to)109 4722 y(in)m (tensi\034ca\347\343o/div)m(ersi\034ca\347\343o.)c(A)27 b(v)-5 b(ari\341)m(v)m(el)27 b Fz(i)g FH(corresp)s(onde)h(ao)f(n)m (\372mero)g(de)h(aplica\347\365)s(es)e(de)i(in)m(tensi-)109 4885 y(\034ca\347\343o/div)m(ersi\034ca\347\343o)g(desde)i(o)e (\372ltimo)e(melhoramen)m(to)h(e)i Fz(i)2419 4900 y Ft(max)2591 4885 y FH(\351)g(o)f(par\342metro)g(que)h(estab)s(elece)g(o)109 5047 y(v)-5 b(alor)30 b(m\341ximo)f(p)s(ermitido)g(para)i Fz(i)p FH(.)43 b(As)32 b(v)-5 b(ari\341)m(v)m(eis)32 b Fz(k)i FH(e)e Fz(q)j FH(represen)m(tam)e(o)e(tamanho)f(da)i (vizinhan\347a)109 5210 y(atual)i(utilizada)e(p)s(elas)j(p)s (erturba\347\365)s(es)h(com)e FE(shift)45 b FH(e)35 b FE(swap)p FH(,)g(resp)s(ectiv)-5 b(amen)m(te.)52 b(Os)36 b(par\342metros)e Fz(k)3849 5225 y Fq(1)109 5373 y FH(e)29 b Fz(q)224 5388 y Fq(1)293 5373 y FH(determinam)f(a)h(vizinhan\347a)f (de)i(menor)f(ordem)f(e)i Fz(k)2231 5388 y Ft(max)2404 5373 y FH(e)f Fz(q)2519 5388 y Ft(max)2693 5373 y FH(determinam)e(a)i (vizinhan\347a)g(de)109 5535 y(maior)g(ordem)h(dos)i(tip)s(os)e(de)i(p) s(erturba\347\365)s(es)g(corresp)s(onden)m(tes.)45 b(Finalmen)m(te,)30 b(a)h(v)-5 b(ari\341)m(v)m(el)30 b Fz(P)44 b FH(\351)32 b(uma)109 5698 y(v)-5 b(ari\341)m(v)m(el)33 b(bin\341ria,)f(que)j(tem)e (v)-5 b(alor)33 b(1)h(se)g(a)g(p)s(erturba\347\343o)g(aplica)e(mo)m (vimen)m(tos)h Fz(shif)11 b(t)34 b FH(e)h(0)e(se)i(aplica)109 5860 y(mo)m(vimen)m(tos)c Fz(sw)s(ap)p FH(.)p eop %%Page: 43 57 43 56 bop 109 -28 a FB(7.3)60 b(Algoritmo)32 b(para)f(o)f(terceiro)i (ob)5 b(jetiv)m(o)2158 b(43)p 109 9 3780 4 v 274 256 a FH(Nas)24 b(linhas)e(1)h(e)h(2)f(do)g(pseudo-c\363)s(digo,)i(tem-se)e (a)g(inicializa\347\343o)c(de)24 b(v)-5 b(ari\341)m(v)m(eis.)40 b(P)m(o)s(de-se)25 b(observ)-5 b(ar)109 418 y(que,)28 b(primeiramen)m(te,)e(utiliza-se)f(p)s(erturba\347\343o)h(com)g(mo)m (vimen)m(tos)g FE(shift)p FH(.)41 b(Na)26 b(linha)f(4,)j(inicializam-) 109 581 y(se)48 b(as)g(vizinhan\347as)f(iniciais)d(dos)k(dois)f(tip)s (os)g(de)h(p)s(erturba\347\343o)f(e,)52 b(em)47 b(seguida,)k (inicializa-se)43 b(a)109 743 y(v)-5 b(ari\341)m(v)m(el)22 b Fz(\036)i FH(com)f(o)g(custo)i(da)e(solu\347\343o)g(atual.)39 b(Uma)23 b(itera\347\343o)g(do)g(la\347o)g Fw(while)f FH(da)i(linha)e(6)h(\351)h(comp)s(osta)109 906 y(p)s(ela)42 b(aplica\347\343o)g(da)i(p)s(erturba\347\343o)g(na)f(solu\347\343o)h (atual)e Fz(\031)2284 869 y Fl(\003)2367 906 y FH(resultando)i(na)f (solu\347\343o)g Fz(\031)3414 869 y Fl(0)3481 906 y FH(\(linha)f(7\),) 109 1068 y(seguida)23 b(p)s(ela)f(aplica\347\343o)g(da)h(busca)h(lo)s (cal)d(em)i Fz(\031)1876 1032 y Fl(0)1923 1068 y FH(\(linha)e(8\).)40 b(Na)23 b(linha)f(seguin)m(te,)k(aplica-se)c(o)h(crit\351rio)109 1231 y(de)k(aceita\347\343o:)39 b(aceita-se)26 b(a)g(solu\347\343o)g (se)h(seu)g(custo)g(for)f(menor)g(ou)g(igual)e(ao)i(custo)h(da)g (solu\347\343o)e(atual.)109 1393 y(P)m(o)s(de-se)30 b(observ)-5 b(ar)30 b(que)g(o)g(pro)s(cedimen)m(to)e(de)i(p)s(erturba\347\343o)g (receb)s(e)h(alguns)e(par\342metros)f(tais)h(como)109 1556 y(o)j(tip)s(o)g(de)h(p)s(erturba\347\343o)g Fz(P)46 b FH(e)33 b(a)f(ordem)h(da)f(vizinhan\347a)g(a)h(ser)g(utilizada,)e Fz(k)36 b FH(ou)c Fz(q)t FH(,)h(dep)s(endendo)h(do)109 1718 y(v)-5 b(alor)31 b(de)j Fz(P)14 b FH(.)45 b(O)33 b(blo)s(co)f Fw(if)g FH(da)h(linha)e(10)i(\340)g(linha)e(15)i(atualiza) e(a)i(vizinhan\347a)f(que)j(dev)m(er\341)f(ser)g(usada)109 1881 y(na)42 b(itera\347\343o)g(seguin)m(te.)74 b(Se)43 b(houv)m(er)h(melhoria)c(na)j(solu\347\343o)f(atual,)i(atualiza-se)d(o) h(melhor)g(custo)109 2043 y(\(linha)c(12\))i(e)h(a)f(vizinhan\347a)g (atual)f(passa)i(a)f(ser)h(a)f(menor;)k(caso)d(con)m(tr\341rio,)g (passa-se)h(a)e(utilizar)109 2206 y(vizinhan\347as)d(maiores)e(na)i(p)s (erturba\347\343o)g(\(linha)f(14\).)56 b(Quando)37 b(o)g(tip)s(o)f(de)h (p)s(erturba\347\343o)g(corren)m(te)109 2368 y(atinge)k(a)i (vizinhan\347a)f(de)h(ordem)f(m\341xima,)g Fz(k)1907 2383 y Ft(max)2093 2368 y FH(ou)h Fz(q)2282 2383 y Ft(max)2469 2368 y FH(\(linha)d(6\),)45 b(o)d(la\347o)g(termina.)72 b(Neste)109 2531 y(momen)m(to,)26 b(o)g(tip)s(o)e(de)j(p)s (erturba\347\343o)f(usado)g(\351)h(tro)s(cado,)f(alternando-se)g(o)g(v) -5 b(alor)24 b(da)i(v)-5 b(ari\341)m(v)m(el)25 b(bin\341ria)109 2693 y Fz(P)45 b FH(\(linha)31 b(17\),)h(e)g(aplica-se)f(o)h(pro)s (cedimen)m(to)g(de)h(in)m(tensi\034ca\347\343o/div)m (ersi\034ca\347\343o)f(na)g(solu\347\343o)f(atual)109 2856 y(\(linha)23 b(18\).)40 b(Na)25 b(linha)e(seguin)m(te,)k (atualiza-se)22 b(a)j(v)-5 b(ari\341)m(v)m(el)24 b(com)g(o)g(melhor)g (custo,)j(se)e(necess\341rio.)42 b(Nas)109 3018 y(linhas)27 b(20)h(e)g(21,)h(atualiza-se)e(a)h(v)-5 b(ari\341)m(v)m(el)27 b Fz(i)i FH(utilizada)d(no)i(crit\351rio)f(de)i(estagna\347\343o)f(do)g (algoritmo.)39 b(Se)109 3181 y(houv)m(e)c(melhoria)c(na)j (solu\347\343o)f(atual,)g(o)h(n)m(\372mero)g(de)g(aplica\347\365)s(es)f (de)i(in)m(tensi\034ca\347\343o/div)m(ersi\034ca\347\343o)109 3343 y(sem)25 b(melhoria)d(\351)k(zerado;)i(caso)d(con)m(tr\341rio,)h (ele)f(\351)g(incremen)m(tado.)40 b(O)25 b(algoritmo)d(termina)h (quando)j(as)109 3506 y(condi\347\365)s(es)j(do)g(la\347o)g Fw(while)f FH(\(linha)f(3\))i(s\343o)g(satisfeitas:)41 b(quando)30 b(o)f(n)m(\372mero)h(m\341ximo)c(de)k(aplica\347\365)s(es) 109 3668 y(de)49 b(in)m(tensi\034ca\347\343o/div)m(ersi\034ca\347\343o) f(desde)i(o)f(\372ltimo)d(melhoramen)m(to)g(\351)j(atingido)e(ou)h (quando)h(o)109 3831 y(temp)s(o)31 b(m\341ximo)g(de)i(execu\347\343o)h (\351)e(excedido.)109 4223 y Fx(7.3)155 b(Algoritmo)54 b(para)f(o)f(terceiro)j(ob)9 b(jetiv)l(o)274 4543 y FH(No)26 b(algoritmo)c(para)j(otimizar)e(o)i(n)m(\372mero)h(de)g(tro)s(cas)f(de) i(cores,)h(os)e(tr\352s)g(ob)5 b(jetiv)m(os)26 b(do)g(problema)109 4705 y(s\343o)40 b(considerados:)59 b(o)40 b(v)-5 b(alor)39 b(do)h(primeiro)e(ob)5 b(jetiv)m(o)40 b(\351)g(preserv)-5 b(ado;)45 b(o)40 b(segundo)h(ainda)e(p)s(o)s(de)h(ser)109 4868 y(aprimorado;)31 b(e)j(o)f(terceiro)g(\351)g(otimizado.)43 b(Como)33 b(a)g(solu\347\343o)f(inicial)e(deste)35 b(algoritmo)29 b(\351)34 b(a)f(solu\347\343o)109 5030 y(obtida)38 b(p)s(or)h(aquele)g (que)i(otimiza)36 b(o)k(segundo)g(ob)5 b(jetiv)m(o)39 b(e)h(este)g(p)s(o)s(de)g(visitar)e(solu\347\365)s(es)h(in)m(vi\341)m (v)m(eis)109 5193 y(\(solu\347\365)s(es)d(com)g(p)s(elo)g(menos)h(um)f (grup)s(o)g(de)h(carros)g(de)g(mesma)f(cor)g(desresp)s(eitando)i(o)e (tamanho)109 5355 y(m\341ximo)26 b(p)s(ermitido\),)i(o)h(primeiro)d (passo)k(deste)g(algoritmo)c(\351)j(restaurar)h(a)e(viabilidade)f(da)i (solu\347\343o)109 5518 y(inicial)i(caso)k(seja)g(necess\341rio.)50 b(Na)34 b(pr\363)m(xima)g(se\347\343o,)h(descrev)m(em-se)i(os)e(pro)s (cedimen)m(tos)f(utilizados)109 5681 y(para)39 b(viabilizar)e(a)j (solu\347\343o.)65 b(Nas)40 b(se\347\365)s(es)h(subseq\374en)m(tes,)46 b(apresen)m(tam-se)41 b(os)f(demais)f(passos)i(do)109 5843 y(algoritmo)29 b(para)j(otimizar)d(o)k(terceiro)f(ob)5 b(jetiv)m(o.)p eop %%Page: 44 58 44 57 bop 109 -28 a FB(7.3)60 b(Algoritmo)32 b(para)f(o)f(terceiro)i (ob)5 b(jetiv)m(o)2158 b(44)p 109 9 3780 4 v 530 159 2938 4 v 530 3302 4 3143 v 590 351 a Fw(pro)s(cedure)33 b Fk(VNS_LPRC)p FH(\(Solu\347\343o)h(inicial)29 b Fz(\031)2260 366 y Fq(0)2300 351 y FH(\);)590 472 y(1)106 b Fz(\031)804 436 y Fl(\003)871 472 y Fs( )27 b Fz(\031)1053 487 y Fq(0)1093 472 y FH(,)32 b Fz(\036)1210 436 y Fl(\003)1277 472 y Fs( )c Fz(custo)p FA(\()p Fz(\031)1728 436 y Fl(\003)1766 472 y FA(\))590 592 y FH(2)106 b Fz(i)28 b Fs( )f FA(0)p FH(,)32 b Fz(P)41 b Fs( )28 b FA(1)590 713 y FH(3)106 b Fw(while)31 b Fz(i)d(<)f(i)1231 728 y Ft(max)1408 713 y Fw(and)33 b FH(fra\347\343o)f(de)h(temp)s(o)f(n\343o)g(excedida)h Fw(do)590 833 y FH(4)260 b Fz(k)31 b Fs( )c Fz(k)1159 848 y Fq(1)1198 833 y FH(,)33 b Fz(q)f Fs( )27 b Fz(q)1503 848 y Fq(1)590 953 y FH(5)260 b Fz(\036)28 b Fs( )f Fz(\036)1170 917 y Fl(\003)590 1074 y FH(6)260 b Fw(while)31 b FH(\()p Fz(P)41 b FA(=)28 b(1)k Fw(and)i Fz(k)c Fs(\024)f Fz(k)1965 1089 y Ft(max)2108 1074 y FH(\))j Fw(or)h FH(\()p Fz(P)41 b FA(=)27 b(0)33 b Fw(and)g Fz(q)f Fs(\024)c Fz(q)3074 1089 y Ft(max)3218 1074 y FH(\))k Fw(do)590 1194 y FH(7)415 b Fz(\031)1113 1158 y Fl(0)1163 1194 y Fs( )33 b Fk(Perturbacao)p FH(\()p Fz(\031)1954 1158 y Fl(\003)1996 1194 y Fz(;)17 b(P)s(;)g(k)s(;)g(q)t FH(\))590 1314 y(8)415 b Fz(\031)1113 1278 y Fl(0)1163 1314 y Fs( )33 b Fk(BuscaLocal)p FH(\()p Fz(\031)1903 1278 y Fl(0)1928 1314 y FH(\))590 1435 y(9)415 b Fz(\031)1113 1399 y Fl(\003)1180 1435 y Fs( )32 b Fk (CriterioAceitacao)p FH(\()p Fz(\031)2276 1399 y Fl(\003)2319 1435 y Fz(;)17 b(\031)2422 1399 y Fl(0)2445 1435 y FH(\))590 1555 y(10)366 b Fw(if)31 b Fz(custo)p FA(\()p Fz(\031)1474 1519 y Fl(\003)1513 1555 y FA(\))d Fz(<)f(\036)1740 1519 y Fl(\003)1812 1555 y Fw(then)590 1676 y FH(11)520 b Fz(k)31 b Fs( )c Fz(k)1468 1691 y Fq(1)1507 1676 y FH(,)33 b Fz(q)e Fs( )d Fz(q)1812 1691 y Fq(1)590 1796 y FH(12)520 b Fz(\036)1266 1760 y Fl(\003)1333 1796 y Fs( )27 b Fz(custo)p FA(\()p Fz(\031)1783 1760 y Fl(\003)1822 1796 y FA(\))590 1916 y FH(13)366 b Fw(else)590 2037 y FH(14)520 b Fz(k)31 b Fs( )c Fz(k)e FA(+)d(1)p FH(,)33 b Fz(q)e Fs( )c Fz(q)f FA(+)c(1)590 2157 y FH(15)366 b Fw(end-if)590 2278 y FH(16)211 b Fw(end-while)590 2398 y FH(17)g Fz(P)41 b Fs( )28 b FA(1)21 b Fs(\000)i Fz(P)590 2518 y FH(18)211 b Fz(\031)958 2482 y Fl(\003)1025 2518 y Fs( )32 b Fk (IntensificacaoDiversifica)q(cao)p FH(\()p Fz(\031)2684 2482 y Fl(\003)2729 2518 y FH(\))590 2639 y(19)211 b Fw(if)32 b Fz(custo)p FA(\()p Fz(\031)1320 2603 y Fl(\003)1359 2639 y FA(\))c Fz(<)f(\036)1586 2603 y Fl(\003)1658 2639 y Fw(then)32 b Fz(\036)1967 2603 y Fl(\003)2034 2639 y Fs( )c Fz(custo)p FA(\()p Fz(\031)2485 2603 y Fl(\003)2523 2639 y FA(\))590 2759 y FH(20)211 b Fw(if)32 b Fz(\036)1055 2723 y Fl(\003)1122 2759 y Fz(<)27 b(\036)33 b Fw(then)f Fz(i)c Fs( )g FA(0)590 2879 y FH(21)211 b Fw(else)32 b Fz(i)c Fs( )g Fz(i)22 b FA(+)g(1)590 3000 y FH(22)57 b Fw(end-while)590 3120 y FH(23)g Fw(return)32 b Fz(\031)1147 3084 y Fl(\003)590 3241 y Fw(end)h Fk(VNS_LPRC)p FH(;)p 3464 3302 V 530 3305 2938 4 v 419 3573 a(Figura)d(7.3:)43 b(Pseudo-c\363)s(digo)32 b(do)h(algoritmo)c(para)j(otimizar)e(o)i (segundo)h(ob)5 b(jetiv)m(o.)109 3841 y FJ(7.3.1)129 b(Restaura\347\343o)43 b(da)h(viabilidade)274 4127 y FH(A)m(o)27 b(se)g(restaurar)g(a)g(viabilidade)c(da)k(solu\347\343o)f (atual,)h(dev)m(e-se)h(ter)f(cuidado)f(para)h(n\343o)f(deteriorar)109 4289 y(os)44 b(ob)5 b(jetiv)m(os)44 b(que)h(foram)d(otimizados)g(an)m (teriormen)m(te.)77 b(P)m(ensando)46 b(nisto,)g(tr\352s)e(pro)s (cedimen)m(tos)109 4452 y(de)d(viabiliza\347\343o)c(foram)i (utilizados.)65 b(Se)41 b(o)f(primeiro)e(pro)s(cedimen)m(to)h(n\343o)i (\351)f(capaz)h(de)g(restaurar)109 4614 y(a)46 b(viabilidade)f(da)i (solu\347\343o,)j(o)c(segundo)i(\351)g(aplicado;)k(e,)f(se)d(este,)k(p) s(or)46 b(sua)i(v)m(ez,)k(tam)m(b)s(\351m)45 b(n\343o)109 4777 y(conseguir)29 b(viabilizar)e(a)i(solu\347\343o,)h(o)f(terceiro)h (e)g(\372ltimo)d(pro)s(cedimen)m(to)i(\351)h(utilizado)d(para)i (restaurar)109 4939 y(a)k(viabilidade.)45 b(Somen)m(te)34 b(o)g(terceiro)g(pro)s(cedimen)m(to)f(aplicado)f(garan)m(te)i(recup)s (erar)g(a)g(viabilidade)109 5102 y(da)e(solu\347\343o,)g(no)h(en)m(tan) m(to,)g(ele)f(p)s(o)s(de)h(deteriorar)e(os)i(demais)f(ob)5 b(jetiv)m(os.)274 5323 y(Os)33 b(pro)s(cedimen)m(tos)f(utilizados)f (s\343o)h(os)h(seguin)m(tes:)254 5618 y Fs(\017)49 b FH(Primeiro)31 b(pro)s(cedimen)m(to)i(\025)h(\311)g(uma)f (heur\355stica)g(que)h(preserv)-5 b(a)35 b(a)e(estrutura)i(da)e (solu\347\343o)h(em)353 5781 y(rela\347\343o)25 b(\340s)i (restri\347\365)s(es)g(de)h(capacidade)f(de)g(alta)e(e)i(de)h(baixa)e (prioridade)f(e)i(utiliza)e(um)h(crit\351rio)353 5943 y(guloso)32 b(para)i(obter)g(uma)f(b)s(oa)g(solu\347\343o)h(para)f(o)h (subproblema)f(de)h(minimizar)c(o)k(n)m(\372mero)g(de)p eop %%Page: 45 59 45 58 bop 109 -28 a FB(7.3)60 b(Algoritmo)32 b(para)f(o)f(terceiro)i (ob)5 b(jetiv)m(o)2158 b(45)p 109 9 3780 4 v 353 256 a FH(tro)s(cas)29 b(de)i(cores.)43 b(A)31 b(estrutura)f(da)g (solu\347\343o)g(\351)g(preserv)-5 b(ada,)32 b(\034xando-se)e(o)g(tip)s (o)f(de)h(carro)g(que)353 418 y(dev)m(e)h(ser)h(escalonado)d(em)h(cada) h(p)s(osi\347\343o)e(de)i(acordo)f(com)g(a)g(solu\347\343o)f(inicial.) 40 b(O)30 b(tip)s(o)f(de)i(um)353 581 y(carro)24 b(\351)h(dado)f(p)s (elo)g(conjun)m(to)h(de)g(restri\347\365)s(es)f(de)h(capacidade)g(a)f (que)i(ele)e(est\341)h(asso)s(ciado.)40 b(P)m(ara)353 743 y(cada)f(p)s(osi\347\343o,)h(escolhe-se)h(o)e(carro)g(com)g(a)g (melhor)f(cor)i(den)m(tre)h(aqueles)f(de)g(mesmo)e(tip)s(o,)353 906 y(utilizando-se)31 b(um)i(crit\351rio)g(baseado)h(em)f(an\341lise)g (an)m(tecipat\363ria:)44 b(a)33 b(melhor)g(cor)h(para)f(uma)353 1068 y(p)s(osi\347\343o)j(\351)h(aquela)f(que)i(p)s(o)s(de)f(iniciar)d (um)j(grup)s(o)f(de)i(mesma)e(cor)h(com)f(o)h(maior)d(tamanho,)353 1231 y(resp)s(eitando)42 b(a)h(estrutura)g(da)g(solu\347\343o)f(e)h(o)f (tamanho)g(m\341ximo)e(de)k(grup)s(os)e(de)i(carros)f(de)353 1393 y(mesma)31 b(cor.)254 1639 y Fs(\017)49 b FH(Segundo)26 b(pro)s(cedimen)m(to)g(\025)f(Utiliza)f(mo)m(vimen)m(tos)h FE(swap)31 b FH(para)26 b(tro)s(car)f(carros)i(que)g(p)s(ertencem)353 1801 y(a)47 b(grup)s(os)h(de)g(carros)g(de)h(mesma)e(cor)h(que)g (est\343o)h(desresp)s(eitando)f(o)g(tamanho)f(m\341ximo)353 1964 y(p)s(ermitido.)37 b(As)22 b(tro)s(cas)g(s\343o)g(realizadas)f (somen)m(te)i(en)m(tre)g(carros)f(de)g(mesmo)f(tip)s(o,)i(preserv)-5 b(ando)353 2126 y(a)22 b(estrutura)i(e)f(o)g(custo)h(da)f (solu\347\343o)f(em)h(rela\347\343o)f(\340s)h(restri\347\365)s(es)g(de) h(alta)d(e)j(de)f(baixa)g(prioridade.)254 2372 y Fs(\017)49 b FH(T)-8 b(erceiro)34 b(pro)s(cedimen)m(to)g(\025)h(Utiliza)d(mo)m (vimen)m(tos)i FE(shift)44 b FH(para)34 b(remo)m(v)m(er)h(carros)g(que) h(p)s(erten-)353 2534 y(cem)31 b(a)g(grup)s(os)g(de)h(carros)f(de)h (mesma)e(cor)i(que)g(est\343o)f(desresp)s(eitando)h(o)f(tamanho)g (m\341ximo)353 2697 y(p)s(ermitido)36 b(e)j(reinseri-los)d(em)j(uma)f (no)m(v)-5 b(a)38 b(p)s(osi\347\343o)g(vi\341)m(v)m(el.)62 b(Aplicam-se)36 b(mo)m(vimen)m(tos)i(que)353 2859 y(causam)32 b(a)g(menor)g(v)-5 b(aria\347\343o)31 b(no)i(custo)g(da)f (solu\347\343o)g(at\351)h(que)g(a)f(solu\347\343o)g(torne-se)h(vi\341)m (v)m(el.)109 3207 y FJ(7.3.2)129 b(P)l(erturba\347\343o)274 3493 y FH(Na)27 b(fase)g(de)g(p)s(erturba\347\343o,)h(utilizam-se)c(os) j(mesmos)g(dois)f(tip)s(os)g(de)i(mo)m(vimen)m(tos)e(utilizados)e(no) 109 3656 y(algoritmo)34 b(an)m(terior)j(\(Se\347\343o)h(7.2.1\):)53 b(mo)m(vimen)m(tos)37 b FE(shift)p FH(,)i(que)f(consideram)f(a)h(v)-5 b(aria\347\343o)36 b(no)i(custo)109 3818 y(da)j(solu\347\343o,)i(e)f (mo)m(vimen)m(tos)e FE(swap)p FH(,)j(que)f(s\343o)g(aplicados)e (aleatoriamen)m(te.)67 b(No)41 b(en)m(tan)m(to,)k(alguns)109 3981 y(asp)s(ectos)i(foram)f(adicionados)f(com)h(o)h(ob)5 b(jetiv)m(o)47 b(de)g(preserv)-5 b(ar)48 b(o)f(custo)g(dos)g(ob)5 b(jetiv)m(os)48 b(que)g(j\341)109 4143 y(foram)31 b(otimizados.)274 4365 y(As)47 b(solu\347\365)s(es)f(p)s(erturbadas)g(atra)m(v)m(\351s)h (de)g(mo)m(vimen)m(tos)e FE(shift)55 b FH(passam)46 b(p)s(or)f(um)h (pro)s(cesso)h(de)109 4527 y(\034ltragem)d(an)m(tes)k(de)f(serem)g (submetidas)f(ao)g(pro)s(cedimen)m(to)g(de)h(busca)h(lo)s(cal.)83 b(Se)47 b(as)g(solu\347\365)s(es)109 4690 y(resultan)m(tes)36 b(desta)f(p)s(erturba\347\343o)h(deteriorarem)d(o)i(primeiro)e(ob)5 b(jetiv)m(o,)36 b(elas)f(s\343o)g(descartadas)h(e)f(a)109 4852 y(busca)d(lo)s(cal)d(\351)i(aplicada)e(na)j(solu\347\343o)e (atual.)42 b(P)m(ara)31 b(que)h(o)f(n)m(\372mero)g(de)h(solu\347\365)s (es)f(descartadas)h(ap)s(\363s)109 5015 y(a)39 b(p)s(erturba\347\343o)h (n\343o)f(seja)i(alto,)f(dev)m(e-se)i(reduzir)d(o)h(tamanho)e(dos)j(mo) m(vimen)m(tos)d(aplicados.)64 b(Na)109 5177 y(p)s(erturba\347\343o)39 b(com)f(mo)m(vimen)m(tos)g FE(swap)p FH(,)i(o)e(que)i(se)g(faz)f(\351)g (preserv)-5 b(ar)40 b(a)f(estrutura)g(da)g(solu\347\343o)g(em)109 5340 y(rela\347\343o)c(\340s)h(restri\347\365)s(es)g(de)h(capacidade)f (de)g(alta)f(prioridade.)52 b(Ou)36 b(seja,)h(realizam-se)d(mo)m(vimen) m(tos)109 5502 y(de)k(tro)s(ca)f(somen)m(te)i(en)m(tre)f(carros)g(que)h (est\343o)f(asso)s(ciados)g(ao)f(mesmo)g(conjun)m(to)h(de)h (restri\347\365)s(es)f(de)109 5665 y(capacidade)f(de)g(alta)e (prioridade)h(\(carros)h(de)g(mesmo)f(tip)s(o\).)55 b(Desta)38 b(forma,)f(o)f(custo)i(da)f(solu\347\343o)109 5827 y(referen)m(te)d(ao) e(primeiro)e(ob)5 b(jetiv)m(o)32 b(\351)h(preserv)-5 b(ado.)p eop %%Page: 46 60 46 59 bop 109 -28 a FB(7.3)60 b(Algoritmo)32 b(para)f(o)f(terceiro)i (ob)5 b(jetiv)m(o)2158 b(46)p 109 9 3780 4 v 274 256 a FH(Como)21 b(no)h(algoritmo)c(an)m(terior,)23 b(de\034ne-se)g(um)e (conjun)m(to)h(de)g(vizinhan\347as)g Fz(N)3134 219 y Fq(1)3124 281 y Ft(k)3174 256 y FH(,)i Fz(k)31 b FA(=)c Fz(k)3461 271 y Fq(1)3500 256 y Fz(;)17 b(:)g(:)g(:)f(;)h(k)3770 271 y Ft(max)3913 256 y FH(,)109 418 y(para)46 b(a)g(p)s (erturba\347\343o)g(com)g(mo)m(vimen)m(tos)f FE(shift)p FH(,)50 b(onde)c Fz(k)k FH(\351)c(o)g(n)m(\372mero)h(de)f(carros)h (remo)m(vidos)f(e)109 581 y(reinseridos,)41 b(e)g(um)e(conjun)m(to)h (de)h(vizinhan\347as)e Fz(N)2051 544 y Fq(2)2041 605 y Ft(q)2091 581 y FH(,)j Fz(q)i FA(=)c Fz(q)2406 596 y Fq(1)2446 581 y Fz(;)17 b(:)g(:)g(:)f(;)h(q)2708 596 y Ft(max)2852 581 y FH(,)42 b(para)d(a)h(p)s(erturba\347\343o)g(de)109 743 y(mo)m(vimen)m(tos)e FE(swap)p FH(,)i(onde)g Fz(q)j FH(\351)c(o)g(n)m(\372mero)h(de)f(tro)s(cas)g(realizadas.)63 b(Neste)40 b(algoritmo,)d(os)j(v)-5 b(alores)109 906 y(de)32 b Fz(k)289 921 y Ft(max)464 906 y FH(e)g Fz(q)582 921 y Ft(max)758 906 y FH(precisam)f(ser)i(menores,)f(para)f(que)i(uma) e(menor)g(quan)m(tidade)h(de)h(solu\347\365)s(es)f(sejam)109 1068 y(rejeitadas)g(p)s(elo)f(crit\351rio)g(de)i(aceita\347\343o.)274 1290 y(Os)j(dois)f(tip)s(os)f(de)i(p)s(erturba\347\343o)f(s\343o)h(tam) m(b)s(\351m)e(aplicados)g(da)h(mesma)g(forma:)47 b(sempre)36 b(que)g(a)109 1452 y(vizinhan\347a)g(m\341xima)f(da)j(p)s (erturba\347\343o)f(corren)m(te)i(for)d(alcan\347ada,)i(o)f(outro)g (tip)s(o)f(de)i(p)s(erturba\347\343o)109 1615 y(passa)33 b(a)f(ser)h(aplicado.)109 1963 y FJ(7.3.3)129 b(Busca)45 b(lo)t(cal)274 2248 y FH(A)33 b(solu\347\343o)f(resultan)m(te)h(da)g (fase)g(de)g(p)s(erturba\347\343o)g(tem)g(o)f(v)-5 b(alor)32 b(do)g(primeiro)f(ob)5 b(jetiv)m(o)32 b(preser-)109 2411 y(v)-5 b(ado)29 b(mas)h(p)s(o)s(de)f(ter)h(o)g(v)-5 b(alor)28 b(do)i(segundo)h(deteriorado.)42 b(En)m(t\343o,)30 b(a)g(busca)h(lo)s (cal)c(pro)s(cura)j(otimizar)109 2574 y(o)35 b(segundo)h(e)f(o)h (terceiro)e(ob)5 b(jetiv)m(os)36 b(do)f(problema.)51 b(Utiliza-se)33 b(um)i(m\351to)s(do)f(de)i(busca)g(lo)s(cal)d(com)109 2736 y(mo)m(vimen)m(tos)d FE(swap)37 b FH(conforme)31 b(descrito)h(no)g(Cap\355tulo)e(5.)43 b(En)m(tretan)m(to,)32 b(os)g(mo)m(vimen)m(tos)f(a)m(v)-5 b(aliados)109 2899 y(restringem-se)25 b(\340queles)h(em)f(que)i(os)f(carros)g (considerados)g(est\343o)f(asso)s(ciados)h(\340s)g(mesmas)f (restri\347\365)s(es)109 3061 y(de)33 b(capacidade)f(de)h(alta)e (prioridade,)g(a)i(\034m)f(de)h(se)g(preserv)-5 b(ar)33 b(o)g(v)-5 b(alor)31 b(do)h(primeiro)e(ob)5 b(jetiv)m(o.)274 3283 y(Se,)36 b(ao)f(\034nal)f(da)h(busca)h(lo)s(cal,)d(a)i (solu\347\343o)f(ainda)g(tiv)m(er)h(o)g(segundo)h(ob)5 b(jetiv)m(o)35 b(deteriorado,)g(ela)109 3445 y(\351)i(descartada.)58 b(Ev)m(en)m(tualmen)m(te,)39 b(o)e(v)-5 b(alor)36 b(do)g(segundo)i(ob)5 b(jetiv)m(o)37 b(tam)m(b)s(\351m)f(p)s(o)s(de)h(ser)h(melhorado)109 3608 y(duran)m(te)33 b(a)f(busca)i(lo)s(cal)c(e,)j(conseq\374en)m (temen)m(te,)j(a)c(solu\347\343o)g(\351)h(aceita.)109 3956 y FJ(7.3.4)129 b(In)l(tensi\034ca\347\343o)45 b(/)f(Div)l (ersi\034ca\347\343o)274 4241 y FH(A)36 b(fase)h(de)f(in)m (tensi\034ca\347\343o/div)m(ersi\034ca\347\343o)g(utilizada)e(neste)j (algoritmo)c(\351)j(semelhan)m(te)h(\340quela)109 4404 y(empregada)48 b(no)h(algoritmo)d(para)j(otimizar)d(o)j(segundo)h(ob)5 b(jetiv)m(o)49 b(e)h(descrita)f(na)g(Se\347\343o)h(7.2.3.)109 4566 y(Aplica-se)28 b(um)g(m\351to)s(do)g(de)i(busca)g(lo)s(cal)c(com)j (mo)m(vimen)m(tos)f FE(shift)38 b FH(e)30 b(outro)e(com)h(mo)m(vimen)m (tos)f FE(swap)109 4729 y FH(a)h(\034m)h(de)g(se)h(explorar)e(mais)g (in)m(tensamen)m(te)h(a)g(vizinhan\347a)f(das)h(solu\347\365)s(es,)h (tirando-se)e(pro)m(v)m(eito)h(das)109 4891 y(caracter\355sticas)f(dos) h(m\351to)s(dos)f(utilizados)f(para)i(visitar)e(mais)h(solu\347\365)s (es)h(no)f(espa\347o)i(de)f(busca.)44 b(Nas)109 5054 y(duas)34 b(buscas)i(lo)s(cais,)d(os)h(mo)m(vimen)m(tos)g(s\343o)g(a)m (v)-5 b(aliados)32 b(considerando-se)j(o)f(custo)h(dos)f(tr\352s)h(ob)5 b(jeti-)109 5217 y(v)m(os)37 b(do)f(problema.)52 b(Desta)37 b(forma,)e(p)s(o)s(de-se)i(explorar)e(solu\347\365)s(es)h(com)g (estruturas)h(diferen)m(tes)g(\(em)109 5379 y(rela\347\343o)31 b(\340s)i(restri\347\365)s(es)g(de)g(capacidade\),)f(preserv)-5 b(ando-se)34 b(o)f(custo)g(da)f(solu\347\343o.)274 5601 y(O)39 b(pro)s(cedimen)m(to)f(\351)h(aplicado)e(sempre)j(que)g(se)g (alterna)e(en)m(tre)i(as)f(p)s(erturba\347\365)s(es,)i(da)e(mesma)109 5763 y(forma)31 b(que)i(no)g(algoritmo)c(an)m(terior.)p eop %%Page: 47 61 47 60 bop 109 -28 a FB(7.3)60 b(Algoritmo)32 b(para)f(o)f(terceiro)i (ob)5 b(jetiv)m(o)2158 b(47)p 109 9 3780 4 v 109 256 a FJ(7.3.5)129 b(Estrutura)45 b(geral)f(do)g(algoritmo)274 541 y FH(Este)37 b(algoritmo)c(considera)j(os)g(tr\352s)h(ob)5 b(jetiv)m(os,)38 b(preserv)-5 b(ando)37 b(o)f(custo)g(do)g(primeiro)e (e)j(otimi-)109 704 y(zando)e(os)h(demais.)51 b(A)36 b(solu\347\343o)f(obtida)f(p)s(elo)g(algoritmo)e(que)37 b(otimiza)32 b(o)k(segundo)g(ob)5 b(jetiv)m(o)35 b(serv)m(e)109 866 y(como)27 b(solu\347\343o)h(inicial)d(para)j(este.)43 b(No)28 b(en)m(tan)m(to,)i(se)f(esta)g(solu\347\343o)e(for)h(in)m (vi\341)m(v)m(el,)h(aplica-se)d(uma)i(fase)109 1029 y(de)33 b(viabiliza\347\343o)c(para)j(torn\341-la)f(vi\341)m(v)m(el.)274 1251 y(A)47 b(estrutura)g(deste)h(algoritmo)43 b(\351)k(semelhan)m(te)f (\340)h(do)f(algoritmo)d(an)m(terior)j(descrita)h(na)f(Se-)109 1413 y(\347\343o)39 b(7.2.5,)h(com)f(exce\347\343o)h(das)g(fases)g(de)g (viabiliza\347\343o)c(e)j(de)h(\034ltragem,)f(que)h(foram)e(in)m(tro)s (duzidas)109 1576 y(como)c(mostra)g(o)h(pseudo-c\363)s(digo)g(da)g (Figura)e(7.4.)51 b(O)36 b(primeiro)c(passo)k(do)f(algoritmo)d(\351)j (viabilizar)109 1738 y(a)g(solu\347\343o)g(inicial)e(\(linha)h(1\),)i (caso)g(seja)g(necess\341rio.)54 b(Este)37 b(passo)f(consiste)h(na)e (aplica\347\343o)f(de)j(tr\352s)109 1901 y(pro)s(cedimen)m(tos)32 b(\(v)m(er)i(Se\347\343o)g(7.3.1\))e(da)h(seguin)m(te)h(forma:)43 b(se)34 b(o)f(primeiro)d(pro)s(cedimen)m(to)j(n\343o)f(con-)109 2063 y(seguir)37 b(restaurar)h(a)f(viabilidade,)f(o)h(segundo)h(\351)g (aplicado;)g(e,)h(se)g(este)f(tam)m(b)s(\351m)e(falhar,)i(aplica-se)109 2226 y(o)43 b(terceiro)h(e)g(\372ltimo)d(pro)s(cedimen)m(to,)46 b(que)f(garan)m(te)e(a)h(recup)s(era\347\343o)g(da)g(viabilidade)d(mas) i(p)s(o)s(de)109 2388 y(deteriorar)26 b(o)h(custo)h(da)f (solu\347\343o.)41 b(O)28 b(pro)s(cesso)g(de)g(\034ltragem)d(foi)h(in)m (tro)s(duzido)g(ap)s(\363s)h(a)g(p)s(erturba\347\343o.)109 2551 y(Se)32 b(a)f(solu\347\343o)g(obtida)f(p)s(ela)h(p)s (erturba\347\343o)g(tem)g(o)g(v)-5 b(alor)30 b(do)i(primeiro)d(ob)5 b(jetiv)m(o)31 b(deteriorado)g(\(linha)109 2713 y(8\),)h(ela)g(\351)h (descartada)g(e)g(se)g(retorna)f(para)g(a)h(solu\347\343o)f(atual)f (\(linha)f(9\).)274 2935 y(A)m(o)41 b(con)m(tr\341rio)f(dos)h(outros)g (dois)g(algoritmos,)f(este)i(n\343o)f(p)s(ossui)g(crit\351rio)e(de)i (estagna\347\343o.)69 b(O)109 3097 y(algoritmo)29 b(termina)i(quando)i (atinge)e(o)h(temp)s(o)g(m\341ximo)e(de)j(execu\347\343o)h(p)s (ermitido)c(\(linha)h(4\).)p eop %%Page: 48 62 48 61 bop 109 -28 a FB(7.3)60 b(Algoritmo)32 b(para)f(o)f(terceiro)i (ob)5 b(jetiv)m(o)2158 b(48)p 109 9 3780 4 v 326 1275 3345 4 v 326 4537 4 3263 v 387 1467 a Fw(pro)s(cedure)33 b Fk(VNS_PCC)p FH(\(Solu\347\343o)g(inicial)c Fz(\031)2005 1482 y Fq(0)2045 1467 y FH(\);)387 1587 y(1)105 b Fw(if)42 b Fz(\031)704 1602 y Fq(0)777 1587 y FH(for)32 b(in)m(vi\341)m(v)m(el)g Fw(then)g Fz(\031)1587 1602 y Fq(0)1655 1587 y Fs( )g Fk(Viabilizacao)p FH(\()p Fz(\031)2492 1602 y Fq(0)2535 1587 y FH(\))387 1708 y(2)105 b Fz(\031)600 1671 y Fl(\003)667 1708 y Fs( )28 b Fz(\031)850 1723 y Fq(0)889 1708 y FH(,)33 b Fz(\036)1007 1671 y Fl(\003)1074 1708 y Fs( )27 b Fz(custo)p FA(\()p Fz(\031)1524 1671 y Fl(\003)1563 1708 y FA(\))387 1828 y FH(3)105 b Fz(P)42 b Fs( )27 b FA(1)387 1948 y FH(4)105 b Fw(while)31 b FH(temp)s(o)h(m\341ximo)e(de)j(execu\347\343o) h(n\343o)f(excedido)g Fw(do)387 2069 y FH(5)260 b Fz(k)31 b Fs( )c Fz(k)956 2084 y Fq(1)995 2069 y FH(,)33 b Fz(q)e Fs( )c Fz(q)1299 2084 y Fq(1)387 2189 y FH(6)260 b Fw(while)31 b FH(\()p Fz(P)41 b FA(=)27 b(1)33 b Fw(and)g Fz(k)e Fs(\024)d Fz(k)1761 2204 y Ft(max)1905 2189 y FH(\))k Fw(or)g FH(\()p Fz(P)41 b FA(=)28 b(0)k Fw(and)i Fz(q)d Fs(\024)d Fz(q)2870 2204 y Ft(max)3014 2189 y FH(\))33 b Fw(do)387 2309 y FH(7)414 b Fz(\031)909 2273 y Fl(0)960 2309 y Fs( )32 b Fk(Perturbacao)p FH(\()p Fz(\031)1750 2273 y Fl(\003)1792 2309 y Fz(;)17 b(P)s(;)g(k)s(;)g(q)t FH(\))387 2430 y(8)414 b Fw(if)42 b FH(o)33 b(custo)g(do)f(primeiro)e (ob)5 b(jetiv)m(o)33 b(de)g Fz(\031)2386 2394 y Fl(0)2442 2430 y FH(for)f(maior)e(que)j(o)g(de)g Fz(\031)3319 2394 y Fl(\003)3391 2430 y Fw(then)387 2550 y FH(9)569 b Fz(\031)1064 2514 y Fl(0)1115 2550 y Fs( )27 b Fz(\031)1301 2514 y Fl(\003)387 2671 y FH(10)365 b Fw(end-if)387 2791 y FH(11)g Fz(\031)909 2755 y Fl(0)960 2791 y Fs( )32 b Fk(BuscaLocal)p FH(\()p Fz(\031)1699 2755 y Fl(0)1725 2791 y FH(\))387 2911 y(12)365 b Fz(\031)909 2875 y Fl(\003)976 2911 y Fs( )32 b Fk(CriterioAceitacao)p FH(\()p Fz(\031)2072 2875 y Fl(\003)2116 2911 y Fz(;)17 b(\031)2219 2875 y Fl(0)2242 2911 y FH(\))387 3032 y(13)365 b Fw(if)32 b Fz(custo)p FA(\()p Fz(\031)1271 2996 y Fl(\003)1310 3032 y FA(\))c Fz(<)f(\036)1537 2996 y Fl(\003)1609 3032 y Fw(then)387 3152 y FH(14)520 b Fz(k)30 b Fs( )e Fz(k)1265 3167 y Fq(1)1304 3152 y FH(,)k Fz(q)g Fs( )27 b Fz(q)1608 3167 y Fq(1)387 3273 y FH(15)520 b Fz(\036)1063 3236 y Fl(\003)1130 3273 y Fs( )27 b Fz(custo)p FA(\()p Fz(\031)1580 3236 y Fl(\003)1619 3273 y FA(\))387 3393 y FH(16)365 b Fw(else)387 3513 y FH(17)520 b Fz(k)30 b Fs( )e Fz(k)d FA(+)d(1)p FH(,)32 b Fz(q)g Fs( )27 b Fz(q)f FA(+)c(1)387 3634 y FH(18)365 b Fw(end-if)387 3754 y FH(19)211 b Fw(end-while)387 3874 y FH(20)g Fz(P)41 b Fs( )27 b FA(1)22 b Fs(\000)h Fz(P)387 3995 y FH(21)211 b Fz(\031)755 3959 y Fl(\003)822 3995 y Fs( )32 b Fk(IntensificacaoDiversificac)q(ao)p FH(\()p Fz(\031)2480 3959 y Fl(\003)2525 3995 y FH(\))387 4115 y(22)211 b Fw(if)32 b Fz(custo)p FA(\()p Fz(\031)1117 4079 y Fl(\003)1156 4115 y FA(\))27 b Fz(<)h(\036)1383 4079 y Fl(\003)1454 4115 y Fw(then)33 b Fz(\036)1764 4079 y Fl(\003)1831 4115 y Fs( )27 b Fz(custo)p FA(\()p Fz(\031)2281 4079 y Fl(\003)2320 4115 y FA(\))387 4236 y FH(23)56 b Fw(end-while)387 4356 y FH(24)g Fw(return)33 b Fz(\031)944 4320 y Fl(\003)387 4476 y Fw(end)g Fk(VNS_PCC)p FH(;)p 3667 4537 V 326 4540 3345 4 v 430 4809 a(Figura)d(7.4:)44 b(Pseudo-c\363)s(digo)31 b(do)i(algoritmo)c(para)j(otimizar)e(o)i (terceiro)g(ob)5 b(jetiv)m(o.)p eop %%Page: 49 63 49 62 bop 109 726 a FD(Cap\355tulo)64 b(8)109 1390 y(Exp)5 b(erimen)-5 b(tos)63 b(Computacionais)274 2092 y FH(Com)48 b(o)f(in)m(tuito)g(de)h(analisar)e(o)i(desemp)s(enho)h(da)f (estrat\351gia)g(desen)m(v)m(olvida)h(para)e(o)h(PSC,)109 2255 y(exp)s(erimen)m(tos)31 b(computacionais)e(foram)g(realizados)h(e) h(os)g(resultados)g(obtidos)f(foram)g(comparados)109 2417 y(com)i(resultados)g(encon)m(trados)i(p)s(or)e(outros)g (algoritmos)e(j\341)i(desen)m(v)m(olvidos)i(para)e(este)i(problema.)274 2639 y(P)m(ara)j(melhor)f(explicar)g(os)i(resultados)f(computacionais)e (com)i(os)g(quais)g(s\343o)g(comparados)g(os)109 2801 y(resultados)c(obtidos)h(p)s(elos)f(testes)i(realizados)d(com)h(os)h (algoritmos)d(prop)s(ostos)j(nesta)g(disserta\347\343o,)109 2964 y(b)s(em)d(como)g(as)g(inst\342ncias)g(de)h(teste)h(que)g(foram)d (utilizadas)f(nos)j(exp)s(erimen)m(tos,)h(faz-se)e(necess\341rio)109 3126 y(esclarecer)24 b(onde)f(tais)g(resultados)g(e)g(inst\342ncias)g (foram)e(disp)s(onibilizadas,)h(o)h(que)h(\351)f(feito)f(na)h(pr\363)m (xima)109 3289 y(se\347\343o.)75 b(Na)43 b(se\347\343o)g(seguin)m(te,)j (s\343o)d(apresen)m(tados)i(os)e(exp)s(erimen)m(tos)g(realizados)f(e)h (os)g(resultados)109 3451 y(obtidos)32 b(p)s(or)g(estes)i(exp)s(erimen) m(tos.)109 3843 y Fx(8.1)155 b(Desa\034o)52 b(R)l(O)l(ADEF)274 4163 y FH(O)47 b(problema)f(de)i(seq\374enciamen)m(to)h(de)f(carros)g (que)g(\351)g(o)f(tema)g(de)h(estudo)g(desta)h(disserta-)109 4326 y(\347\343o)34 b(foi)f(prop)s(osto)h(p)s(ela)g(ind\372stria)f (automobil\355stica)d(Renault)k(para)g(um)g(desa\034o)h(promo)m(vido)e (p)s(ela)109 4488 y(So)s(ciedade)44 b(F)-8 b(rancesa)45 b(de)f(P)m(esquisa)i(Op)s(eracional)d(\(R)m(O)m(ADEF\).)i(Neste)g (desa\034o,)j(55)c(equip)s(es)h(se)109 4651 y(inscrev)m(eram)29 b(com)f(o)g(ob)5 b(jetiv)m(o)29 b(de)g(solucionar)f(o)g(problema)f (prop)s(osto.)42 b(O)29 b(concurso,)h(que)g(acon)m(tece)109 4813 y(p)s(erio)s(dicamen)m(te)h(a)h(cada)g(dois)g(anos,)h(\351)g (dividido)e(em)h(duas)h(etapas:)254 5143 y Fs(\017)49 b FH(Etapa)34 b(classi\034cat\363ria)e(\025)i(Nesta)h(etapa,)f(algumas) f(inst\342ncias)g(de)i(teste,)h(c)m(hamadas)e(de)g(con-)353 5305 y(jun)m(to)39 b(de)g(teste)h(A,)f(s\343o)g(disp)s(onibilizadas)d (para)i(as)i(equip)s(es)f(e)h(as)f(mesmas)f(s\343o)h(utilizadas)353 5468 y(para)32 b(a)m(v)-5 b(aliar)30 b(e)j(classi\034car)f(aquelas)g (que)i(passam)e(para)g(etapa)h(seguin)m(te.)254 5713 y Fs(\017)49 b FH(Etapa)27 b(\034nal)g(\025)g(Nesta)h(etapa,)h(um)e(no) m(v)m(o)h(conjun)m(to)g(de)g(inst\342ncias,)g(c)m(hamado)g(de)g(conjun) m(to)g(de)353 5876 y(teste)36 b(B,)g(\351)f(disp)s(onibilizado)d(para)j (as)h(equip)s(es)g(\034nalistas)e(melhor)g(a)5 b(justarem)35 b(seus)i(algorit-)p eop %%Page: 50 64 50 63 bop 109 -28 a FB(8.1)60 b(Desa\034o)31 b(R)m(O)m(ADEF)2810 b(50)p 109 9 3780 4 v 353 256 a FH(mos.)41 b(No)29 b(en)m(tan)m(to,)h (as)f(inst\342ncias)f(utilizadas)f(para)h(a)m(v)-5 b(aliar)27 b(as)i(equip)s(es)h(s\343o)e(desconhecidas,)353 418 y(diferen)m(temen)m (te)i(da)f(etapa)g(an)m(terior.)42 b(A)30 b(equip)s(e)f(que)i(obt\351m) e(os)g(melhores)g(resultados)h(nesta)353 581 y(fase)i(v)m(ence)j(o)d (concurso.)274 891 y(A)h(etapa)f(classi\034cat\363ria)f(do)h(concurso)i (tev)m(e)g(in\355cio)c(em)i(junho)h(de)g(2003)f(e)h(terminou)e(em)h (fev)m(e-)109 1053 y(reiro)23 b(de)j(2004,)f(quando)h(os)f(resultados)f (obtidos)h(p)s(elas)f(equip)s(es)i(para)e(o)g(conjun)m(to)i(de)f(teste) h(A)f(foram)109 1216 y(divulgados.)56 b(A)37 b(etapa)g(\034nal)g(tev)m (e)h(in\355cio)d(em)h(maio)g(de)h(2004)f(e)i(terminou)e(em)g(outubro)h (de)h(2004.)109 1378 y(Os)32 b(resultados)g(obtidos)f(p)s(elas)h(equip) s(es)g(\034nalistas)f(foram)g(divulgados)g(em)g(fev)m(ereiro)h(de)h (2005)e(e)h(as)109 1541 y(melhores)c(solu\347\365)s(es)h(encon)m (tradas)h(nestes)g(resultados)f(foram)f(utilizadas)e(para)j(a)m(v)-5 b(aliar)26 b(o)j(algoritmo)109 1703 y(prop)s(osto)38 b(nesta)h(disserta\347\343o.)61 b(Este)40 b(algoritmo)35 b(\351)k(parte)f(in)m(tegran)m(te)h(do)f(trabalho)f(desen)m(v)m(olvido) 109 1866 y(p)s(or)42 b(uma)f(equip)s(e)i(e)f(submetido)g(\340)g(fase)h (\034nal)e(do)h(concurso)i(R)m(O)m(ADEF.)f(Este)g(trabalho)e(incluiu) 109 2028 y(algoritmos)30 b(para)j(resolv)m(er)h(os)f(tr\352s)h(tip)s (os)f(de)h(problemas)e(apresen)m(tados)j(na)e(Se\347\343o)h(2.3.)45 b(A)34 b(equip)s(e)109 2191 y(foi)25 b(formada)g(p)s(elo)g(professor)i (Celso)g(C.)g(Rib)s(eiro)d(e)j(p)s(elos)f(p)s(\363s-graduandos)g (Caroline)f(T.)i(M.)g(Ro)s(c)m(ha,)109 2353 y(Daniel)k(Aloise,)h (Thiago)f(F.)h(Noronha)h(e)f(Sebasti\341n)h(Urrutia.)274 2575 y(No)23 b(concurso,)i(foram)d(disp)s(onibilizadas)d(inst\342ncias) j(para)h(os)g(tr\352s)g(tip)s(os)f(de)h(problemas)f(existen-)109 2737 y(tes,)28 b(sendo)f(no)f(total)f(19)h(inst\342ncias)f(do)i (primeiro)d(tip)s(o,)i(23)g(inst\342ncias)f(do)h(segundo)i(e)e(19)g (inst\342ncias)109 2900 y(do)40 b(terceiro.)66 b(O)39 b(conjun)m(to)i(de)g(inst\342ncias)e(do)h(problema)f(utilizadas)f(nos)i (testes)i(\351)e(formado)f(p)s(or)109 3062 y(to)s(das)j(as)h(19)g(disp) s(onibilizadas)c(para)k(o)f(tip)s(o)g(de)h(problema)e(estudado)j (\(primeiro)c(tip)s(o\).)73 b(Estas)109 3225 y(inst\342ncias)31 b(s\343o)i(descritas)g(a)f(seguir)h(e)f(p)s(o)s(dem)g(ser)h(obtidas)f (em)g([16].)274 3447 y(A)c(tab)s(ela)e(a)i(seguir)f(apresen)m(ta)i(as)f (principais)d(informa\347\365)s(es)i(a)g(resp)s(eito)g(das)h (inst\342ncias)f(utiliza-)109 3609 y(das.)42 b(As)30 b(primeiras)e(quatro)h(linhas)f(da)i(tab)s(ela)e(corresp)s(ondem)h (\340s)h(inst\342ncias)f(que)h(fazem)f(parte)g(do)109 3772 y(conjun)m(to)24 b(de)h(teste)h(A)e(e)h(as)g(demais)e(corresp)s (ondem)i(ao)f(conjun)m(to)h(de)f(teste)i(B.)e(P)m(ara)h(cada)f (inst\342ncia,)109 3934 y(apresen)m(tam-se)31 b(o)g(seu)h(nome)f(ou)g (iden)m(ti\034ca\347\343o)f Fz(id)p FH(,)h(o)g(n)m(\372mero)g(de)g (carros)h(a)e(serem)i(escalonados)f Fz(n)p FH(,)109 4097 y(o)i(n)m(\372mero)g(de)h(restri\347\365)s(es)f(de)h(capacidade)f(de)h (alta)e(prioridade)g Fz(m)2613 4112 y Ft(h)2691 4097 y FH(e)i(de)g(baixa)e(prioridade)g Fz(m)3714 4112 y Ft(l)3740 4097 y FH(,)i(as)109 4259 y(taxas)d(de)h(utiliza\347\343o)c(m\351dia)i Fz(t)1252 4223 y Ft(med)1252 4285 y(h)1418 4259 y FH(e)i(m\341xima)c Fz(t)1897 4223 y Ft(max)1897 4285 y(h)2072 4259 y FH(das)k (restri\347\365)s(es)f(de)h(capacidade)f(de)g(alta)f(priori-)109 4422 y(dade)36 b(e)f(as)h(taxas)g(de)g(utiliza\347\343o)c(m\351dia)i Fz(t)1706 4385 y Ft(med)1706 4448 y(l)1878 4422 y FH(e)h(m\341xima)e Fz(t)2365 4385 y Ft(max)2365 4448 y(l)2545 4422 y FH(das)j (restri\347\365)s(es)f(de)h(capacidade)g(de)109 4584 y(baixa)27 b(prioridade.)41 b(Al\351m)27 b(disso,)j(s\343o)e(apresen)m (tados)i(o)f(n)m(\372mero)f(de)h(cores)g(diferen)m(tes)h(na)e (inst\342ncia,)109 4747 y(denotado)k(p)s(or)g Fz(c)p FH(,)h(e)g(o)f(tamanho)f(m\341ximo)g(p)s(ermitido)f(de)j(grup)s(os)f (de)h(carros)g(de)g(mesma)f(cor)g Fz(g)t FH(.)274 4968 y(P)m(o)s(de-se)g(observ)-5 b(ar)32 b(que)h(existem)e(inst\342ncias)g (com)g(caracter\355sticas)g(div)m(ersas.)44 b(Os)32 b(dados)f(apre-)109 5131 y(sen)m(tados,)48 b(isolados)43 b(ou)i(em)f(conjun)m(to,)k (in\035uenciam)43 b(diretamen)m(te)h(no)g(grau)g(de)h(di\034culdade)f (de)109 5293 y(solu\347\343o)28 b(das)h(inst\342ncias.)42 b(Inst\342ncias)29 b(com)f(v)-5 b(alores)28 b(altos)g(de)h Fz(n)p FH(,)h Fz(m)2637 5308 y Ft(h)2711 5293 y FH(e)f Fz(m)2868 5308 y Ft(l)2924 5293 y FH(s\343o)f(inst\342ncias)g(maiores,) 109 5456 y(que)34 b(resultam)e(em)h(itera\347\365)s(es)g(mais)f(len)m (tas)i(do)f(algoritmo.)43 b(Outras)33 b(an\341lises)g(tam)m(b)s(\351m)f (p)s(o)s(dem)g(ser)109 5618 y(feitas)25 b(com)f(base)j(nos)f(dados)g (apresen)m(tados)h(na)e(T)-8 b(ab)s(ela)25 b(8.1.)41 b(Inst\342ncias)25 b(que)i(p)s(ossuem)f(uma)f(m\351dia)109 5781 y(alta)k(das)j(taxas)f(de)h(utiliza\347\343o)d(das)i (restri\347\365)s(es)h(de)f(capacidade)g(resultam)g(em)f(um)h(alto)f(n) m(\372mero)h(de)109 5943 y(viola\347\365)s(es)j(dessas)j (restri\347\365)s(es,)f(como)e(\351)i(o)f(caso)g(das)h(inst\342ncias)f Fy(024_V2_S22_J1)p FH(,)f Fy(025_S22_J3)p eop %%Page: 51 65 51 64 bop 109 -28 a FB(8.1)60 b(Desa\034o)31 b(R)m(O)m(ADEF)2810 b(51)p 109 9 3780 4 v 653 308 a FH(T)-8 b(ab)s(ela)32 b(8.1:)43 b(Dados)33 b(das)g(inst\342ncias)e(dos)i(conjun)m(tos)h(de)f (teste)g(A)g(e)g(B.)p 410 446 3144 4 v 408 567 4 121 v 799 531 a Fz(id)p 1271 567 V 507 w(n)p 1565 567 V 169 w(m)1702 546 y Ft(h)p 1795 567 V 1846 531 a Fz(m)1931 546 y Ft(l)p 2006 567 V 2057 531 a Fz(t)2092 495 y Ft(max)2092 557 y(h)p 2285 567 V 2337 531 a Fz(t)2372 495 y Ft(med)2372 557 y(h)p 2558 567 V 2609 531 a Fz(t)2644 495 y Ft(max)2644 557 y(l)p 2836 567 V 2889 531 a Fz(t)2924 495 y Ft(med)2924 557 y(l)p 3109 567 V 3188 531 a Fz(c)p 3306 567 V 176 w(g)p 3552 567 V 410 570 3144 4 v 410 587 V 408 707 4 121 v 460 671 a Fy(024_38_3)p 1271 707 V 416 w FH(1274)p 1565 707 V 139 w(5)p 1795 707 V 172 w(8)p 2006 707 V 133 w(0.96)p 2285 707 V 102 w(0.85)p 2558 707 V 102 w(0.95)p 2836 707 V 102 w(0.54)p 3109 707 V 99 w(13)p 3306 707 V 123 w(10)p 3552 707 V 408 828 V 460 791 a Fy(024_38_5)p 1271 828 V 416 w FH(1329)p 1565 828 V 139 w(5)p 1795 828 V 172 w(8)p 2006 828 V 133 w(0.96)p 2285 828 V 102 w(0.85)p 2558 828 V 102 w(0.96)p 2836 828 V 102 w(0.39)p 3109 828 V 99 w(13)p 3306 828 V 123 w(10)p 3552 828 V 408 948 V 460 912 a Fy(025_38_1)p 1271 948 V 416 w FH(1232)p 1565 948 V 139 w(4)p 1795 948 V 147 w(18)p 2006 948 V 109 w(0.76)p 2285 948 V 102 w(0.65)p 2558 948 V 102 w(1.12)p 2836 948 V 102 w(0.70)p 3109 948 V 99 w(24)p 3306 948 V 123 w(10)p 3552 948 V 408 1068 V 460 1032 a Fy(048_39_1)p 1271 1068 V 440 w FH(618)p 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(o)s(dem)f(ser)h(obtidos)f(em)g([16].)274 3132 y(Duran)m(te)44 b(o)e(desen)m(v)m(olvimen)m(to)h(do)f(algoritmo,)f(div)m(ersas)j (estrat\351gias)e(e)h(conjun)m(tos)g(de)g(par\342-)109 3294 y(metros)k(foram)f(testados)j(visando)e(a)h(conseguir)f(um)h(b)s (om)e(desemp)s(enho)j(na)e(comp)s(eti\347\343o.)88 b(Os)109 3457 y(algoritmos)37 b(foram)i(a)5 b(justados)41 b(da)g(melhor)e(forma) g(p)s(oss\355v)m(el)i(a)f(\034m)g(de)h(obter)g(resultados)g(de)g(b)s (oa)109 3619 y(qualidade)i(em)g(rela\347\343o)g(aos)h(resultados)g (obtidos)f(p)s(elas)h(demais)f(equip)s(es)i(na)e(primeira)f(fase)i(do) 109 3782 y(desa\034o)38 b(e)h(melhorar)d(os)i(resultados)g(encon)m (trados)h(p)s(or)f(um)f(outro)h(algoritmo,)e(submetido)h(\340)h(fase) 109 3944 y(de)28 b(classi\034ca\347\343o)g(do)g(Desa\034o)h(R)m(O)m (ADEF)g(2005,)f(den)m(tro)g(do)g(mesmo)f(limite)e(de)k(temp)s(o)e(de)i (execu\347\343o)109 4107 y(\(600)i(segundos\).)274 4328 y(Como)k(resultado)g(dos)i(in)m(\372meros)e(testes)i(realizados,)f(o)f 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(es,)j(uma)c(an)m(tes)i(da)f(busca)g(lo)s(cal)e(e)109 5466 y(a)33 b(outra)h(duran)m(te)g(a)g(reinicializa\347\343o)29 b(\(este)35 b(par\342metro)e(n\343o)g(est\341)h(expl\355cito)f(no)g (pseudo-c\363)s(digo)g(do)109 5628 y(algoritmo)38 b(da)k(Figura)f (6.3\).)71 b(Utilizou-se)40 b Fz(\013)45 b FA(=)f(25)p FH(,)g Fz(\014)50 b FA(=)44 b(50)d FH(e)i Fz(i)2660 5643 y Ft(max)2848 5628 y FA(=)h(3)p FH(.)72 b(Conforme)41 b(foi)g(dito)109 5791 y(an)m(teriormen)m(te,)c Fz(\013)h FH(dev)m(e)g(ter)f(v)-5 b(alor)35 b(menor)h(que)i Fz(\014)6 b FH(.)56 b(Na)37 b(fase)g(de)g(p)s(erturba\347\343o,)h(aplicam-se)c (cinco)p eop %%Page: 53 67 53 66 bop 109 -28 a FB(8.2)60 b(Resultados)31 b(obtidos)2768 b(53)p 109 9 3780 4 v 109 256 a FH(mo)m(vimen)m(tos)24 b(\(cinco)i(carros)g(en)m(v)m(olvidos)g(em)f(viola\347\365)s(es)g (s\343o)g(remo)m(vidos)h(e)g(reinseridos)f(na)h(solu\347\343o\).)109 418 y(A)i(p)s(erturba\347\343o)g(aplicada)e(duran)m(te)j(a)f(fase)h(de) f(reinicializa\347\343o)c(\351)29 b(mais)e(forte)h(que)h(a)f(an)m (terior)f(e)h(con-)109 581 y(siste)g(na)g(aplica\347\343o)e(de)i(50)g (mo)m(vimen)m(tos)f(de)i(reinser\347\343o.)42 b(Al\351m)26 b(desses)31 b(par\342metros,)d(utiliza-se)e(um)109 743 y(outro)33 b(na)g(fase)h(de)g(reinicializa\347\343o)29 b(que)35 b(diz)e(resp)s(eito)g(ao)g(n)m(\372mero)g(de)h(aplica\347\365) s(es)f(da)g(p)s(erturba\347\343o)109 906 y(mais)h(forte)h(na)h (reinicializa\347\343o)31 b(an)m(tes)37 b(de)f(se)g(aplicar)e(a)h (heur\355stica)g(construtiv)-5 b(a:)49 b(dep)s(ois)36 b(de)g(duas)109 1068 y(reinicializa\347\365)s(es)k(com)j(p)s (erturba\347\343o)h(desde)h(a)f(\372ltima)d(melhoria,)j(utiliza-se)d (uma)i(no)m(v)-5 b(a)44 b(solu\347\343o)109 1231 y(como)34 b(p)s(on)m(to)i(de)g(partida.)52 b(Finalmen)m(te,)35 b(precisa-se)h(de\034nir)f(p)s(or)h(quan)m(to)g(temp)s(o,)g(no)f (m\341ximo,)f(o)109 1393 y(algoritmo)21 b(para)26 b(o)f(primeiro)e(ob)5 b(jetiv)m(o)25 b(p)s(o)s(de)h(ser)g(executado,)i(caso)e(o)f (crit\351rio)f(de)i(estagna\347\343o)f(ainda)109 1556 y(n\343o)32 b(tenha)h(sido)f(atingido.)41 b(A)33 b(fra\347\343o)e(de)j (temp)s(o)d(de)i(execu\347\343o)h(estab)s(elecida)e(foi)g(550)f (segundos.)274 1777 y(No)41 b(algoritmo)d(desen)m(v)m(olvido)k(para)f (otimizar)e(o)i(segundo)h(ob)5 b(jetiv)m(o,)44 b(os)e(par\342metros)f (s\343o)g(os)109 1940 y(tamanhos)47 b(inicial)d(e)k(\034nal)f(das)h (estruturas)g(de)g(vizinhan\347a)f(utilizadas)f(na)i(p)s (erturba\347\343o)f(\()p Fz(k)3758 1955 y Fq(1)3845 1940 y FH(e)109 2102 y Fz(k)160 2117 y Ft(max)344 2102 y FH(para)41 b(mo)m(vimen)m(tos)f FE(shift)p FH(,)j Fz(q)1418 2117 y Fq(1)1499 2102 y FH(e)e Fz(q)1626 2117 y Ft(max)1811 2102 y FH(para)g(mo)m(vimen)m(tos)f FE(swap)6 b FH(\))40 b(e)h(o)g(n)m(\372mero)g(m\341ximo)e(de)109 2265 y(aplica\347\365)s(es) d(de)i(in)m(tensi\034ca\347\343o/div)m(ersi\034ca\347\343o)f(sem)g (melhoria)e(\()p Fz(i)2601 2280 y Ft(max)2745 2265 y FH(\),)k(que)f(estab)s(elece)h(o)e(crit\351rio)109 2427 y(de)43 b(estagna\347\343o)f(do)g(algoritmo.)70 b(Ap)s(\363s)42 b(v)-5 b(\341rios)42 b(exp)s(erimen)m(tos)g(realizados,)i(os)f(v)-5 b(alores)41 b(adotados)109 2590 y(foram)34 b Fz(k)442 2605 y Fq(1)514 2590 y FA(=)f(3)p FH(,)k Fz(k)787 2605 y Ft(max)964 2590 y FA(=)c(8)p FH(,)j Fz(q)1228 2605 y Fq(1)1301 2590 y FA(=)d(5)j FH(e)g Fz(q)1617 2605 y Ft(max)1794 2590 y FA(=)d(10)p FH(.)53 b(O)35 b(v)-5 b(alor)35 b(de)h Fz(i)2603 2605 y Ft(max)2783 2590 y FH(\351)g(a)5 b(justado)36 b(de)g(acordo)g(com)109 2752 y(o)j(comp)s(ortamen)m(to)e(do)i(algoritmo,)f(conforme)g(descrito)i(a)f (seguir.)63 b(Se)40 b(o)f(\372ltimo)d(melhoramen)m(to)109 2915 y(foi)g(obtido)h(an)m(tes)h(da)g(primeira)e(aplica\347\343o)f(de)k (in)m(tensi\034ca\347\343o/div)m(ersi\034ca\347\343o,)f(faz-se)g Fz(i)3470 2930 y Ft(max)3651 2915 y FA(=)f(20)p FH(.)109 3077 y(Se)42 b(o)g(\372ltimo)d(melhoramen)m(to,)j(no)g(en)m(tan)m(to,)j (foi)c(conseguido)h(nas)g(dez)h(primeiras)d(aplica\347\365)s(es)h(de) 109 3240 y(in)m(tensi\034ca\347\343o/div)m(ersi\034ca\347\343o,)d Fz(i)1387 3255 y Ft(max)1568 3240 y FA(=)f(50)p FH(.)58 b(Finalmen)m(te,)38 b(caso)g(con)m(tr\341rio,)g(tem-se)g Fz(i)3422 3255 y Ft(max)3602 3240 y FA(=)f(150)p FH(.)109 3402 y(Este)32 b(crit\351rio)d(evita)i(que)h(temp)s(o)e(seja)h(desp)s (erdi\347ado)h(em)e(inst\342ncias)h(f\341ceis,)g(p)s(or\351m)f (grandes.)44 b(Em)109 3565 y(inst\342ncias)i(deste)j(tip)s(o,)h(o)d (algoritmo)d(consegue)k(encon)m(trar)g(a)g(melhor)e(solu\347\343o)g (nas)i(primeiras)109 3727 y(itera\347\365)s(es)34 b(e)g(a)g (execu\347\343o)i(de)f(itera\347\365)s(es)f(desnecess\341rias)i(custa)f (caro)f(p)s(ois)g(exige)g(m)m(uito)f(temp)s(o)h(em)109 3890 y(fun\347\343o)c(do)h(tamanho)f(da)g(inst\342ncia.)42 b(O)30 b(temp)s(o)g(de)i(execu\347\343o)g(m\341ximo)c(p)s(ermitido)g (caso)j(o)g(crit\351rio)109 4052 y(de)i(estagna\347\343o)f(acima)f (n\343o)h(seja)h(alcan\347ado)f(\351)h(580)f(segundos.)274 4274 y(No)39 b(terceiro)g(algoritmo,)e(existem)i(os)g(mesmos)g 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(de)f(teste)h(A.)f(Os)h(v)-5 b(alores)37 b(mostrados)h(para)f(o)h (algoritmo)d(prop)s(osto)109 5471 y(corresp)s(ondem)d(\340)f(m\351dia)f (das)i(solu\347\365)s(es)g(obtidas)f(nas)h(20)f(execu\347\365)s(es)j (realizadas.)41 b(Os)32 b(v)-5 b(alores)31 b(mos-)109 5633 y(trados)46 b(como)g(melhor)f(resultado)i(conhecido)f(corresp)s (ondem)h(\340)g(melhor)e(solu\347\343o)h(obtida)g(p)s(elos)109 5796 y(demais)34 b(algoritmos)e(submetidos)j(ao)f(concurso.)53 b(Os)35 b(v)-5 b(alores)34 b(das)i(colunas)f(HPR)m(C,)h(LPR)m(C,)g(PCC) p eop %%Page: 54 68 54 67 bop 109 -28 a FB(8.2)60 b(Resultados)31 b(obtidos)2768 b(54)p 109 9 3780 4 v 109 256 a FH(e)46 b(Custo)g(corresp)s(ondem)g (aos)g(v)-5 b(alores)45 b(do)g(primeiro,)i(segundo)f(e)g(terceiro)f(ob) 5 b(jetiv)m(os)46 b(e)g(o)g(v)-5 b(alor)109 418 y(corresp)s(onden)m(te) 38 b(da)e(fun\347\343o)g(de)g(custo,)i(resp)s(ectiv)-5 b(amen)m(te.)55 b(A)36 b(fun\347\343o)g(de)h(custo)f(utiliza)e(os)i(p)s (esos)109 581 y(determinados)h(p)s(ela)h(organiza\347\343o)f(do)h (concurso,)j(cujos)e(v)-5 b(alores)38 b(s\343o)g(1000000,)g(1000)g(e)g (1)g(para)g(o)109 743 y(primeiro,)28 b(segundo)i(e)h(terceiro)e(ob)5 b(jetiv)m(os,)31 b(resp)s(ectiv)-5 b(amen)m(te.)43 b(P)m(o)s(de-se)31 b(observ)-5 b(ar)30 b(que,)i(em)m(b)s(ora)d(as)109 906 y(m\351dias)d(dos)i(resultados)f(encon)m(trados)i(p)s(elo)d(algoritmo)e (prop)s(osto)j(n\343o)g(tenham)g(sido)g(sup)s(eriores)h(\340s)109 1068 y(melhores)c(solu\347\365)s(es)h(conhecidas,)i(ele)d(obtev)m(e)i (resultados)f(altamen)m(te)f(comp)s(etitiv)m(os,)h(visto)f(que)i(esta) 109 1231 y(tab)s(ela)38 b(apresen)m(ta)i(a)f(m\351dia)f(dos)i (resultados,)h(ao)e(in)m(v)m(\351s)i(do)e(melhor)f(resultado)h(encon)m (trado)h(p)s(elo)109 1393 y(algoritmo)g(prop)s(osto.)76 b(Observ)-5 b(a-se)44 b(que,)j(em)c(m\351dia,)i(foram)d(obtidas)h (solu\347\365)s(es)h(com)f(o)g(mesmo)109 1556 y(v)-5 b(alor)39 b(do)i(primeiro)d(ob)5 b(jetiv)m(o)41 b(que)h(a)e(melhor)g (solu\347\343o)g(conhecida.)68 b(Com)40 b(exce\347\343o)j(da)d (inst\342ncia)109 1718 y Fy(025_38_1)p FH(,)j(o)f(algoritmo)d(encon)m (tra)k(em)f(m\351dia)f(solu\347\365)s(es)i(cujos)g(v)-5 b(alores)41 b(do)i(segundo)g(ob)5 b(jetiv)m(o)109 1881 y(s\343o)33 b(p)s(oucas)g(unidades)g(acima)e(do)i(v)-5 b(alor)32 b(na)g(melhor)g(solu\347\343o)g(conhecida.)45 b(A)33 b(partir)f(desta)h(tab)s(ela,)109 2043 y(tam)m(b)s(\351m)41 b(p)s(o)s(de-se)j(concluir)e(que)h(este)i(conjun)m(to)e(de)g (inst\342ncias)g(\351)g(f\341cil)e(no)i(que)h(diz)f(resp)s(eito)f(\340) 109 2206 y(otimiza\347\343o)29 b(do)k(primeiro)d(ob)5 b(jetiv)m(o,)32 b(dado)g(que)i(sempre)f(se)g(consegue)h(o)e(melhor)f(v) -5 b(alor)31 b(conhecido.)208 2493 y(T)-8 b(ab)s(ela)32 b(8.2:)43 b(M\351dia)32 b(dos)h(resultados)g(obtidos)f(para)g(as)h (inst\342ncias)e(do)i(conjun)m(to)g(de)g(teste)g(A.)p 377 2632 3215 4 v 375 2732 4 100 v 853 2732 V 1203 2702 a Fe(Algoritmo)26 b(prop)r(osto)p 2260 2732 V 704 w(Melhor)h(resultado) p 3590 2732 V 375 2831 V 580 2801 a Fd(id)p 853 2831 V 253 w Fe(HPR)n(C)100 b(LPR)n(C)112 b(PCC)243 b(Custo)p 2260 2831 V 99 w(HPR)n(C)100 b(LPR)n(C)g(PCC)178 b(Custo)p 3590 2831 V 377 2834 3215 4 v 377 2851 V 375 2951 4 100 v 427 2921 a Fc(024_38_3)p 853 2951 V 227 w Fe(4.0)220 b(1.1)99 b(351.1)e(4001451.1)p 2260 2951 V 292 w(4)285 b(0)151 b(302)98 b(4000302)p 3590 2951 V 375 3050 V 427 3020 a Fc(024_38_5)p 853 3050 V 227 w Fe(4.0)178 b(36.4)99 b(339.6)e(4036739.6)p 2260 3050 V 292 w(4)243 b(34)151 b(309)98 b(4034309)p 3590 3050 V 375 3150 V 427 3120 a Fc(025_38_1)p 853 3150 V 227 w Fe(0.0)137 b(121.4)98 b(774.3)f(1221744.3)p 2260 3150 V 292 w(0)243 b(99)151 b(720)181 b(99720)p 3590 3150 V 375 3250 V 427 3220 a Fc(048_39_1)p 853 3250 V 227 w Fe(0.0)d(63.2)99 b(304.0)180 b(63504.0)p 2260 3250 V 293 w(0)243 b(61)151 b(290)181 b(61290)p 3590 3250 V 377 3253 3215 4 v 274 3620 a FH(Os)30 b(resultados)f(obtidos)g(para)g(as)g(inst\342ncias)g(do)g(conjun)m(to)h (de)g(teste)g(B)f(s\343o)h(mostrados)e(na)i(T)-8 b(a-)109 3783 y(b)s(ela)24 b(8.3.)40 b(A)25 b(tab)s(ela)f(tam)m(b)s(\351m)g (apresen)m(ta)i(as)f(m\351dias)f(das)h(solu\347\365)s(es)g(encon)m (tradas)h(nas)f(20)g(execu\347\365)s(es)109 3945 y(em)33 b(compara\347\343o)f(com)g(a)h(melhor)f(solu\347\343o)h(conhecida)g (para)g(estas)h(inst\342ncias.)45 b(Observ)-5 b(a-se)34 b(que)g(o)109 4108 y(algoritmo,)25 b(mesmo)j(comparando)g(a)g(m\351dia) f(das)i(solu\347\365)s(es)g(com)f(a)g(melhor)f(solu\347\343o,)i (conseguiu)g(ob-)109 4270 y(ter)h(melhor)f(resultado)h(nas)g (inst\342ncias)g Fy(028_ch1_S22_J2)e FH(e)j Fy(029_S21_J6)d FH(e)j(resultados)f(m\351dios)109 4433 y(de)42 b(mesma)e(qualidade)h (que)h(a)f(melhor)f(solu\347\343o)h(conhecida)g(nas)h(inst\342ncias)f Fy(028_ch2_S23_J3)p FH(,)109 4595 y Fy(035_ch1_S22_J3)p FH(,)27 b Fy(035_ch2_S22_J3)p FH(,)g Fy(048_)g(ch1_S22_J3)g FH(e)h Fy(064_ch2_)f(S22_J4)p FH(.)41 b(A)m(credita-)109 4758 y(se)28 b(que)h(os)f(resultados)g(encon)m(trados)h(para)f(as)g (inst\342ncias)f Fy(028_ch2_S23_J3)p FH(,)g Fy(035_ch1_S22_J3)p FH(,)109 4920 y Fy(035_ch2_S22_J3)h FH(e)i Fy(064_ch2_)f(S22_J4)f FH(sejam)i(v)-5 b(alores)29 b(\363timos,)g(p)s(ois)g(solu\347\365)s(es) h(de)g(custo)g(igual)109 5083 y(ao)51 b(da)i(melhor)d(conhecida)j (foram)e(encon)m(tradas)i(em)f(to)s(das)g(as)g(execu\347\365)s(es)j(do) d(algoritmo)d(em)109 5245 y(temp)s(o)d(de)j(execu\347\343o)g(considera) m(v)m(elmen)m(te)f(curto.)89 b(Nas)48 b(demais)f(inst\342ncias,)j(com)d (exce\347\343o)i(da)109 5408 y Fy(024_V2_S22_J1)p FH(,)30 b(os)i(resultados)g(obtidos)g(apresen)m(tam)g(v)-5 b(alores)31 b(piores)h(ap)s(enas)g(no)g(terceiro)g(ob-)109 5570 y(jetiv)m(o,)c(que) g(\351)g(o)g(de)g(menor)f(p)s(eso)h(no)f(custo)h(da)g(solu\347\343o,)g (em)f(rela\347\343o)g(\340)g(melhor)f(solu\347\343o)h(conhecida.)109 5733 y(Al\351m)33 b(disso,)j(observ)-5 b(a-se)36 b(que,)h(na)e(maioria) c(destas)36 b(inst\342ncias,)f(o)g(v)-5 b(alor)34 b(do)h(terceiro)f(ob) 5 b(jetiv)m(o)35 b(na)109 5895 y(m\351dia)d(das)h(solu\347\365)s(es)g (est\341)h(ap)s(enas)g(p)s(oucas)f(unidades)h(acima)d(do)j(seu)g(v)-5 b(alor)32 b(no)h(melhor)f(resultado)p eop %%Page: 55 69 55 68 bop 109 -28 a FB(8.2)60 b(Resultados)31 b(obtidos)2768 b(55)p 109 9 3780 4 v 109 256 a FH(conhecido.)51 b(Em)35 b(rela\347\343o)f(\340)g(inst\342ncia)g Fy(024_V2_S22_J1)p FH(,)g(observ)-5 b(a-se)36 b(que)g(o)f(v)-5 b(alor)34 b(do)h(primeiro)109 418 y(ob)5 b(jetiv)m(o,)29 b(na)f(m\351dia,)g(\351) h(um)e(p)s(ouco)i(pior)e(-)h(de)g(fato,)h(menos)f(de)h(uma)e(unidade)i (de)f(diferen\347a)h(-)e(e)i(isto)109 581 y(\351)j(um)f(indicativ)m(o)f (de)j(que)g(esta)f(\351)g(a)g(inst\342ncia)f(mais)f(dif\355cil)f(para)i (o)h(subproblema)f(de)i(minimizar)27 b(o)109 743 y(n)m(\372mero)32 b(de)h(viola\347\365)s(es)e(de)j(restri\347\365)s(es)e(de)h(capacidade) g(de)g(alta)e(prioridade.)210 1030 y(T)-8 b(ab)s(ela)32 b(8.3:)43 b(M\351dia)32 b(dos)h(resultados)g(obtidos)f(para)g(as)h (inst\342ncias)e(do)i(conjun)m(to)g(de)g(teste)g(B.)p 115 1169 3739 4 v 113 1269 4 100 v 863 1269 V 1276 1239 a Fe(Algoritmo)27 b(prop)r(osto)p 2398 1269 V 829 w(Melhor)g(resultado) p 3852 1269 V 113 1368 V 454 1339 a Fd(id)p 863 1368 V 388 w Fe(HPR)n(C)104 b(LPR)n(C)112 b(PCC)367 b(Custo)p 2398 1368 V 99 w(HPR)n(C)100 b(LPR)n(C)g(PCC)302 b(Custo)p 3852 1368 V 115 1372 3739 4 v 115 1388 V 113 1488 4 100 v 165 1458 a Fc(022_S22_J1)p 863 1488 V 413 w Fe(0.0)224 b(3.0)98 b(111.6)347 b(3111.6)p 2398 1488 V 293 w(0)285 b(3)151 b(109)347 b(3109)p 3852 1488 V 113 1588 V 165 1558 a Fc(023_S23_J3)p 863 1588 V 372 w Fe(48.0)223 b(0.0)98 b(316.2)181 b(48000316.2)p 2398 1588 V 250 w(48)284 b(0)151 b(316)181 b(48000316)p 3852 1588 V 113 1687 V 165 1657 a Fc(024_V2_S22_J1)p 863 1687 V 127 w Fe(1074.2)139 b(871.1)97 b(545.1)h(1075071645.1)p 2398 1687 V 166 w(1074)200 b(850)150 b(430)98 b(1074850430)p 3852 1687 V 113 1787 V 165 1757 a Fc(025_S22_J3)p 863 1787 V 413 w Fe(0.0)h(3912.0)e(501.8)223 b(3912501.8)p 2398 1787 V 291 w(0)160 b(3912)150 b(479)223 b(3912479)p 3852 1787 V 113 1887 V 165 1857 a Fc(028_ch1_S22_J2)p 863 1887 V 185 w Fe(54.0)g(3.0)140 b(74.5)181 b(54003074.5)p 2398 1887 V 250 w(54)284 b(3)192 b(76)182 b(54003076)p 3852 1887 V 113 1986 V 165 1956 a Fc(028_ch2_S23_J3)p 863 1986 V 226 w Fe(0.0)g(70.0)f(6.0)307 b(70006.0)p 2398 1986 V 292 w(0)243 b(70)234 b(6)307 b(70006)p 3852 1986 V 113 2086 V 165 2056 a Fc(029_S21_J6)p 863 2086 V 372 w Fe(35.0)98 b(2150.0)f(165.8)181 b(37150165.8)p 2398 2086 V 250 w(35)159 b(2150)150 b(167)181 b(37150167)p 3852 2086 V 113 2185 V 165 2156 a Fc(035_ch1_S22_J3)p 863 2185 V 185 w Fe(67.0)g(52.0)140 b(49.0)181 b(67052049.0)p 2398 2185 V 250 w(67)242 b(52)192 b(49)182 b(67052049)p 3852 2185 V 113 2285 V 165 2255 a Fc(035_ch2_S22_J3)p 863 2285 V 143 w Fe(385.0)140 b(341.0)97 b(205.0)140 b(385341205.0)p 2398 2285 V 207 w(385)201 b(341)150 b(205)140 b(385341205)p 3852 2285 V 113 2385 V 165 2355 a Fc(039_ch1_S22_J4)p 863 2385 V 226 w Fe(0.0)182 b(29.0)98 b(160.4)306 b(29160.4)p 2398 2385 V 292 w(0)243 b(29)151 b(117)306 b(29117)p 3852 2385 V 113 2484 V 165 2454 a Fc(039_ch3_S22_J4)p 863 2484 V 226 w Fe(0.0)224 b(0.0)98 b(197.7)389 b(197.1)p 2398 2484 V 293 w(0)285 b(0)151 b(197)389 b(197)p 3852 2484 V 113 2584 V 165 2554 a Fc(048_ch1_S22_J3)p 863 2584 V 226 w Fe(0.0)224 b(0.0)98 b(200.0)389 b(200.0)p 2398 2584 V 293 w(0)285 b(0)151 b(200)389 b(200)p 3852 2584 V 113 2684 V 165 2654 a Fc(048_ch2_S22_J3)p 863 2684 V 226 w Fe(3.0)224 b(0.0)98 b(340.0)223 b(3000340.0)p 2398 2684 V 291 w(3)285 b(0)151 b(337)223 b(3000337)p 3852 2684 V 113 2783 V 165 2753 a Fc(064_ch1_S22_J3)p 863 2783 V 226 w Fe(0.0)h(0.0)98 b(194.2)389 b(194.2)p 2398 2783 V 293 w(0)285 b(0)151 b(182)389 b(182)p 3852 2783 V 113 2883 V 165 2853 a Fc(064_ch2_S22_J4)p 863 2883 V 226 w Fe(0.0)182 b(69.0)98 b(130.0)306 b(69130.0)p 2398 2883 V 292 w(0)243 b(69)151 b(130)306 b(69130)p 3852 2883 V 115 2886 3739 4 v 274 3253 a FH(Comparando-se)40 b(as)g(duas)h(tab)s(elas,)g(p)s(o)s(de-se)f(observ)-5 b(ar)41 b(que)g(as)f(inst\342ncias)f(do)h(conjun)m(to)h(de)109 3416 y(teste)g(B)e(s\343o,)j(de)f(maneira)d(geral,)i(mais)f(f\341ceis)h (de)g(resolv)m(er)g(que)h(as)f(inst\342ncias)g(do)f(conjun)m(to)i(de) 109 3578 y(teste)36 b(A.)f(P)m(ara)g(o)g(conjun)m(to)g(de)h(teste)g(B,) f(acredita-se)f(que)i(se)g(consegue)h(otimizar)32 b(p)s(elo)i(menos)h (os)109 3741 y(dois)i(primeiros)e(ob)5 b(jetiv)m(os)39 b(do)e(problema)f(em)h(quase)i(to)s(das)f(as)g(inst\342ncias,)g(enquan) m(to)h(que,)h(para)109 3904 y(o)c(outro)g(conjun)m(to)h(de)h (inst\342ncias,)f(acredita-se)f(que)i(somen)m(te)f(se)g(consegue)h (otimizar)c(somen)m(te)j(o)109 4066 y(primeiro)i(ob)5 b(jetiv)m(o.)72 b(\311,)43 b(p)s(ortan)m(to,)h(nestas)f(inst\342ncias)e (que)i(se)g(observ)-5 b(a)42 b(maior)e(diferen\347a)i(en)m(tre)109 4229 y(as)e(solu\347\365)s(es)g(obtidas)f(p)s(elo)g(algoritmo)d(prop)s (osto.)65 b(Isto)40 b(p)s(o)s(de)f(ser)i(v)m(eri\034cado)f(ao)f(se)i (observ)-5 b(ar)40 b(os)109 4391 y(v)-5 b(alores)33 b(das)i(T)-8 b(ab)s(ela)33 b(8.4)h(e)h(T)-8 b(ab)s(ela)33 b(8.5.)49 b(Na)34 b(T)-8 b(ab)s(ela)33 b(8.4,)i(t\352m-se)f(as)g(melhoras)f (solu\347\365)s(es)i(obtidas)109 4554 y(para)h(as)g(inst\342ncias)g(do) g(conjun)m(to)g(de)h(teste)g(A)g(e,)g(na)g(T)-8 b(ab)s(ela)35 b(8.5,)i(t\352m-se)f(as)g(melhores)g(solu\347\365)s(es)109 4716 y(para)e(as)h(inst\342ncias)f(do)h(conjun)m(to)g(de)g(teste)h(B.)f (Em)g(am)m(bas)f(as)h(tab)s(elas,)g(os)g(n)m(\372meros)g(destacados)109 4879 y(em)k(negrito)g(indicam)e(o)j(algoritmo)c(que)k(encon)m(trou)h (melhor)d(resultado)h(e)h(as)g(colunas)g(onde)g(eles)109 5041 y(aparecem)33 b(indicam)f(o)i(ob)5 b(jetiv)m(o)34 b(de)g(maior)e(p)s(eso)i(resp)s(ons\341)m(v)m(el)h(p)s(ela)e (diferen\347a)h(en)m(tre)h(as)f(solu\347\365)s(es.)109 5204 y(Estas)39 b(tab)s(elas)e(tam)m(b)s(\351m)g(p)s(ermitem)f(v)m (eri\034car)i(que)h(se)g(obt\351m)f(solu\347\365)s(es)g(pr\363)m(ximas) f(e,)j(em)e(alguns)109 5366 y(casos,)30 b(melhores)f(que)h(as)f (melhores)g(solu\347\365)s(es)g(conhecidas,)h(mesmo)e(que,)j(na)e (m\351dia,)g(os)g(resultados)109 5529 y(n\343o)j(sejam)g(t\343o)g (signi\034cativ)m(os.)274 5750 y(P)m(o)s(de-se)37 b(notar)e(que)i(as)f (m\351dias)e(do)i(segundo)h(e)f(terceiro)f(ob)5 b(jetiv)m(os)36 b(da)g(T)-8 b(ab)s(ela)35 b(8.2)g(s\343o)h(rela-)109 5913 y(tiv)-5 b(amen)m(te)35 b(distan)m(tes)h(das)g(melhores)f (solu\347\365)s(es)h(da)g(T)-8 b(ab)s(ela)35 b(8.4.)53 b(Os)36 b(resultados)g(das)g(T)-8 b(ab)s(elas)36 b(8.3)p eop %%Page: 56 70 56 69 bop 109 -28 a FB(8.2)60 b(Resultados)31 b(obtidos)2768 b(56)p 109 9 3780 4 v 257 308 a FH(T)-8 b(ab)s(ela)31 b(8.4:)43 b(Melhor)32 b(solu\347\343o)g(encon)m(trada)h(para)g(as)f (inst\342ncias)g(do)h(conjun)m(to)g(de)g(teste)g(A.)p 416 446 3138 4 v 414 546 4 100 v 892 546 V 1203 516 a Fe(Algoritmo)26 b(prop)r(osto)p 2222 546 V 665 w(Melhor)h(resultado)p 3552 546 V 414 646 V 619 616 a Fd(id)p 892 646 V 252 w Fe(HPR)n(C)100 b(LPR)n(C)g(PCC)178 b(Custo)p 2222 646 V 99 w(HPR)n(C)100 b(LPR)n(C)g(PCC)178 b(Custo)p 3552 646 V 416 649 3138 4 v 416 666 V 414 765 4 100 v 466 735 a Fc(024_38_3)p 892 765 V 291 w Fe(4)285 b(0)151 b(312)98 b(4000312)p 2222 765 V 292 w(4)285 b(0)151 b(302)98 b(4000302)p 3552 765 V 414 865 V 466 835 a Fc(024_38_5)p 892 865 V 291 w Fe(4)244 b(34)150 b(331)98 b(4034331)p 2222 865 V 292 w(4)243 b(34)151 b(309)98 b(4034309)p 3552 865 V 414 965 V 466 935 a Fc(025_38_1)p 892 965 V 291 w Fe(0)202 b(110)150 b(733)140 b(110733)p 2222 965 V 292 w(0)231 b Fb(99)151 b Fe(720)181 b(99720)p 3552 965 V 414 1064 V 466 1034 a Fc(048_39_1)p 892 1064 V 291 w Fe(0)244 b(61)150 b(299)181 b(61299)p 2222 1064 V 293 w(0)243 b(61)151 b(290)181 b(64314)p 3552 1064 V 416 1067 3138 4 v 259 1427 a FH(T)-8 b(ab)s(ela)31 b(8.5:)43 b(Melhor)32 b(solu\347\343o)g(encon)m(trada)i(para)e(as)g (inst\342ncias)g(do)h(conjun)m(to)g(de)g(teste)g(B.)p 156 1566 3658 4 v 154 1665 4 100 v 903 1665 V 1276 1635 a Fe(Algoritmo)27 b(prop)r(osto)p 2357 1665 V 789 w(Melhor)g(resultado) p 3812 1665 V 154 1765 V 494 1735 a Fd(id)p 903 1765 V 388 w Fe(HPR)n(C)100 b(LPR)n(C)g(PCC)303 b(Custo)p 2357 1765 V 99 w(HPR)n(C)100 b(LPR)n(C)g(PCC)302 b(Custo)p 3812 1765 V 156 1768 3658 4 v 156 1785 V 154 1884 4 100 v 205 1854 a Fc(022_S22_J1)p 903 1884 V 478 w Fe(0)285 b(3)132 b Fb(107)348 b Fe(3107)p 2357 1884 V 294 w(0)285 b(3)151 b(109)347 b(3109)p 3812 1884 V 154 1984 V 205 1954 a Fc(023_S23_J3)p 903 1984 V 437 w Fe(48)284 b(0)151 b(316)181 b(48000316)p 2357 1984 V 250 w(48)285 b(0)151 b(316)181 b(48000316)p 3812 1984 V 154 2084 V 205 2054 a Fc(024_V2_S22_J1)p 903 2084 V 192 w Fe(1074)200 b(854)150 b(502)98 b(1074865002)p 2357 2084 V 166 w(1074)182 b Fb(850)151 b Fe(430)98 b(1074850430)p 3812 2084 V 154 2183 V 205 2153 a Fc(025_S22_J3)p 903 2183 V 478 w Fe(0)161 b(3912)149 b(480)223 b(3912480)p 2357 2183 V 292 w(0)160 b(3912)131 b Fb(479)223 b Fe(3912479)p 3812 2183 V 154 2283 V 205 2253 a Fc(028_ch1_S22_J2)p 903 2283 V 250 w Fe(54)284 b(3)180 b Fb(72)i Fe(54003072)p 2357 2283 V 250 w(54)285 b(3)192 b(76)182 b(54003076)p 3812 2283 V 154 2383 V 205 2353 a Fc(028_ch2_S23_J3)p 903 2383 V 291 w Fe(0)244 b(70)233 b(6)307 b(70006)p 2357 2383 V 293 w(0)243 b(70)234 b(6)306 b(70006)p 3812 2383 V 154 2482 V 205 2452 a Fc(029_S21_J6)p 903 2482 V 437 w Fe(35)160 b(2150)130 b Fb(162)182 b Fe(37150162)p 2357 2482 V 250 w(35)160 b(2150)150 b(167)181 b(37150167)p 3812 2482 V 154 2582 V 205 2552 a Fc(035_ch1_S22_J3)p 903 2582 V 250 w Fe(67)243 b(52)192 b(49)181 b(67052049)p 2357 2582 V 250 w(67)243 b(52)192 b(49)182 b(67052049)p 3812 2582 V 154 2681 V 205 2652 a Fc(035_ch2_S22_J3)p 903 2681 V 208 w Fe(385)201 b(341)150 b(205)140 b(385341205)p 2357 2681 V 208 w(385)201 b(341)150 b(205)139 b(385341205)p 3812 2681 V 154 2781 V 205 2751 a Fc(039_ch1_S22_J4)p 903 2781 V 291 w Fe(0)244 b(29)150 b(154)306 b(29154)p 2357 2781 V 293 w(0)243 b(29)132 b Fb(117)306 b Fe(29117)p 3812 2781 V 154 2881 V 205 2851 a Fc(039_ch3_S22_J4)p 903 2881 V 291 w Fe(0)285 b(0)132 b Fb(196)390 b Fe(196)p 2357 2881 V 294 w(0)285 b(0)151 b(197)388 b(197)p 3812 2881 V 154 2980 V 205 2950 a Fc(048_ch1_S22_J3)p 903 2980 V 291 w Fe(0)285 b(0)151 b(200)389 b(200)p 2357 2980 V 294 w(0)285 b(0)151 b(200)388 b(200)p 3812 2980 V 154 3080 V 205 3050 a Fc(048_ch2_S22_J3)p 903 3080 V 291 w Fe(3)285 b(0)151 b(339)223 b(3000339)p 2357 3080 V 292 w(3)285 b(0)132 b Fb(337)223 b Fe(3000337)p 3812 3080 V 154 3180 V 205 3150 a Fc(064_ch1_S22_J3)p 903 3180 V 291 w Fe(0)285 b(0)151 b(190)389 b(190)p 2357 3180 V 294 w(0)285 b(0)132 b Fb(182)389 b Fe(182)p 3812 3180 V 154 3279 V 205 3249 a Fc(064_ch2_S22_J4)p 903 3279 V 291 w Fe(0)244 b(69)150 b(130)306 b(69130)p 2357 3279 V 293 w(0)243 b(69)151 b(130)305 b(69130)p 3812 3279 V 156 3282 3658 4 v 109 3656 a FH(e)84 b(8.5,)44 b(p)s(or)e(outro)f(lado,)j(apresen)m(tam)e(diferen\347as)g(p)s(equenas) i(ap)s(enas)f(no)f(terceiro)f(ob)5 b(jetiv)m(o)42 b(na)109 3819 y(maioria)30 b(dos)k(casos,)h(p)s(or)f(se)g(tratarem)f(de)h (inst\342ncias)f(mais)f(f\341ceis.)47 b(Em)34 b(tr\352s)g(das)g(quatro) g(inst\342n-)109 3981 y(cias)d(do)g(conjun)m(to)h(de)g(teste)h(A,)f (consegue-se)h(obter)f(solu\347\343o)e(de)j(mesma)d(qualidade)h(que)h (a)g(melhor)109 4144 y(solu\347\343o)j(conhecida)h(considerando-se)g (os)g(dois)f(primeiros)e(ob)5 b(jetiv)m(os.)54 b(P)m(ara)36 b(o)f(conjun)m(to)h(de)g(teste)109 4306 y(B,)e(observ)-5 b(a-se)35 b(um)f(certo)g(equil\355brio)e(en)m(tre)j(os)f(resultados)h (comparados.)48 b(O)34 b(algoritmo)d(prop)s(osto)109 4469 y(obtev)m(e)38 b(solu\347\365)s(es)f(melhores)f(em)g(quatro)h (inst\342ncias)f(e,)i(p)s(or)e(outro)h(lado,)f(obtev)m(e)j (solu\347\365)s(es)d(piores)109 4631 y(em)c(outras)g(cinco.)43 b(Nas)33 b(demais)f(inst\342ncias,)g(am)m(b)s(os)g(as)h(solu\347\365)s (es)f(p)s(ossuem)h(o)f(mesmo)g(custo.)274 4853 y(A)41 b(inst\342ncia)f Fy(028_ch2_S23_J3)p FH(,)h(em)m(b)s(ora)g(p)s(equena)h (e)f(de)h(f\341cil)d(solu\347\343o,)k(foi)c(a)i(que)h(exigiu)109 5015 y(maior)35 b(trabalho)h(p)s(or)h(parte)h(dos)g(viabilizadores)d (\(v)m(er)j(Se\347\343o)g(7.3.1\).)58 b(Mesmo)37 b(assim,)h(n\343o)f (se)i(fez)109 5178 y(necess\341ria)23 b(a)g(aplica\347\343o)e(do)i (terceiro)f(pro)s(cedimen)m(to)h(de)g(viabiliza\347\343o.)37 b(Desta)24 b(forma,)f(em)g(nenh)m(uma)109 5340 y(das)43 b(inst\342ncias)f(testadas,)k(os)d(v)-5 b(alores)42 b(do)g(primeiro)f (e)i(segundo)g(ob)5 b(jetiv)m(os)43 b(foram)f(deteriorados)109 5503 y(quando)33 b(viabilizando)c(as)k(solu\347\365)s(es.)274 5724 y(A)m(dicionalmen)m(te,)46 b(apresen)m(tam-se)f(os)g(resultados)g (obtidos)f(p)s(elo)f(algoritmo)e(prop)s(osto)k(para)109 5887 y(o)39 b(conjun)m(to)h(de)g(teste)g(X,)g(utilizado)d(para)i (classi\034car)g(as)h(equip)s(es)g(na)g(fase)g(\034nal.)63 b(Os)40 b(resultados)p eop %%Page: 57 71 57 70 bop 109 -28 a FB(8.2)60 b(Resultados)31 b(obtidos)2768 b(57)p 109 9 3780 4 v 109 256 a FH(foram)40 b(obtidos)i(a)g(partir)e (de)j(exp)s(erimen)m(tos)f(computacionais)f(realizados)g(p)s(ela)g (organiza\347\343o)f(da)109 418 y(comp)s(eti\347\343o)d(e)i (determinaram)e(a)h(classi\034ca\347\343o)g(\034nal)g(do)h(algoritmo)c (implemen)m(tado)h(em)i(rela\347\343o)109 581 y(\340s)32 b(18)f(equip)s(es)i(\034nalistas.)42 b(O)32 b(conjun)m(to)h(de)f(teste) h(X)f(\351)g(formado)f(p)s(or)g(tr\352s)i(inst\342ncias)e(cujos)i (dados)109 743 y(s\343o)39 b(apresen)m(tados)h(na)f(T)-8 b(ab)s(ela)38 b(8.6)g(e)h(para)g(as)g(quais)g(os)g(resultados)g (obtidos)f(s\343o)h(mostrados)f(na)109 906 y(T)-8 b(ab)s(ela)40 b(8.7.)70 b(Os)41 b(v)-5 b(alores)41 b(apresen)m(tados)i(na)e (\372ltima)e(tab)s(ela)h(corresp)s(ondem)i(\340s)f(medias)g(dos)g(re-) 109 1068 y(sultados)32 b(encon)m(trados)h(em)e(cinco)h(execu\347\365)s (es)i(do)e(algoritmo)d(prop)s(osto)i(e)i(s\343o)f(comparados)f(com)g(a) 109 1231 y(melhor)j(m\351dia)g(den)m(tre)j(os)e(outros)h(algoritmos)c (submetidos)k(\340)f(fase)h(\034nal.)51 b(A)36 b(partir)e(da)i(tab)s (ela,)f(\351)109 1393 y(p)s(oss\355v)m(el)d(v)m(er)i(que)g(o)e (algoritmo)e(obtev)m(e)k(um)e(b)s(om)g(desemp)s(enho)h(quando)h (comparado)d(aos)i(demais)109 1556 y(algoritmos.)48 b(Obtev)m(e-se)37 b(melhor)d(resultado)h(em)g(duas)h(inst\342ncias:)48 b(em)35 b(uma)f(delas,)i(melhorou-se)109 1718 y(no)41 b(segundo)h(ob)5 b(jetiv)m(o)41 b(e,)i(na)e(outra,)i(encon)m(trou-se)f (o)f(mesmo)f(resultado)h(que)h(o)e(melhor)g(den)m(tre)109 1881 y(to)s(das)35 b(as)i(outras)f(equip)s(es.)54 b(Na)36 b(terceira)g(inst\342ncia,)g(n\343o)f(se)i(conseguiu)f(obter)h(a)e (melhor)g(solu\347\343o)109 2043 y(em)d(decorr\352ncia)h(do)f(v)-5 b(alor)31 b(alcan\347ado)h(para)g(o)g(terceiro)g(ob)5 b(jetiv)m(o.)780 2330 y(T)-8 b(ab)s(ela)32 b(8.6:)43 b(Dados)33 b(das)g(inst\342ncias)f(do)g(conjun)m(to)h(de)g(teste)h(X.)p 526 2469 2917 4 v 524 2570 4 101 v 881 2540 a Fd(id)p 1305 2570 V 462 w(n)p 1571 2570 V 157 w(m)1695 2552 y Fa(h)p 1787 2570 V 1838 2540 a Fd(m)1911 2552 y Fa(l)p 1985 2570 V 2036 2540 a Fd(t)2066 2510 y Fa(max)2066 2563 y(h)p 2251 2570 V 2302 2540 a Fd(t)2332 2510 y Fa(med)2332 2563 y(h)p 2510 2570 V 2561 2540 a Fd(t)2591 2510 y Fa(max)2591 2563 y(l)p 2776 2570 V 2827 2540 a Fd(t)2857 2510 y Fa(med)2857 2563 y(l)p 3035 2570 V 3110 2540 a Fd(c)p 3217 2570 V 164 w(g)p 3441 2570 V 526 2573 2917 4 v 526 2590 V 524 2689 4 100 v 576 2659 a Fc(025_S49_J1)p 1305 2689 V 314 w Fe(1071)p 1571 2689 V 135 w(6)p 1787 2689 V 144 w(14)p 1985 2689 V 116 w(0.92)p 2251 2689 V 113 w(0.80)p 2510 2689 V 114 w(1.20)p 2776 2689 V 113 w(0.55)p 3035 2689 V 104 w(19)p 3217 2689 V 120 w(60)p 3441 2689 V 524 2789 V 576 2759 a Fc(028_CH1_S50_J4)p 1305 2789 V 116 w Fe(460)p 1571 2789 V 156 w(9)p 1787 2789 V 144 w(17)p 1985 2789 V 116 w(0.98)p 2251 2789 V 113 w(0.59)p 2510 2789 V 114 w(2.57)p 2776 2789 V 113 w(1.07)p 3035 2789 V 104 w(15)p 3217 2789 V 99 w(100)p 3441 2789 V 524 2889 V 576 2859 a Fc(028_CH2_S51_J1)p 1305 2889 V 136 w Fe(78)p 1571 2889 V 178 w(1)p 1787 2889 V 164 w(5)p 1985 2889 V 138 w(0.85)p 2251 2889 V 113 w(0.85)p 2510 2889 V 114 w(0.90)p 2776 2889 V 113 w(0.38)p 3035 2889 V 125 w(4)p 3217 2889 V 120 w(100)p 3441 2889 V 526 2892 2917 4 v 208 3325 a FH(T)-8 b(ab)s(ela)32 b(8.7:)43 b(M\351dia)32 b(dos)h(resultados)g (obtidos)f(para)g(as)h(inst\342ncias)e(do)i(conjun)m(to)g(de)g(teste)g (X.)p 131 3464 3707 4 v 129 3563 4 100 v 911 3563 V 1281 3533 a Fe(Algoritmo)26 b(prop)r(osto)p 2359 3563 V 798 w(Melhor)h(resultado)p 3836 3563 V 129 3663 V 486 3633 a Fd(id)p 911 3663 V 404 w Fe(HPR)n(C)100 b(LPR)n(C)112 b(PCC)284 b(Custo)p 2359 3663 V 100 w(HPR)n(C)100 b(LPR)n(C)141 b(PCC)284 b(Custo)p 3836 3663 V 131 3666 3707 4 v 131 3683 V 129 3783 4 100 v 181 3753 a Fc(025_S49_J1)p 911 3783 V 445 w Fe(0.0)137 b(160.0)98 b(602.2)181 b(160602.2)p 2359 3783 V 227 w(0.0)137 b(160.0)98 b Fb(407.6)181 b Fe(160407.6)p 3836 3783 V 129 3882 V 181 3852 a Fc(028_CH1_S50_J4)p 911 3882 V 185 w Fe(36.0)108 b Fb(341.4)139 b Fe(95.4)99 b(36341495.4)p 2359 3882 V 185 w(36.0)136 b(360.0)167 b(92.4)99 b(36360092.4)p 3836 3882 V 129 3982 V 181 3952 a Fc(028_CH2_S51_J1)p 911 3982 V 226 w Fe(0.0)220 b(0.0)182 b(3.0)389 b(3.0)p 2359 3982 V 230 w(0.0)220 b(0.0)210 b(3.0)389 b(3.0)p 3836 3982 V 131 3985 3707 4 v 274 4352 a FH(\311)25 b(m)m(uito)f(imp)s(ortan)m(te)f(dizer)i(que)h(os)f (resultados)g(apresen)m(tados)h(como)e(os)h(melhores)g(conhecidos)109 4515 y(n\343o)40 b(foram)f(obtidos)h(p)s(or)g(um)f(mesmo)h(algoritmo,)f (o)h(que)h(aumen)m(ta)g(a)f(relev)m(\352ncia)g(do)h(algoritmo)109 4677 y(apresen)m(tado)33 b(nesta)h(disserta\347\343o.)274 4899 y(T)-8 b(o)s(dos)38 b(os)f(resultados)h(apresen)m(tados)g(foram)e (obtidos)h(em)g(execu\347\365)s(es)j(de)d(600)g(segundos.)59 b(No)109 5062 y(en)m(tan)m(to,)42 b(este)f(limite)c(de)k(temp)s(o)e(p)s (o)s(de)g(ser)i(m)m(uito)e(restritiv)m(o)g(em)g(rela\347\343o)g(\340)h (qualidade)f(das)h(so-)109 5224 y(lu\347\365)s(es)34 b(que)i(p)s(o)s(dem)e(ser)i(obtidas.)49 b(Muito)35 b(pro)m(v)-5 b(a)m(v)m(elmen)m(te,)36 b(se)f(um)g(limite)c(de)36 b(temp)s(o)e(maior) e(fosse)109 5387 y(determinado,)k(solu\347\365)s(es)g(de)h(melhor)e (qualidade)h(seriam)f(encon)m(tradas.)56 b(A)36 b(\034m)g(de)h(se)g(v)m (eri\034car)f(se)109 5549 y(este)h(limite)c(acarreta)j(uma)f(p)s(erda)h (consider\341)m(v)m(el)h(na)f(qualidade)f(das)i(solu\347\365)s(es,)g (foram)d(realizados)109 5712 y(testes)45 b(com)e(algumas)e (inst\342ncias)i(utilizando)e(diferen)m(tes)k(temp)s(os)e(de)h (execu\347\343o,)k(que)d(v)-5 b(ariaram)109 5874 y(de)38 b(50)f(a)h(1000)f(segundos.)60 b(F)-8 b(oram)36 b(realizadas)h(dez)i (execu\347\365)s(es)h(com)d(cada)h(um)f(destes)j(limites)35 b(de)p eop %%Page: 58 72 58 71 bop 109 -28 a FB(8.2)60 b(Resultados)31 b(obtidos)2768 b(58)p 109 9 3780 4 v 109 256 a FH(temp)s(o)43 b(para)g(as)h (inst\342ncias)f Fy(025_38_1)p FH(,)i Fy(024_V2_S22_J1)d FH(e)j Fy(028_ch2_S23_J3)p FH(.)75 b(P)m(ara)44 b(que)109 418 y(estes)29 b(exp)s(erimen)m(tos)f(fossem)g(realizados,)f(foi)g (necess\341rio)h(alterar)f(as)h(fra\347\365)s(es)f(de)i(temp)s(o)e (atribu\355das)109 581 y(aos)45 b(algoritmos)d(desen)m(v)m(olvidos)47 b(para)e(os)h(dois)f(primeiros)f(ob)5 b(jetiv)m(os.)82 b(As)46 b(fra\347\365)s(es)g(foram)e(atri-)109 743 y(bu\355das)g(prop)s (orcionalmen)m(te)e(aos)j(v)-5 b(alores)44 b(determinados)g(para)g(600) f(segundos,)49 b(resultando)c(em)109 906 y FA(\(550)p Fz(=)p FA(600\))p Fz(:t)35 b FH(e)i FA(\(580)p Fz(=)p FA(600\))p Fz(:t)f FH(para)g(os)i(algoritmos)33 b(para)k(otimizar)d(o)j (primeiro)d(e)j(segundo)h(ob)5 b(jeti-)109 1068 y(v)m(os,)28 b(resp)s(ectiv)-5 b(amen)m(te,)28 b(onde)e Fz(t)h FH(\351)f(o)g(no)m(v) m(o)h(limite)22 b(de)27 b(temp)s(o)e(utilizado.)39 b(Os)26 b(resultados)g(obtidos)g(p)s(or)109 1231 y(estes)i(exp)s(erimen)m(tos)f (s\343o)g(mostrados)g(nos)g(gr\341\034cos)g(das)g(Figuras)f(8.1,)54 b(8.2)27 b(e)54 b(8.3.)41 b(Cada)27 b(p)s(on)m(to)g(nos)109 1393 y(gr\341\034cos)h(represen)m(ta)h(o)f(custo)h(m\351dio)d(das)i (solu\347\365)s(es)g(encon)m(tradas)h(em)f(fun\347\343o)g(do)g(temp)s (o)f(de)h(execu-)109 1556 y(\347\343o.)43 b(No)31 b(gr\341\034co)g (para)g(a)h(inst\342ncia)e Fy(025_38_1)g FH(\(Figura)f(8.1\),)j(p)s(o)s (de-se)f(observ)-5 b(ar)32 b(que)h(o)e(v)-5 b(alor)30 b(do)109 1718 y(primeiro)g(ob)5 b(jetiv)m(o)32 b(encon)m(trado)h(em)f (to)s(dos)g(os)g(temp)s(os)g(de)h(execu\347\343o)h(foi)d(o)h(mesmo,)g (ou)g(seja,)h(esta)109 1881 y(inst\342ncia)40 b(\351)i(considerada)g (f\341cil)e(em)h(rela\347\343o)g(ao)g(primeiro)e(ob)5 b(jetiv)m(o)42 b(do)g(problema.)69 b(P)m(erceb)s(e-se)109 2043 y(tam)m(b)s(\351m)28 b(que)j(h\341)f(m)m(uito)e(ganho)i(na)g (qualidade)f(do)h(segundo)g(ob)5 b(jetiv)m(o)30 b(at\351)g(600)f (segundos.)44 b(De)31 b(600)109 2206 y(a)40 b(1000)g(segundos,)k(o)c (ganho)h(\351)g(menos)f(signi\034cativ)m(o)f(e)i(as)g(solu\347\365)s (es)g(melhoram)d(em)i(m\351dia)g(oito)109 2368 y(unidades)28 b(no)h(segundo)g(ob)5 b(jetiv)m(o.)42 b(No)29 b(gr\341\034co)f(para)g (a)g(inst\342ncia)f Fy(024_V2_S22_J1)g FH(\(Figura)g(8.2\),)109 2531 y(que)h(\351)f(uma)f(inst\342ncia)g(dif\355cil)e(para)j(o)f 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fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 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repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def /BoxColFill { gsave Rec /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor fill grestore } def % % PostScript Level 1 Pattern Fill routine % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill { gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate 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b(que)j(mostra)d(a)h(qualidade)f(da)i(solu\347\343o)e (em)h(fun\347\343o)g(do)g(temp)s(o)g(de)h(execu\347\343o)109 5641 y(para)e(a)g(inst\342ncia)f Fy(024_V2_S22_J1)p FH(.)p eop %%Page: 60 74 60 73 bop 109 -28 a FB(8.2)60 b(Resultados)31 b(obtidos)2768 b(60)p 109 9 3780 4 v 530 3850 a currentpoint currentpoint translate 0.97865 0.97865 scale neg exch neg exch translate 530 3850 a @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 3600 @rwi @setspecial %%BeginDocument: 028_ch2_S23_J3.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: 028_ch2_EP_ENP_RAF_S23_J3.eps %%Creator: gnuplot 4.0 patchlevel 0 %%CreationDate: Mon Mar 28 13:23:49 2005 %%DocumentFonts: (atend) %%BoundingBox: 50 50 410 302 %%Orientation: Portrait %%EndComments /gnudict 256 dict def gnudict begin /Color false def /Solid false def /gnulinewidth 5.000 def /userlinewidth gnulinewidth def /vshift -46 def /dl {10.0 mul} def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def /Rounded false def /reencodeISO { dup dup findfont dup length dict begin { 1 index /FID ne { def }{ pop pop } ifelse } forall currentdict /CharStrings known { CharStrings /Idieresis known { /Encoding ISOLatin1Encoding def } if } if currentdict end definefont } def /ISOLatin1Encoding [ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright /parenleft/parenright/asterisk/plus/comma/minus/period/slash /zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon /less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N /O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright /asciicircum/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m /n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef 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/otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis /yacute/thorn/ydieresis ] def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /N {newpath moveto} bind def /C {setrgbcolor} bind def /f {rlineto fill} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop 0 setgray Solid {pop []} if 0 setdash} ifelse } def /BL { stroke userlinewidth 2 mul setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /AL { stroke userlinewidth 2 div setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /UL { dup gnulinewidth mul /userlinewidth exch def dup 1 lt {pop 1} if 10 mul /udl exch def } def /PL { stroke userlinewidth setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /LTw { PL [] 1 setgray } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 1 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def /BoxColFill { gsave Rec /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor fill grestore } def % % PostScript Level 1 Pattern Fill routine % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % 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b(que)i(o)f(algoritmo)d(desen)m(v)m(olvido)k(se)g (mostrou)f(bastan)m(te)h(comp)s(etitiv)m(o,)f(sup)s(erando,)j(em)d (alguns)109 5479 y(casos,)47 b(as)e(melhores)e(solu\347\365)s(es)h (conhecidas.)78 b(P)m(ara)44 b(o)g(conjun)m(to)g(de)h(inst\342ncias)e (disp)s(onibilizado)109 5642 y(na)37 b(primeira)e(fase)j(do)f (desa\034o,)i(observ)m(ou-se)g(que)g(o)e(algoritmo)d(prop)s(osto)j (encon)m(trou)h(solu\347\343o)f(de)109 5804 y(mesmo)32 b(custo)i(que)h(a)e(melhor)f(solu\347\343o)h(conhecida)h(na)f(maioria)d (das)k(inst\342ncias.)46 b(P)m(ara)33 b(o)g(segundo)p eop %%Page: 62 76 62 75 bop 109 -28 a FB(9)60 b(Conclus\365)s(es)3149 b(62)p 109 9 3780 4 v 109 256 a FH(conjun)m(to)27 b(de)h(inst\342ncias,)g(o)f (resultado)f(foi)g(ainda)g(melhor,)h(conseguindo)h(a)f(melhor)e (solu\347\343o)i(conhe-)109 418 y(cida)k(para)h(algumas)e (inst\342ncias.)43 b(Apresen)m(tou-se,)34 b(ainda,)d(os)h(resultados)g (obtidos)g(p)s(elo)f(algoritmo)109 581 y(prop)s(osto)46 b(que)i(foram)d(usados)j(para)e(classi\034c\341-lo)f(na)i(fase)g (\034nal)f(do)h(Desa\034o)g(R)m(O)m(ADEF)h(2005.)109 743 y(Observ)m(ou-se)f(que)f(conseguiu-se)g(obter)g(melhor)e(resultado) h(m\351dio)f(que)i(os)g(demais)e(algoritmos)109 906 y(submetidos)36 b(\340)h(fase)g(\034nal)f(em)g(duas)h(das)g(tr\352s)h(inst\342ncias)e (utilizadas.)54 b(Estes)38 b(resultados)f(p)s(ossibi-)109 1068 y(litaram)e(que)40 b(o)e(algoritmo)d(prop)s(osto)j(nesta)i (disserta\347\343o)e(obtiv)m(esse)i(a)f(segunda)g(colo)s(ca\347\343o)e (geral)109 1231 y(den)m(tre)c(os)g(algoritmos)c(de)k(to)s(das)g(as)g (equip)s(es)g(\034nalistas)e(no)i(Desa\034o)g(R)m(O)m(ADEF)h(2005.)274 1452 y(Como)k(p)s(ersp)s(ectiv)-5 b(as)38 b(de)h(trabalhos)f(futuros,)i (p)s(o)s(de-se)f(citar)e(o)h(uso)h(de)g(algumas)d(estrat\351gias)109 1615 y(que)46 b(obtiv)m(eram)e(sucesso)i(na)f(aplica\347\343o)e(a)i (problemas)f(de)h(seq\374enciamen)m(to,)k(como)c(constru\347\343o)109 1777 y(de)e(v)m(o)s(cabul\341rio)e([3].)75 b(Al\351m)42 b(disso,)j(p)s(o)s(de-se)e(a)5 b(justar)44 b(o)e(algoritmo)e(desen)m(v) m(olvido)k(a)e(problemas)109 1940 y(semelhan)m(tes)e(encon)m(trados)h (em)e(outras)h(ind\372strias)f(automobil\355sticas,)f(com)h(algumas)f (restri\347\365)s(es)109 2102 y(adicionais)30 b(ou)i(diferen)m(tes.)45 b(A)32 b(ind\372stria)f(P)m(eugeot,)j(p)s(or)e(exemplo,)g(enfren)m(ta)h (um)f(problema)f(seme-)109 2265 y(lhan)m(te,)h(mas)g(disp)s(\365)s(e)g (de)h(menos)g(temp)s(o)e(para)h(obter)h(os)g(escalonamen)m(tos)f (di\341rios)f(dos)i(carros.)p eop %%Page: 63 77 63 76 bop 1527 651 a FD(Refer\352ncias)157 1245 y FH([1])49 b FF(M.)38 b(Dincbas,)f(M.)h(Simonis)g(e)g(P.)g(V.)f(Hentenr)-8 b(yck.)46 b Fw(Solving)38 b(the)h(car)g(sequencing)309 1366 y(problem)49 b(in)h(constrain)m(t)f(logic)g(programming.)75 b FH(In:)67 b FE(Pr)-5 b(o)g(c)g(e)g(e)g(dings)44 b(of)g(the)i(Eur)-5 b(op)g(e)g(an)309 1486 y(Confer)g(enc)g(e)33 b(on)i(A)n(rti\034cial)f (Intel)5 b(ligenc)-5 b(e)33 b(\(ECAI-88\))t FH(,)e(p.)i(290\025295,)e (1998.)157 1683 y([2])49 b FF(A.)37 b(Drexl,)e(A.)i(Kimms)h(e)f(L.)f (Ma)-8 b(tthieben.)43 b Fw(Algorithms)35 b(for)j(the)g(car)g (sequencing)309 1804 y(and)44 b(the)f(lev)m(el)e(sc)m(heduling)h (problem.)56 b FH(Relat\363rio)35 b(T\351cnico,)k(Departmen)m(t)f(of)f (Business)309 1924 y(A)m(dministration,)30 b(Univ)m(ersit)m(y)j(of)f (Kiel,)f(2002.)157 2121 y([3])49 b FF(E.)41 b(L.)g(R.)f(Fernandes.)56 b Fw(Heur\355sticas)41 b(para)i(o)g(problema)f(de)h(seq\374enciamen)m (to)g(de)309 2242 y(DNA)k(p)s(or)h(hibrida\347\343o.)70 b FH(Disserta\347\343o)42 b(de)g(Mestrado,)j(Departamen)m(to)d(de)g (Inform\341tica,)309 2362 y(P)m(on)m(tif\355cia)31 b(Univ)m(ersidade)i (Cat\363lica)d(do)j(Rio)e(de)i(Janeiro,)f(2005.)157 2559 y([4])49 b FF(I.)33 b(Gent.)38 b Fw(T)-9 b(w)m(o)33 b(results)h(on)g (car)g(sequencing)h(problems.)j FH(Relat\363rio)27 b(T\351cnico,)k (Depart-)309 2680 y(men)m(t)i(of)f(Computer)g(Science,)i(Univ)m(ersit)m (y)f(of)f(Strathclyde,)h(1998.)157 2877 y([5])49 b FF(J.)34 b(Gottlieb,)f(M.)h(Pucht)-8 b(a)32 b(e)i(C.)f(Solnon)38 b Fw(A)c(study)h(of)g(greedy)-9 b(,)35 b(lo)s(cal)e(searc)m(h,)j(and) 309 2997 y(an)m(t)41 b(colon)m(y)g(optimization)d(approac)m(hes)k(for)f (car)g(sequencing)h(problems.)52 b FH(In:)e FE(Ap-)309 3118 y(plic)-5 b(ations)31 b(of)g(Evolutionary)h(Computing)37 b FH(\(Lecture)30 b(Notes)f(in)g(Computer)g(Science,)h(v.)g(2611\).)309 3238 y(Springer,)i(p.)h(246\025257,)e(2003.)157 3436 y([6])49 b FF(P.)36 b(Hansen)f(e)h(N.)g(Mladeno)m(vic.)41 b Fw(V)-9 b(ariable)36 b(Neigh)m(b)s(orho)s(o)s(d)g(Searc)m(h)p FH(.)43 b(In:)h(F.)31 b(Glo)m(v)m(er)309 3556 y(e)g(G.)e(K)m(o)s(c)m (hen)m(b)s(erger)j(\(Eds.\).)p FE(Handb)-5 b(o)g(ok)32 b(of)h(Metaheuristics)p FH(.)d(Klu)m(w)m(er)g(A)m(cademic)g (Publishers,)309 3676 y(p.)j(321\025353,)e(2002.)157 3874 y([7])49 b FF(P.)36 b(V.)f(Hentenr)-8 b(yck,)34 b(H.)h(Simonis)h(e)g(M.)f(Dincbas.)42 b Fw(Constrain)m(t)35 b(satisfation)h(using)309 3994 y(constrain)m(t)g(logic)g(programming.) 42 b FE(A)n(rti\034cial)34 b(Intel)5 b(ligenc)-5 b(e)7 b FH(,)31 b(v.)i(58,)f(p.)h(113\025159,)e(1992.)157 4191 y([8])49 b FF(T.)34 b(Kis.)41 b Fw(On)c(the)e(complexit)m(y)f(of)i(the) f(car)h(sequencing)g(problem.)k FE(Op)-5 b(er)g(ations)33 b(R)-5 b(ese-)309 4312 y(ar)g(ch)35 b(L)-5 b(etters)8 b FH(,)33 b(v.)g(32,)f(p.)h(331\025335,)e(2004)157 4509 y([9])49 b FF(H.)j(P.)h(Lourenco,)h(O.)e(Mar)-8 b(tin)52 b(e)g(T.)g(St\374tzle.)86 b Fw(Iterated)55 b(Lo)s(cal)g(Searc)m(h)p FH(.)90 b(In:)309 4629 y(F.)34 b(Glo)m(v)m(er)f(e)i(G.)e(K)m(o)s(c)m (hen)m(b)s(erger)i(\(Eds.\).)g FE(Handb)-5 b(o)g(ok)35 b(of)h(Metaheuristics)p FH(.)e(Klu)m(w)m(er)g(A)m(cademic)309 4750 y(Publishers,)f(p.)g(321\025353,)e(2002.)109 4947 y([10])48 b FF(B.)41 b(D.)f(P)-8 b(arello,)41 b(W.)f(C.)g(Kaba)-8 b(t)40 b(e)h(L.)f(W)m(os.)57 b Fw(Job-shop)43 b(sc)m(heduling)f(using)h (auto-)309 5067 y(mated)f(reasoning:)60 b(a)43 b(case)f(study)h(of)f (the)h(car)f(sequencing)g(problem.)55 b FE(Journal)39 b(of)309 5188 y(the)c(A)n(utomate)-5 b(d)35 b(R)-5 b(e)g(asoning)9 b FH(,)31 b(v.)i(2,)f(p.)h(1\02542,)f(1986.)109 5385 y([11])48 b FF(J.-C.)37 b(R\351gin)g(e)h(J.)f(Puget.)46 b Fw(A)39 b(\034ltering)e(algorithm)f(for)j(global)f(seq\374encing)h (cons-)309 5505 y(train)m(ts.)63 b FH(In:)57 b FE(Principles)40 b(and)h(Pr)-5 b(atic)g(e)41 b(of)f(Constr)-5 b(aint)41 b(Pr)-5 b(o)g(gr)g(amming)47 b FH(\(Lecture)40 b(Notes)g(in)309 5626 y(Computer)33 b(Science,)g(v.)g(1330\).)f(Springer,)g(p.)h (32\02546,)e(1997.)109 5823 y([12])48 b FF(L.)28 b(Schra)m(ge.)g Fw(A)g(more)g(p)s(ortable)g(F)m(OR)-9 b(TRAN)27 b(random)h(n)m(um)m(b)s (er)g(generator.)j FE(A)n(CM)309 5943 y(T)-7 b(r)i(ansactions)33 b(on)i(Mathematic)-5 b(al)34 b(Softwar)-5 b(e)7 b FH(,)32 b(v.)h(5,)g(p.)f(132\025138,)f(1979.)p eop %%Page: 64 78 64 77 bop 109 -28 a FB(Refer\352ncias)3243 b(64)p 109 9 3780 4 v 109 256 a FH([13])48 b FF(B.)f(Smith.)73 b Fw(Succeed-\034rst)49 b(or)g(fail-\034rst:)73 b(a)49 b(case)h(study)f(in)g(v)-6 b(ariable)48 b(and)i(v)-6 b(alue)309 376 y(ordering.)43 b FH(In:)h FE(Pr)-5 b(o)g(c)g(e)g(e)g (dings)33 b(of)i(P)-7 b(A)n(CT'97)14 b FH(,)30 b(p.)j(321\025330,)e (1997.)109 579 y([14])48 b FF(C.)j(Solnon.)86 b Fw(Solving)53 b(p)s(erm)m(utation)g(constraitn)h(satisfaction)f(problems)g(with)309 700 y(arti\034cial)45 b(an)m(ts.)69 b FH(In:)61 b FE(Pr)-5 b(o)g(c)g(e)g(e)g(dings)42 b(of)g(Eur)-5 b(op)g(e)g(an)42 b(Confer)-5 b(enc)g(e)41 b(on)i(A)n(rti\034cial)f(Intel)5 b(ligenc)-5 b(e)309 820 y(\(ECAI-2000\))t FH(.)31 b(IOS)i(Press,)h(p.)f (118\025122,)e(2000.)109 1023 y([15])48 b FF(T.)32 b(W)-11 b(ar)g(wick)32 b(e)h(E.)f(Tsang.)37 b Fw(T)-9 b(ac)m(king)33 b(car)g(sequencing)h(problems)f(using)g(a)h(genetic)309 1144 y(algorithm.)41 b FE(Evolutionary)35 b(Computation)7 b FH(,)32 b(v.)h(3,)g(p.)g(267\025298,)e(1995.)109 1347 y([16])48 b FF(V.-D.)140 b(Cung)p FH(.)130 b Fw(R)m(O)m(ADEF)151 b(Challenge)g(2005)p FH(.)132 b(Refer\352ncia)g(on-line)e(em)309 1468 y(h)m(ttp://www.prism.uvsq.fr/)p Fs(\030)p FH(vdc/roadef/c)m (hallenges/2005/,)104 b(\372ltima)85 b(visita)j(em)g(25)309 1588 y(de)33 b(mar\347o)f(de)h(2005.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF