7.3 Trabalhos futuros
A pesquisa cientíĄca não é como um projeto, que possui começo, meio e Ąm. Trata- se de algo muito maior, englobando projetos, equipes e instituições. Não citar trabalhos futuros em qualquer produção cientíĄca que seja (artigo, monograĄa, dissertação, tese etc.) é atestar que a pesquisa acabou e que será ŞengavetadaŤ.
Continuando a análise experimental de algoritmos, pretende-se explorar melhor a apli- cação ao Problema Quadrático de Alocação, além de aplicar a outros problemas de oti- mização combinatória, especiĄcamente a problemas multiobjetivo, tais como as versões multiobjetivo do Problema da Árvore Geradora Mínima e do Caminho mais Curto. As ver- sões multiobjetivo dos problemas já abordados nesta tese (PCV e PQA) também poderão ser abordadas em novos experimentos computacionais.
Pretende-se também explorar mais recursos da AMHM, tais como a combinação de metaheurísticas de trajetória com partes de metaheurísticas baseadas em população e a aplicação de novos métodos decisão e de aprendizagem. Assim, serão realizados mais expe- rimentos computacionais para testar as novas funcionalidades. O uso de séries temporais (WOOLDRIDGE, 2012) também será utilizado para observar a execução dos algoritmos ao longo do tempo, a Ąm de veriĄcar e analisar o comportamento das metaheurísticas utilizadas.
No âmbito da pesquisa aplicada, pretende-se trabalhar tanto com alunos em nível de graduação como em nível técnico a aplicação da AMHM em problemas práticos do mundo real, nas áreas de Computação, Automação Industrial e Eletrônica.
113
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123
APÊNDICE A Ű O Problema do Caixeiro Vi-
ajante
O Problema do Caixeiro Viajante (PCV) é um dos mais tradicionais e conhecidos problemas de otimização combinatória (MACULAN; CAMPELLO, 1994; GOLDBARG; LUNA, 2005). Os problemas de roteamento lidam em sua maior parte com passeios (ou
tours) sobre pontos de demanda ou oferta. Dentre os tipos de passeio, um dos mais
importantes é o denominado hamiltoniano. Seu nome é devido a William Rowan Hamilton que em 1857 propôs um jogo chamado Around the World, mostrado na Ągura 19.
Figura 19 Ű Jogo Around the World, proposto por Hamilton
O jogo era feito sobre um dodecaedro em que cada vértice estava associado a uma cidade importante da época. O desaĄo consistia em encontrar uma rota através dos vértices do dodecaedro que iniciasse e terminasse em uma mesma cidade passando uma única vez em cada cidade. Em homenagem a Hamilton, uma solução do seu jogo passou a ser chamada de ciclo hamiltoniano, conforme é mostrada na Ągura 20.
124 APÊNDICE A. O Problema do Caixeiro Viajante
Devido à sua ampla aplicabilidade e diĄculdade de resolução por métodos exatos, uma grande quantidade de heurísticas são propostas por diversos pesquisadores. Uma revisão do PCV e alguns métodos utilizados para sua resolução são apresentados por Gutin e Punnen (2002) e um histórico do problema, com algumas aplicações no mundo real, é apresentado porApplegate et al. (2006).
Um grafo, numa deĄnição bem simples, é um conjunto de vértices e arestas. Os vértices são pontos que podem representar cidades, depósitos, postos de trabalho ou atendimento, por exemplo. As arestas são linhas que conectam os vértices, representando relações entre os vértices. Por exemplo, as arestas podem representar ruas ou estradas entre duas cidades. Um circuito hamiltoniano é um passeio por todos os vértices de um grafo retornando ao vértice origem, passando por cada um dos outros vértices apenas uma vez.
O PCV é um problema de otimização associado ao da determinação dos caminhos hamiltonianos em um grafo qualquer, cujo objetivo é encontrar, em um grafo 𝐺 = (𝑉, 𝐸), em que 𝑉 é o conjunto de vértices do grafo e 𝐸 consiste nas arestas que ligam esses vértices, com |𝑉 | = 𝑛 ≥ 3 e 𝑐ij ≥ 0 associado a cada uma das arestas (𝑖, 𝑗), o caminho
hamiltoniano de menor custo. Este problema de otimização, formalmente, é considerado intratável, pertencendo à classe NP-Árdua (KARP,1975).
O PCV é importante devido a pelo menos três de suas características: grande aplicação prática, grande relação com outros modelos e grande diĄculdade de solução exata. Em suas diversas variações, o PCV está presente em inúmeros problemas práticos, como por exemplo:
• Programação de operações de máquinas em manufatura (FINKE; KUSIAK, 1987). • Otimização do movimento de ferramentas de corte (CHAUNY et al., 1987).