Orientador: Cid Carvalho de Souza / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação / Made available in DSpace on 2018-08-19T04:31:47Z (GMT). No. of bitstreams: 1 Braga_AndreideAlmeidaSampaio_M.pdf: 1060769 bytes, checksum: 789d9000e49ebe5d5a54a275c6018cb6 (MD5) Previous issue date: 2011 / Resumo: O problema de particionamento de conjuntos (SPP, do inglês set partitioning problem) é considerado um dos problemas de otimização combinatória com mais vasta gama de aplicações. Para solucioná-lo, utilizam-se comumente métodos tradicionais para a resolução de problemas NP - Difíceis. Nesta dissertação, estuda-se o uso da combinação de relaxação Lagrangiana com planos de corte. Relaxação Lagrangiana é uma técnica que tem sido usada com bastante sucesso para atacar vários problemas NP-Difíceis. Os algoritmos relax-and-cut, em especial, onde se adicionam dinamicamente planos de corte a relaxações Lagrangianas, têm ganhado bastante destaque nas últimas décadas. Em [15], Cavalcante et al. aplicam um algoritmo relax-and-cut ao SPP e obtém ótimos resultados. No entanto, tal algoritmo, bem como implementações em geral da citada combinação, são ainda passíveis de refinamentos e extensões. O estudo proposto aqui é realizado por meio das seguintes extensões do referido algoritmo: a implementação de uma partida quente para o multiplicador de uma inequação adicionada; a incorporação do algoritmo a uma enumeração, gerando, assim, um branch-and-cut baseado em relaxação Lagrangiana para o SPP; a implementação do citado branch-and-cut com o emprego de relaxações alternativas e a implementação de uma versão distribuída do algoritmo / Abstract: The set partitioning problem (SPP) is considered one of the combinatorial optimization problems with the widest range of applications. To solve the SPP, one commonly uses traditional methods for NP-Hard problem solving. In this dissertation, we study the use of the combination of Lagrangean relaxation with cutting planes. Lagrangean relaxation is a technique that has been used quite successfully to tackle several NP-Hard problems. In particular, relax-and-cut algorithms, in which cutting planes are added dynamically to Lagrangean relaxations, have gained much importance in the last decades. In [15], Cavalcante et al. applied a relax-and-cut algorithm to the SPP and obtained promising results. However, that algorithm, as well as implementations of the mentioned combination in general, are still subject to refinements and extensions. The study proposed here is carried out through the following extensions of that algorithm: the implementation of a warm start to the multiplier of an added inequality; the incorporation of the algorithm to an enumeration, thus generating a Lagrangean relaxation based branch-and-cut for the SPP; the implementation of that branch-and-cut with the use of alternative relaxations and the implementation of a distributed version of the algorithm / Mestrado / Ciência da Computação / Mestre em Ciência da Computação

Crew pairing and vehicle routing are combinatorial optimization problems that have been studied for many years by researchers worldwide. The aim of this research work is to investigate effective methods for solving large scale crew pairing problems and vehicle routing problems. In the airline industry, to address the complex nature of crew pairing problems, we propose a duty tree method followed by a primal-dual subproblem simplex method. The duty tree approach captures the constraints that apply to crew pairings and generate candidate pairings taking advantage of various proposed strategies. A huge number of legal pairings are stored in the duty tree and can be enumerated. A set partitioning formulation is then constructed, and the problem is solved using a primal-dual subproblem simplex method tailored to the duty tree approach. Computational experiments are conducted to show the effectiveness of the methods. We also present our efforts addressing the capacitated vehicle routing problem (CVRP) that is the basic version of many other variants of the problem. We do not attempt to solve the CVRP instances that have been solved to optimality. Instead, we focus on investigating good solutions for large CVRP instances, with particular emphasis on those benchmark problems from the public online library that have not yet been solved to optimality by other researchers and determine whether we can find new best-known solutions. In this research, we propose a route network that can store a huge number of routes with all routes being legal, a set partitioning formulation that can handle many columns, and the primal-dual subproblem simplex method to find a solution. The computational results show that our proposed methods can achieve better solutions than the existing best-known solutions for some difficult instances. Upon convergence of the primal-dual subproblem simplex method on the giant-tour based networks, we use the near optimal primal and dual solution as well as solve the elementary shortest path problem with resource constraints to achieve the linear programming relaxation global optimal solution.

ALVES, Alexsandro de Oliveira. Integração de heurísticas lagrangeanas com algoritmos exatos para a otimização de particionamento de conjuntos. 2007. 49 f. : Dissertação (mestrado) - Universidade Federal do Ceará, Centro de Ciências, Departamento de Computação, Fortaleza-CE, 2007. / Submitted by guaracy araujo (guaraa3355@gmail.com) on 2016-05-20T18:05:04Z No. of bitstreams: 1 2007_dis_aoalves.pdf: 434539 bytes, checksum: d7550e0ddf22c4c083e44734e59375f7 (MD5) / Approved for entry into archive by guaracy araujo (guaraa3355@gmail.com) on 2016-05-20T18:08:40Z (GMT) No. of bitstreams: 1 2007_dis_aoalves.pdf: 434539 bytes, checksum: d7550e0ddf22c4c083e44734e59375f7 (MD5) / Made available in DSpace on 2016-05-20T18:08:40Z (GMT). No. of bitstreams: 1 2007_dis_aoalves.pdf: 434539 bytes, checksum: d7550e0ddf22c4c083e44734e59375f7 (MD5) Previous issue date: 2007 / In this work we evaluate both exact and heuristic methods for the set partitioning problem (SPP). These heuristics are based on greedy algorithms, tabu search and subgradient optimization. Computational experiments performed on benchmark instances of the problem indicate that our heuristics are competitive with existing ones from the literature in obtaining both lower and upper bounds of good quality in reasonable execution time. We use a Branch and Bound algorithm that allows to prove optimality of solutions obtained by our heuristics for a large set of benchmark instances of the SPP. Thus, we show that our heuristics are efficient in obtaining feasible solutions of good quality for this problem. / Neste trabalho avaliamos métodos heurísticos e exatos para o Problema de Particionamento de Conjuntos (PPC). Realizamos testes computacionais com heurísticas lagrangeanas baseadas em algoritmos gulosos, busca tabu e método de otimização pelo subgradiente. Os resultados obtidos, comparados com os da literatura, comprovam a eficiência de nossas heurísticas na obtenção de limites inferiores e superiores de boa qualidade, em tempo computacional razoável, para instâncias da literatura. Utilizamos um esquema de Branch and Bound para tentar resolver instâncias do PPC à otimalidade e para comprovar a qualidade dos resultados alcançados por nossas heurísticas.

FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico / Neste trabalho avaliamos mÃtodos heurÃsticos e exatos para o Problema de Particionamento de Conjuntos (PPC). Realizamos testes computacionais com heurÃsticas lagrangeanas baseadas em algoritmos gulosos, busca tabu e mÃtodo de otimizaÃÃo pelo subgradiente. Os resultados obtidos, comparados com os da literatura, comprovam a eficiÃncia de nossas heurÃsticas na obtenÃÃo de limites inferiores e superiores de boa qualidade, em tempo computacional razoÃvel, para instÃncias da literatura. Utilizamos um esquema de Branch and Bound para tentar resolver instÃncias do PPC ÃÂotimalidade e para comprovar a qualidade dos resultados alcanÃados por nossas heurÃsticas. / In this work we evaluate both exact and heuristic methods for the set partitioning problem (SPP). These heuristics are based on greedy algorithms, tabu search and subgradient optimization. Computational experiments performed on benchmark instances of the problem indicate that our heuristics are competitive with existing ones from the literature in obtaining both lower and upper bounds of good quality in reasonable execution time. We use a Branch and Bound algorithm that allows to prove optimality of solutions obtained by our heuristics for a large set of benchmark instances of the SPP. Thus, we show that our heuristics are efficient in obtaining feasible solutions of good quality for this problem.

Le problème d'allocation de postes d'amarrage (PAPA) est l'un des principaux problèmes de décision aux terminaux portuaires qui a été largement étudié. Dans des recherches antérieures, le PAPA a été reformulé comme étant un problème de partitionnement généralisé (PPG) et résolu en utilisant un solveur standard. Les affectations (colonnes) ont été générées a priori de manière statique et fournies comme entrée au modèle %d'optimisation. Cette méthode est capable de fournir une solution optimale au problème pour des instances de tailles moyennes. Cependant, son inconvénient principal est l'explosion du nombre d'affectations avec l'augmentation de la taille du problème, qui fait en sorte que le solveur d'optimisation se trouve à court de mémoire. Dans ce mémoire, nous nous intéressons aux limites de la reformulation PPG. Nous présentons un cadre de génération de colonnes où les affectations sont générées de manière dynamique pour résoudre les grandes instances du PAPA. Nous proposons un algorithme de génération de colonnes qui peut être facilement adapté pour résoudre toutes les variantes du PAPA en se basant sur différents attributs spatiaux et temporels. Nous avons testé notre méthode sur un modèle d'allocation dans lequel les postes d'amarrage sont considérés discrets, l'arrivée des navires est dynamique et finalement les temps de manutention dépendent des postes d'amarrage où les bateaux vont être amarrés. Les résultats expérimentaux des tests sur un ensemble d'instances artificielles indiquent que la méthode proposée permet de fournir une solution optimale ou proche de l'optimalité même pour des problème de très grandes tailles en seulement quelques minutes. / The berth allocation problem (BAP) is one of the key decision problems at port terminals and it has been widely studied. In previous research, the BAP has been formulated as a generalized set partitioning problem (GSPP) and solved using standard solver. The assignments (columns) were generated a priori in a static manner and provided as an input to the optimization model. The GSPP approach is able to solve to optimality relatively large size problems. However, a main drawback of this approach is the explosion in the number of feasible assignments of vessels with increase in problem size which leads in turn to the optimization solver to run out of memory. In this research, we address the limitation of the GSPP approach and present a column generation framework where assignments are generated dynamically to solve large problem instances of the berth allocation problem at port terminals. We propose a column generation based algorithm to address the problem that can be easily adapted to solve any variant of the BAP based on different spatial and temporal attributes. We test and validate the proposed approach on a discrete berth allocation model with dynamic vessel arrivals and berth dependent handling times. Computational experiments on a set of artificial instances indicate that the proposed methodology can solve even very large problem sizes to optimality or near optimality in computational time of only a few minutes.