Modelos matemáticos e algoritmos para problemas combinatórios

Detalhes bibliográficos
Autor(a) principal: Ravelo, Santiago Valdes
Data de Publicação: 2011
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFG
dARK ID: ark:/38995/001300000dcph
Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/5354
Resumo: This work considers three relevant NP-hard problems. The firstone is the one-dimensional cutting stock problem in which the non-used material in the cutting patterns may be used in the future. For this problem we analyze the existing mathematical models, propose new models, design a heuristic and two metaheuristic approaches, being their performances improved by using parallel programming, and solve instances, practical and randomly generated, from the literature. The computational experiments were quite good for all tested instances. The second problem we consider is the stable roommates problem (a variant of the stable matching problem). For this we give two mathematical programming models, sequential and parallel implementations of a Tabu Search, and a Branch-andBound. Also, we report computational experiments to instances of the problem. The last problem we consider is the compartmentalized knapsack problem (a generalization of the knapsack problem) for which we analyze a quadratic integer model and give a linear integer model. We design a greedy heuristic and a GRASP algorithm, that uses path-relinking, and solve randomly generated instances. All parallel implementations use Graphics Processing Units (GPUs).
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spelling Meneses, Claudio Nogueira dehttp://lattes.cnpq.br/5821173105448845Meneses, Cláudio Nogueira deLongo, Humberto JoséMorabito, Reinaldohttp://lattes.cnpq.br/2614542224940249Ravelo, Santiago Valdes2016-03-17T17:35:15Z2011-02-18RAVELO, Santiago Valdes. Modelos matemáticos e algoritmos para problemas combinatórios. 2011. 94 f. Dissertação (Mestrado em Ciência da Computação) - Universidade Federal de Goiás, Goiânia, 2011.http://repositorio.bc.ufg.br/tede/handle/tede/5354ark:/38995/001300000dcphThis work considers three relevant NP-hard problems. The firstone is the one-dimensional cutting stock problem in which the non-used material in the cutting patterns may be used in the future. For this problem we analyze the existing mathematical models, propose new models, design a heuristic and two metaheuristic approaches, being their performances improved by using parallel programming, and solve instances, practical and randomly generated, from the literature. The computational experiments were quite good for all tested instances. The second problem we consider is the stable roommates problem (a variant of the stable matching problem). For this we give two mathematical programming models, sequential and parallel implementations of a Tabu Search, and a Branch-andBound. Also, we report computational experiments to instances of the problem. The last problem we consider is the compartmentalized knapsack problem (a generalization of the knapsack problem) for which we analyze a quadratic integer model and give a linear integer model. We design a greedy heuristic and a GRASP algorithm, that uses path-relinking, and solve randomly generated instances. All parallel implementations use Graphics Processing Units (GPUs).Este trabalho considera três problemas, NP-difíceis, relevantes de estudo em otimização combinatória. O primeiro deles é o problema de corte uni-dimensional de objetos, onde o material não usado pelos padrões de corte pode ser usado no futuro. Para este problema analisamos os modelos matemáticos existentes, propomos novos modelos, projetamos uma heurística construtiva e duas metaheurísticas, sendo seus desempenhos melhorados com programação paralela, e resolvemos instâncias, práticas e aleatórias, encontradas na literatura; sendo os experimentos computacionais muito bons para todas as intânciastestadas.Osegundoproblemaqueconsideramoséoproblemadoscompanheiros estáveis (stable roommates problem), uma variante do problema de emparelhamento estável (stable matching problem). Para este propomos dois modelos matemáticos, uma implementação sequencial e uma paralela de uma Tabu Search, e um Branch-andBound. Também reportamos experimentos computacionais para instâncias do problema. O último problema considerado é o da mochila compartimentada (uma generalização do problema clássico da mochila), para o qual analisamos uma modelagem quadrática inteira e propomos um modelo linear inteiro; também projetamos uma heurística gulosa, um algoritmo GRASP, que usa path-relinking, e resolvemos intâncias geradas aleatóriamente. 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dc.title.por.fl_str_mv Modelos matemáticos e algoritmos para problemas combinatórios
title Modelos matemáticos e algoritmos para problemas combinatórios
spellingShingle Modelos matemáticos e algoritmos para problemas combinatórios
Ravelo, Santiago Valdes
Otimização combinatória
Problema de corte
Stable matching problem
Problema da mochila
Modelos matemáticos
Heurísticas
Combinatorial optimization
Cutting problem
Stable matching problem
Knapsack problem
Mathematical models
Heuristics
CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO
title_short Modelos matemáticos e algoritmos para problemas combinatórios
title_full Modelos matemáticos e algoritmos para problemas combinatórios
title_fullStr Modelos matemáticos e algoritmos para problemas combinatórios
title_full_unstemmed Modelos matemáticos e algoritmos para problemas combinatórios
title_sort Modelos matemáticos e algoritmos para problemas combinatórios
author Ravelo, Santiago Valdes
author_facet Ravelo, Santiago Valdes
author_role author
dc.contributor.advisor1.fl_str_mv Meneses, Claudio Nogueira de
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/5821173105448845
dc.contributor.referee1.fl_str_mv Meneses, Cláudio Nogueira de
dc.contributor.referee2.fl_str_mv Longo, Humberto José
dc.contributor.referee3.fl_str_mv Morabito, Reinaldo
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/2614542224940249
dc.contributor.author.fl_str_mv Ravelo, Santiago Valdes
contributor_str_mv Meneses, Claudio Nogueira de
Meneses, Cláudio Nogueira de
Longo, Humberto José
Morabito, Reinaldo
dc.subject.por.fl_str_mv Otimização combinatória
Problema de corte
Stable matching problem
Problema da mochila
Modelos matemáticos
Heurísticas
topic Otimização combinatória
Problema de corte
Stable matching problem
Problema da mochila
Modelos matemáticos
Heurísticas
Combinatorial optimization
Cutting problem
Stable matching problem
Knapsack problem
Mathematical models
Heuristics
CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO
dc.subject.eng.fl_str_mv Combinatorial optimization
Cutting problem
Stable matching problem
Knapsack problem
Mathematical models
Heuristics
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO
description This work considers three relevant NP-hard problems. The firstone is the one-dimensional cutting stock problem in which the non-used material in the cutting patterns may be used in the future. For this problem we analyze the existing mathematical models, propose new models, design a heuristic and two metaheuristic approaches, being their performances improved by using parallel programming, and solve instances, practical and randomly generated, from the literature. The computational experiments were quite good for all tested instances. The second problem we consider is the stable roommates problem (a variant of the stable matching problem). For this we give two mathematical programming models, sequential and parallel implementations of a Tabu Search, and a Branch-andBound. Also, we report computational experiments to instances of the problem. The last problem we consider is the compartmentalized knapsack problem (a generalization of the knapsack problem) for which we analyze a quadratic integer model and give a linear integer model. We design a greedy heuristic and a GRASP algorithm, that uses path-relinking, and solve randomly generated instances. All parallel implementations use Graphics Processing Units (GPUs).
publishDate 2011
dc.date.issued.fl_str_mv 2011-02-18
dc.date.accessioned.fl_str_mv 2016-03-17T17:35:15Z
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dc.identifier.citation.fl_str_mv RAVELO, Santiago Valdes. Modelos matemáticos e algoritmos para problemas combinatórios. 2011. 94 f. Dissertação (Mestrado em Ciência da Computação) - Universidade Federal de Goiás, Goiânia, 2011.
dc.identifier.uri.fl_str_mv http://repositorio.bc.ufg.br/tede/handle/tede/5354
dc.identifier.dark.fl_str_mv ark:/38995/001300000dcph
identifier_str_mv RAVELO, Santiago Valdes. Modelos matemáticos e algoritmos para problemas combinatórios. 2011. 94 f. Dissertação (Mestrado em Ciência da Computação) - Universidade Federal de Goiás, Goiânia, 2011.
ark:/38995/001300000dcph
url http://repositorio.bc.ufg.br/tede/handle/tede/5354
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dc.publisher.none.fl_str_mv Universidade Federal de Goiás
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dc.publisher.initials.fl_str_mv UFG
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv Instituto de Informática - INF (RG)
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