Modelos matemáticos e algoritmos para problemas combinatórios

• 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:/38995/001300000d6w9
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/5354
• 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

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).