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Métodos de geração de colunas para problemas de atribuição

Column generation methods for assignment problems

Senne, Edson Luiz F.; Lorena, Luiz Antonio N.; Salomão, Silvely Nogueira de A.

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Resumo

Este trabalho apresenta métodos de geração de colunas para dois importantes problemas de atribuição: o Problema Generalizado de Atribuição (PGA) e o Problema de Atribuição de Antenas a Comutadores (PAAC). O PGA é um dos mais representativos problemas de Otimização Combinatória e consiste em otimizar a atribuição de n tarefas a m agentes, de forma que cada tarefa seja atribuída a exatamente um agente e a capacidade de cada agente seja respeitada. O PAAC consiste em atribuir n antenas a m comutadores em uma rede de telefonia celular, de forma a minimizar os custos de cabeamento entre antenas e comutadores e os custos de transferência de chamadas entre comutadores. A abordagem tradicional de geração de colunas é comparada com as propostas neste trabalho, que utilizam a relaxação lagrangeana/surrogate. São apresentados testes computacionais que demonstram a efetividade dos algoritmos propostos.

Palavras-chave

Otimização combinatória, problemas de atribuição, relaxação lagrangeana/surrogate, geração de colunas

Abstract

This work presents column generation methods for two important assignment problems: the Generalized Assignment Problem (GAP) and the problem of assigning cells to switches in cellular mobile networks (PACS). GAP is one of the most representative combinatorial optimisation problems and can be stated as the problem of optimising the assignment of n jobs to m agents, such that each job is assigned to exactly one agent and the resource capacity of each agent is not violated. PACS consists of determining a cell assignment pattern which minimizes cabling costs between a cell and a switch and transfer costs between cells assigned to different switches, while respecting certain constraints, especially those related to limited switch's capacity. The traditional column generation process is compared with the proposed algorithms that combine the column generation and lagrangean/surrogate relaxation. Computational experiments are presented in order to confirm the effectiveness of the proposed algorithms.

Keywords

Combinatorial optimization, assignment problems, lagrangean/surrogate relaxation, column generation

References



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