Aplicação do algoritmo volumétrico à resolução aproximada e exacta do problema do caixeiro viajante assimétrico

Ana Maria Rocha †

Edite M.G.P. Fernandes †

João Soares * ‡

† Departamento de Produção e Sistemas, Universidade do Minho

arocha@dps.uminho.pt

emgpf@dps.uminho.pt

‡ Departamento de Matemática, Universidade de Coimbra

jsoares@mat.uc.pt

 

Title: Application of the volume algorithm to the approximate and exact solving of the asymmetric traveling salesman problem.

Abstract

In this paper we present computational results with the volume algorithm, a variant of the subgradient method, when solving the linear relaxation that stems from the extended disaggregated flow formulation of the Asymmetric Travelling Salesman Problems. Computational experiments were performed on a selection of instances from the TSPLib and some randomly generated instances according to the Dimacs  Implementation  Challenge. We have also tried ATSP heuristics within the volume algorithm. Computational experiments show moderated success on medium-scale instances.

Keywords: Asymmetric travelling salesman problem, Disaggregated flow formulation, Lagrangian relaxation.

Resumo

Neste artigo apresentamos resultados computacionais obtidos com o algoritmo volumétrico, uma variante do método do subgradiente, na resolução da relaxação linear que decorre da formulação estendida de fluxo desagregado para o problema do Caixeiro Viajante Assimétrico. As experiências computacionais foram realizadas numa selecção de instâncias da TSPLib e num conjunto de instâncias geradas aleatoriamente de acordo com o Dimacs  Implementation  Challenge. Também experimentámos a  aplicação de heurísticas durante a execução do algoritmo volumétrico. As experiências computacionais mostram sucesso moderado com instâncias de média dimensão.

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* João Soares acknowledges partial financial support from Fundação para a Ciência e Tecnologia (Projecto POCTI/MAT/14243/1998).