Ana Ramires *
João Soares1 †
* Departamento de Matemática Universidade Portucalense 4200 Porto, Portugal. amr@uportu.pt
† Departamento de Matemática Universidade de Coimbra 3000 Coimbra, Portugal. and Centro de Matemática da Universidade de Coimbra. jsoares@mat.uc.pt
Title: An improved lower bound for the asymmetric traveling salesman problem based on the assignment problem
Abstract:
]]> In this article we decribe how to compute a lower bound for the asymmetric traveling salesman problem that dominates the bound that comes from the assignment relaxation, through the solving of a sequence of assignment problems. The algorithm that we propose is a first-order method based on the exponential penalty function. Directions of movement are derived from a disjunctive relaxation that we proposed as being one of two possible classes, one based on cycles, the other based on cliques.Keywords: Optimization, Combinatorial Optimization, Lower Bounds, Asymmetric Traveling Salesman, Disjunctive Programming
Resumo:
Neste artigo explicamos como obter um limite inferior para o valor óptimo do problema do caixeiro viajante assimétrico melhor do que o que advém do problema de afectação através da resolução sucessiva de problemas de afectação. O algoritmo que propomos é um método de primeira ordem baseado na função de penalidade exponencial cujas direcções de deslocamento são definidas com base numa relaxação disjuntiva que propomos ser de dois tipos, uma baseada em ciclos e a outra baseada em cliques.
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]]> 1 João Soares acknowledges partial finantial support from Fundação para a Ciência e Tecnologia (Projecto POCTI/MAT/14243/1998). ]]>