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Heuristiques et approche polyedrale du probleme de voyageur de commerce international

Abstract : This thesis deals with a generalization of the traveling salesman problem in which the nodes are partitionned into clusters which can be tought as countries and the salesman has to visit exactly one node in each cluster. The problem is to find such a solution of minimum length. We call it the international traveling salesman problem and we denote it by ITSP. First, we give some heuristic for the ITSP and a new heuristic for the TSP based on notions introduced by Glover. Then, we describe a polynomial reduction of the ITSP to the TSP and we give a new formulation of the ITSP as an integer linear program. Then, we focus on the polyhedral approach of the ITSP. We define the graphical relaxation of the ITSP and we give results on the dimension and the facial structure of the corresponding polyhedron. We study the polyhedral relationship between the ITSP and its graphical relaxation. We give several classes of facet-inducing inequalities of the ITSP polytope and we study some properties of its facets. This polyhedral study allows us to design a branch an cut algorithm to solve the ITSP starting with such an algorithm for the TSP. We present some exact algorithms and heuristics for the separation problem of the main classes of facet-inducing inequalities. Computationnal results are finally reported.
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https://tel.archives-ouvertes.fr/tel-00004978
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Submitted on : Monday, February 23, 2004 - 11:32:27 AM
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Djawad Bouali. Heuristiques et approche polyedrale du probleme de voyageur de commerce international. Modélisation et simulation. Institut National Polytechnique de Grenoble - INPG, 1996. Français. ⟨tel-00004978⟩

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