Nouvelles propositions pour la résolution exacte du sac à dos multi-objectif unidimensionnel en variables binaires

Abstract : The purpose of this work is the exact solution of a problem from the field of multi-criteria combinatorial optimisation. Our goal his twofold. First, we aim at confirming the efficiency of the so-named two-phases algorithms. Then, we set a generalisation of the branch and bound procedures, popular in the mono-criteria case but almost non-existent in the multi-criteria case. Our work is based on the unidimensional multi-criteria knapsack problem with binary variables, a classic from combinatorial optimisation, found as a sub problem in many optimisation problems. The first part concerns the reduction of the instances of the problem. We expose several properties allowing to a priori find some parts of the structure of all efficient solutions. Then, we describe an efficient two-phases procedure for this problem. Initially in the bi-criteria case, we improve the original procedure from Visée et al. (1998) before defining a new procedure to efficiently find the solutions in the second phase. This algorithm is extended to the tri- and multi-criteria case in the next part. Finally, the generalisation of the branch and bound procedure is the last part of our work. We focus on several difficulties, to which we answer with two new procedures. Numerical experiments show that these procedures can solve instances in acceptable time. Nevertheless, the two-phases algorithms outperform these procedures, just like the best known procedures for this problem.
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Computer Science [cs]. Université de Nantes, 2010. French


https://tel.archives-ouvertes.fr/tel-00488215
Contributor : Julien Jorge <>
Submitted on : Tuesday, June 1, 2010 - 2:37:39 PM
Last modification on : Wednesday, June 24, 2015 - 10:57:00 AM

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Julien Jorge. Nouvelles propositions pour la résolution exacte du sac à dos multi-objectif unidimensionnel en variables binaires. Computer Science [cs]. Université de Nantes, 2010. French. <tel-00488215>

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