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Contribution à la programmation en nombre entier

Vincent Boyer 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : The Multi-Knapsack Problem is a traditional problem of optimization belonging to the class of the NP-hard problems. This problem occurs in particular as a subproblem of many combinatorial optimization problems. Traditional methods, such as dynamic programming or branch-andbound, used for the exact solution have been treated abundantly in the literature. They have nevertheless weaknesses if they are used alone. The cooperative methods permit one to benefits from their specificities and to propose powerful heuristics or efficient exact methods. Heuristics approaches are proposed and compared with other heuristics from the literature. A cooperative method is compared with a branch-and-bound algorithm. Numerical tests were carried out on various difficult problems from the literature and on randomly generated problems. At last, we consider in particular two techniques in order to generate difficult problems. They are based on problems with equality constraints and the analysis of the Z transform of the knapsack problem.
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Submitted on : Friday, May 16, 2008 - 2:25:01 PM
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  • HAL Id : tel-00280134, version 1

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Vincent Boyer. Contribution à la programmation en nombre entier. Mathématiques [math]. INSA de Toulouse, 2007. Français. ⟨tel-00280134⟩

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