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Etude de Resolution Search pour la programmation linéaire en variables binaires

Abstract : In this thesis, we are interested in the exact resolution of 0-1 integer linear programming problems. Our work revolves around the study of Resolution search (Chvátal (1997)) for solving the 0-1 multidimensional knapsack problem. As a first step, we propose an implicit enumeration algorithm based on an analysis of the reduced costs at the optimality of the problem's LP-relaxation and on the decomposition of the search space in hyperplanes. We propose an original branching strategy which focuses on pruning the search tree as soon as possible. This strategy is effective for solving difficult instances, however, it makes the algorithm depends on the knowledge of a good starting solution. In a second step, we propose an exact method combining Resolution search with an implicit enumeration similar to the first algorithm. The resulting cooperation enables to obtain good solutions rapidly and to prove the optimality of several larger instances. Finally, we present an application of Resolution Search to a scheduling problem in the field of telecommunications.
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Contributor : Sylvain Boussier <>
Submitted on : Wednesday, May 6, 2009 - 4:38:01 PM
Last modification on : Tuesday, January 14, 2020 - 10:38:05 AM
Long-term archiving on: : Thursday, June 10, 2010 - 9:03:56 PM


  • HAL Id : tel-00381912, version 1



Sylvain Boussier. Etude de Resolution Search pour la programmation linéaire en variables binaires. Modélisation et simulation. Université Montpellier II - Sciences et Techniques du Languedoc, 2008. Français. ⟨tel-00381912⟩



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