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Les Méthodes Hybrides en Optimisation Combinatoire :
Algorithmes Exacts et Heuristiques

Abstract : The thesis is in the field of the particular field of operations research and combinatorial optimisation that is the modeling and algorithmic resolution. In this thesis we propose to study two
particular NP-Hard variant problems of the binary knapsack type. More precisely, we treat the
Knapsack Sharing Problem namely KSP and the Mutiple Choice Multidimensional Knapsack
Problem namely MMKP. The first part of this dissertation is concerning to develop approxiamate
algorithms for the two evoked variants of the 01 knapsask problem. The second part is
particularly concerning with the exact resolution of the MMKP. The exact approach which we
propose is of branch-and bound type which : (i) computes of lower and upper bounds and (ii)
develops a son-brother double node branches with a best first startegy of exploration.
Indeed, the first part gets the study of the two problems KSP and MMKP. We are interested
to develop approximate algorithms based upon local search strategies. First and concerning the
KSP, we propose a first version of an approximate algorithm based upon tabu search strategy.
Second, we enhance this version by combining the intensification of the search in the space of
solutions and the diversifiaction of the obtained solution. Experimental results shows the fastness
ofthe first version and the effectiveness and the efficiency of the second one. Next, we propose
two iterative local search methods for the MMKP. The first one is an heuristic based guided
local search end the second is a heuristic that we call a reactive local search approach with some
improving degrading and debloking strategies of the solution based local swapping search.
In the second part of the dissertation, we propose an optimal method based branch-and-bound for
solving the MMKP. First, we propose to transform the MMKP into an MMKPaux problem which
is a Multiple-Choice Knapsack Problem MCKP.We compute an upper bound for MMKPaux and
we establish the theoritical result for which an upper bound for MMKPaux is also an upper bound
for MMKP. After, we deal with the computing of lower and upper bounds which are necessary
to reduce the space search in a branch-and-bound approach. Add to this, the resolution strongly
depends on the density and the size of the treated instances. The experimental study shows
the the efficiency of the proposed algorithm which is able tos solve different groups of instances
of small and medium sizes. Finally, we explain the limits of the branch-and-bound developed
algorithm which are because of the the complexity of the studied model.
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Contributor : Abdelkader Sbihi <>
Submitted on : Friday, April 28, 2006 - 3:14:09 PM
Last modification on : Monday, April 12, 2021 - 3:50:04 PM
Long-term archiving on: : Saturday, April 3, 2010 - 9:31:38 PM


  • HAL Id : tel-00012188, version 1



Abdelkader Sbihi. Les Méthodes Hybrides en Optimisation Combinatoire :
Algorithmes Exacts et Heuristiques. Mathématiques [math]. Université Panthéon-Sorbonne - Paris I, 2003. Français. ⟨tel-00012188⟩



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