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A branch-and-bound algorithm to solve large scale integer quadratic multidimensional knapsack problem

Abstract : The separable quadratic multi-knapsack problem (QMKP) consists in maximizing a concave separable quadratic integer (non pure binary) function subject to m linear capacity constrainsts. In this paper we develop a branch-and-bound algorithm to solve (QMKP) to optimality. This method is based on the computation of a tight upper bound for (QMKP) wich is derived from a linearization and a surrogate relaxation. Our branch-and-bound also incorporates pre-processing procedures. The computational performance of our branch-andèbound is copared to that of three exact methods: a branch-and-bound algorithm developed by Djerdjour et al. (1988), a 0-1 linearization ethod originally applied to the separable quadratic knapsack problem with a single constraint that we extend to the case of m constraints, a standard branch-and-bound algorithm (Cplex 9.0 quadratic optimization). Our branch-and-bound clearly outperforms other methods for large instances (up to 2000 variables and constraints).
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https://hal.archives-ouvertes.fr/hal-01125244
Contributor : Laboratoire Cedric <>
Submitted on : Friday, March 6, 2015 - 11:03:32 AM
Last modification on : Monday, February 3, 2020 - 3:40:14 PM

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  • HAL Id : hal-01125244, version 1

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Dominique Quadri, Eric Soutif, Pierre Tolla. A branch-and-bound algorithm to solve large scale integer quadratic multidimensional knapsack problem. SOFSEM'07, Harrachov, R?publique Tch?que, Jan 2007, X, France. pp.456-464. ⟨hal-01125244⟩

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