An exact method based on Lagrangian decomposition for the 0–1 quadratic knapsack problem

The 0–1 quadratic knapsack problem (QKP) consists in maximizing a quadratic pseudo-Boolean function with positive coefficients subject to a linear capacity constraint. In this paper we present an exact method to solve this problem. This method makes use of the computation of an upper bound for (QKP)...

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Bibliographic Details
Published inEuropean journal of operational research Vol. 157; no. 3; pp. 565 - 575
Main Authors Billionnet, Alain, Soutif, Éric
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 16.09.2004
Elsevier
Elsevier Sequoia S.A
SeriesEuropean Journal of Operational Research
Subjects
0–1 quadratic programming
Branch-and-bound
Computational Complexity
Computational results
Computer Science
Knapsack
Knapsack problem
Lagrangian decomposition
Mathematical programming
Optimization
Studies
Branch-and-bound
Lagrangian decomposition
Knapsack
Computational results
0–1 quadratic programming
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Summary:The 0–1 quadratic knapsack problem (QKP) consists in maximizing a quadratic pseudo-Boolean function with positive coefficients subject to a linear capacity constraint. In this paper we present an exact method to solve this problem. This method makes use of the computation of an upper bound for (QKP) which is derived from Lagrangian decomposition. It allows us to find the optimum of instances with up to 150 variables whatever their density, and with up to 300 variables for medium and low density.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0377-2217
1872-6860
DOI:10.1016/S0377-2217(03)00244-3