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

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

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Article ID: iaor20052361
Country: Netherlands
Volume: 157
Issue: 3
Start Page Number: 565
End Page Number: 575
Publication Date: Sep 2004
Journal: European Journal of Operational Research
Authors: ,
Keywords: combinatorial analysis
Abstract:

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.

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