A dynamic programming based procedure for the multidimensional 0-1 knapsack problem

Abstract : This paper presents a preprocessing procedure for the 0-1 multidimensional knapsack problem. First, a non-increasing sequence of upper bounds is generated by solving LP-relaxations. Then, a non-decreasing sequence of lower bounds is built using dynamic programming. The comparison of the two sequences allows either to prove that the best feasible solution obtained is optimal, or to fix a subset of variables to their optimal values. In addition, a heuristic solution is obtained. Computational experiments with a set of large-scale instances show the efficiency of our reduction scheme. Particularly, it is shown that our approach allows to reduce the CPU time of a leading commercial software.
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https://hal.archives-ouvertes.fr/hal-00445839
Contributor : Stefan Balev <>
Submitted on : Monday, January 11, 2010 - 2:33:27 PM
Last modification on : Sunday, March 24, 2019 - 11:06:16 AM

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  • HAL Id : hal-00445839, version 1

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Stefan Balev, Nicola Yanev, Arnaud Fréville, Rumen Andonov. A dynamic programming based procedure for the multidimensional 0-1 knapsack problem. European Journal of Operational Research, Elsevier, 2008, 186 (1), pp.63-76. ⟨hal-00445839⟩

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