An effective dynamic programming algorithm for the minimum-cost maximal knapsack packing problem

Fabio Furini, Ivana Ljubić and Markus Sinnl

European Journal of Operational Research, 2017, vol. 262, issue 2, 438-448

Abstract: Given a set of items with profits and weights and a knapsack capacity, we study the problem of finding a maximal knapsack packing that minimizes the profit of the selected items. We propose an effective dynamic programming (DP) algorithm which has a pseudo-polynomial time complexity. We demonstrate the equivalence between this problem and the problem of finding a minimal knapsack cover that maximizes the profit of the selected items. In an extensive computational study on a large and diverse set of benchmark instances, we demonstrate that the new DP algorithm outperforms a state-of-the-art commercial mixed-integer programming (MIP) solver applied to the two best performing MIP models from the literature.

Keywords: Combinatorial optimization; Maximal knapsack packing; Minimal knapsack cover; Dynamic programming; Integer programming (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:262:y:2017:i:2:p:438-448

DOI: 10.1016/j.ejor.2017.03.061

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