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

Furini, Fabio; Ljubić, Ivana; Sinnl, Markus (2017), An effective dynamic programming algorithm for the minimum-cost maximal knapsack packing problem, European Journal of Operational Research, 262, 2, p. 438-448. 10.1016/j.ejor.2017.03.061

Type
Article accepté pour publication ou publié
Date
2017
Journal name
European Journal of Operational Research
Volume
262
Number
2
Publisher
Elsevier
Pages
438-448
Publication identifier
Metadata
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Author(s)
Furini, Fabio
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Ljubić, Ivana
ESSEC Business School
Sinnl, Markus
Department of Statistics and Operations Research
Abstract (EN)
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.
Subjects / Keywords
Combinatorial optimization; Maximal knapsack packing; Minimal knapsack cover; Dynamic programming; Integer programming