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

Furini, Fabio; Ljubić, Ivana; Sinnl, Markus

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

Nom de la revue

European Journal of Operational Research

Volume

262

Numéro

Éditeur

Elsevier

Pages

438-448

Identifiant publication

10.1016/j.ejor.2017.03.061

Métadonnées

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Auteur(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

Résumé (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.

Mots-clés

Combinatorial optimization; Maximal knapsack packing; Minimal knapsack cover; Dynamic programming; Integer programming