Heuristic algorithms for the multiple-choice multidimensional knapsack problem

Mhand Hifi (1, 2) , Mustapha Michrafy (1) , Abdelkader Sbihi (1)

1 CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique
2 LaRIA - Laboratoire de Recherche en Informatique d'Amiens

In this paper, we propose several heuristics for approximately solving the multiple-choice multidimensional knapsack problem (noted MMKP), an NP-Hard combinatorial optimization problem. The first algorithm is a constructive approach used especially for constructing an initial feasible solution for the problem. The second approach is applied in order to improve the quality of the initial solution. Finally, we introduce the main algorithm, which starts by applying the first approach and tries to produce a better solution to the MMKP. The last approach can be viewed as a two-stage procedure: (i) the first stage is applied in order to penalize a chosen feasible solution and, (ii) the second stage is used in order to normalize and to improve the solution given by the firs stage. The performance of the proposed approaches has been evaluated based problem instances extracted from the literature. Encouraging results have been obtained.

Mots clés: Combinatorial optimization; guided local search; heuristic; knapsack

Domaines: Mathématique discrète [cs.DM]; Recherche opérationnelle [math.OC]; Algorithme et structure de données [cs.DS]

Mhand Hifi, Mustapha Michrafy, Abdelkader Sbihi. Heuristic algorithms for the multiple-choice multidimensional knapsack problem. Journal of the Operational Research Society, 2004, 55, pp.1323-1332. ⟨10.1057/palgrave.jors.2601796⟩. ⟨hal-00125572v2⟩