An exact algorithm for the knapsack sharing problem

Authors:
Mhand Hifi;Hedi M'Halla;Slim Sadfi
Affiliations:
LaRIA, Laboratoire de Recherche en Informatique d'Amiens and CERMSEM, Maison des Sciences Economiques, Université and LRIA-LPBD, EA 3387, EPHE, France;CERMSEM, Maison des Sciences Economiques, Université Paris 1, 106-112, bd de l'Hôpital, 75647 Paris Cedex 13, France;LaRIA, Laboratoire de Recherche en Informatique d'Amiens and CERMSEM, Maison des Sciences Economiques, Université, France
Venue:
Computers and Operations Research
Year:
2005

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Abstract

In this paper, we develop an exact algorithm for solving the knapsack sharing problem. The algorithm is a new version of the method proposed in Hifi and Sadfi (J. Combin. Optim. 6 (2002) 35). It seems quite efficient in the sense that it solves quickly some large problem instances. Its main principle consists of (i) finding a good set of capacities, representing a set of critical elements, using a heuristic approach, and (ii) varying the values of the obtained set in order to stabilize the optimal solution of the problem. Then, by exploiting dynamic programming properties, we obtain good equilibrium which lead to significant improvements. The performance of the proposed algorithm, based on a set of medium and large problem instances, is compared to the standard version of Hifi and Sadfi (2002). Encouraging results have been obtained.