Title: An algorithm for the disjunctively constrained knapsack problem

Authors: Mhand Hifi; Nabil Otmani

Addresses: Université de Picardie Jules Verne, Equipe ROAD, Unité de Recherche MIS, 5 rue du Moulin Neuf, Amiens 80000, France ' Université de Picardie Jules Verne, Equipe ROAD, Unité de Recherche MIS, 5 rue du Moulin Neuf, Amiens 80000, France

Abstract: This paper proposes an adaptation of the scatter search (SS) meta-heuristic for approximately solving the disjunctively constrained knapsack problem (DCKP). The DCKP can be viewed as a variant of the standard knapsack problem with special disjunctive constraints. Two versions of SS are presented which are organised following the usual structure of SS. The method is analysed computationally on a set of problem instances of the literature and compared to the results provided by the Cplex solver and other algorithms of the literature. For these instances, most of which cannot be solved to proven optimality in a reasonable time, the proposed method provides results of high quality within reasonable computational time.

Keywords: heuristics; disjunctive constraints; knapsack problem; optimisation; scatter search.

DOI: 10.1504/IJOR.2012.044026

International Journal of Operational Research, 2012 Vol.13 No.1, pp.22 - 43

Published online: 11 Jan 2015 *

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