Iterative Relaxation-Based Heuristics for the Multiple-choice Multidimensional Knapsack Problem

Authors:
Saïd Hanafi;Raïd Mansi;Christophe Wilbaut
Affiliations:
Univ Lille Nord de France, Lille, France F-59000 and UVHC, LAMIH, Valenciennes, France F-59313 and CNRS, UMR 8530, Valenciennes, France F-59313;Univ Lille Nord de France, Lille, France F-59000 and UVHC, LAMIH, Valenciennes, France F-59313 and CNRS, UMR 8530, Valenciennes, France F-59313;Univ Lille Nord de France, Lille, France F-59000 and UVHC, LAMIH, Valenciennes, France F-59313 and CNRS, UMR 8530, Valenciennes, France F-59313
Venue:
HM '09 Proceedings of the 6th International Workshop on Hybrid Metaheuristics
Year:
2009

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Abstract

The development of efficient hybrid methods for solving hard optimization problems is not new in the operational research community. Some of these methods are based on the complete exploration of small neighbourhoods. In this paper, we apply iterative relaxation-based heuristics that solves a series of small sub-problems generated by exploiting information obtained from a series of relaxations to the multiple---choice multidimensional knapsack problem. We also apply local search methods to improve the solutions generated by these algorithms. The method is evaluated on a set of problem instances from the literature, and compared to the results reached by both Cplex solver and an efficient column generation---based algorithm. The results of the method are encouraging with 9 new best lower bounds among 33 problem instances.