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Annals of Operations Research

, Volume 183, Issue 1, pp 125–142 | Cite as

Improved convergent heuristics for the 0-1 multidimensional knapsack problem

  • Saïd HanafiEmail author
  • Christophe Wilbaut
Article

Abstract

At the end of the seventies, Soyster et al. (Eur. J. Oper. Res. 2:195–201, 1978) proposed a convergent algorithm that solves a series of small sub-problems generated by exploiting information obtained through a series of linear programming relaxations. This process is suitable for the 0-1 mixed integer programming problems when the number of constraints is relatively smaller when compared to the number of variables. In this paper, we first revisit this algorithm, once again presenting it and some of its properties, including new proofs of finite convergence. This algorithm can, in practice, be used as a heuristic if the number of iterations is limited. We propose some improvements in which dominance properties are emphasized in order to reduce the number of sub problems to be solved optimally. We also add constraints to these sub-problems to speed up the process and integrate adaptive memory. Our results show the efficiency of the proposed improvements for the 0-1 multidimensional knapsack problem.

Keywords

Relaxation Heuristic Multidimensional knapsack problem 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.LAMIH-SIADE, UMR 8530Université de Valenciennes et du Hainaut-CambrésisValenciennes Cedex 9France

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