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Improved convergent heuristics for the 0-1 multidimensional knapsack problem

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  • Saïd Hanafi
  • Christophe Wilbaut

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. Copyright Springer Science+Business Media, LLC 2011

Suggested Citation

  • Saïd Hanafi & Christophe Wilbaut, 2011. "Improved convergent heuristics for the 0-1 multidimensional knapsack problem," Annals of Operations Research, Springer, vol. 183(1), pages 125-142, March.
    • Handle: RePEc:spr:annopr:v:183:y:2011:i:1:p:125-142:10.1007/s10479-009-0546-z
    DOI: 10.1007/s10479-009-0546-z
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    References listed on IDEAS

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    1. Wilbaut, Christophe & Hanafi, Said, 2009. "New convergent heuristics for 0-1 mixed integer programming," European Journal of Operational Research, Elsevier, vol. 195(1), pages 62-74, May.
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    Cited by:

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    3. Al-Shihabi, Sameh, 2021. "A Novel Core-Based Optimization Framework for Binary Integer Programs- the Multidemand Multidimesional Knapsack Problem as a Test Problem," Operations Research Perspectives, Elsevier, vol. 8(C).
    4. Saïd Hanafi & Raca Todosijević, 2017. "Mathematical programming based heuristics for the 0–1 MIP: a survey," Journal of Heuristics, Springer, vol. 23(4), pages 165-206, August.

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