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An exact algorithm for the multiple-choice multidimensional knapsack problem

Author

Listed:
  • Mhand Hifi

    (LaRIA et CERMSEM)

  • Slim Sadfi

    (LaRIA et CERMSEM)

  • Abdelkader Sbihi

    (CERMSEM)

Abstract

In this paper, we propose an optimal algorithm for the Multiple-choice Multidimensional Knapsack Problem MMKP. The main principle of the approach is twofold: (i) to generate an initial solution, and (ii) at different levels of the tree search to determine a new upper bound used with a best-first search strategy. The developed method was able to optimally solve the MMKP. The performance of the exact algorithm is evaluated on a set of small and medium instances. This algorithm is parallelizable and it is one of its important feature

Suggested Citation

  • Mhand Hifi & Slim Sadfi & Abdelkader Sbihi, 2004. "An exact algorithm for the multiple-choice multidimensional knapsack problem," Cahiers de la Maison des Sciences Economiques b04024, Université Panthéon-Sorbonne (Paris 1).
    • Handle: RePEc:mse:wpsorb:b04024
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    File URL: https://halshs.archives-ouvertes.fr/halshs-03322716
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    Cited by:

    1. repec:hal:spmain:info:hdl:2441/5l6uh8ogmqildh09h56484hg0 is not listed on IDEAS
    2. N. Cherfi & M. Hifi, 2010. "A column generation method for the multiple-choice multi-dimensional knapsack problem," Computational Optimization and Applications, Springer, vol. 46(1), pages 51-73, May.
    3. Sylvain Barde, 2015. "Back to the Future: Economic Self-Organisation and Maximum Entropy Prediction," Computational Economics, Springer;Society for Computational Economics, vol. 45(2), pages 337-358, February.
    4. Sylvain Barde, 2011. "Ignorance is bliss: rationality, information and equilibrium," Sciences Po publications 2011-04, Sciences Po.
    5. Sylvain Barde, 2012. "Back to the future: economic rationality and maximum entropy prediction," Studies in Economics 1202, School of Economics, University of Kent.

    More about this item

    Keywords

    Combinatorial optimization; branch and bound; sequential algorithm; Knapsack problem;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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