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Heuristic algorithms for the multiple-choice multidimensional knapsack problem

Author

Listed:
  • M Hifi

    (LaRIA, UPJV
    CERMSEM-CNRS UMR 8095, Universite de Paris 1)

  • M Michrafy

    (CERMSEM-CNRS UMR 8095, Universite de Paris 1)

  • A Sbihi

    (LaRIA, UPJV)

Abstract

In this paper, we propose several heuristics for approximately solving the multiple-choice multidimensional knapsack problem (noted MMKP), an NP-Hard combinatorial optimization problem. The first algorithm is a constructive approach used especially for constructing an initial feasible solution for the problem. The second approach is applied in order to improve the quality of the initial solution. Finally, we introduce the main algorithm, which starts by applying the first approach and tries to produce a better solution to the MMKP. The last approach can be viewed as a two-stage procedure: (i) the first stage is applied in order to penalize a chosen feasible solution and, (ii) the second stage is used in order to normalize and to improve the solution given by the firs stage. The performance of the proposed approaches has been evaluated based problem instances extracted from the literature. Encouraging results have been obtained.

Suggested Citation

  • M Hifi & M Michrafy & A Sbihi, 2004. "Heuristic algorithms for the multiple-choice multidimensional knapsack problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1323-1332, December.
    • Handle: RePEc:pal:jorsoc:v:55:y:2004:i:12:d:10.1057_palgrave.jors.2601796
    DOI: 10.1057/palgrave.jors.2601796
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    References listed on IDEAS

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    Cited by:

    1. Lai, David S.W. & Caliskan Demirag, Ozgun & Leung, Janny M.Y., 2016. "A tabu search heuristic for the heterogeneous vehicle routing problem on a multigraph," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 86(C), pages 32-52.
    2. M Hifi & M Michrafy, 2006. "A reactive local search-based algorithm for the disjunctively constrained knapsack problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(6), pages 718-726, June.
    3. Gao, Chao & Lu, Guanzhou & Yao, Xin & Li, Jinlong, 2017. "An iterative pseudo-gap enumeration approach for the Multidimensional Multiple-choice Knapsack Problem," European Journal of Operational Research, Elsevier, vol. 260(1), pages 1-11.
    4. Sylvain Barde, 2012. "Back to the future: economic rationality and maximum entropy prediction," Studies in Economics 1202, School of Economics, University of Kent.
    5. Lamanna, Leonardo & Mansini, Renata & Zanotti, Roberto, 2022. "A two-phase kernel search variant for the multidimensional multiple-choice knapsack problem," European Journal of Operational Research, Elsevier, vol. 297(1), pages 53-65.
    6. V. Van Peteghem & M. Vanhoucke, 2009. "An Artificial Immune System for the Multi-Mode Resource-Constrained Project Scheduling Problem," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 09/555, Ghent University, Faculty of Economics and Business Administration.
    7. 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.
    8. Jaeyoung Yang & Yong-Hyuk Kim & Yourim Yoon, 2022. "A Memetic Algorithm with a Novel Repair Heuristic for the Multiple-Choice Multidimensional Knapsack Problem," Mathematics, MDPI, vol. 10(4), pages 1-15, February.
    9. Ewa M. Bednarczuk & Janusz Miroforidis & Przemysław Pyzel, 2018. "A multi-criteria approach to approximate solution of multiple-choice knapsack problem," Computational Optimization and Applications, Springer, vol. 70(3), pages 889-910, July.
    10. Mancini, Simona & Ciavotta, Michele & Meloni, Carlo, 2021. "The Multiple Multidimensional Knapsack with Family-Split Penalties," European Journal of Operational Research, Elsevier, vol. 289(3), pages 987-998.
    11. 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.
    12. Caserta, Marco & Voß, Stefan, 2019. "The robust multiple-choice multidimensional knapsack problem," Omega, Elsevier, vol. 86(C), pages 16-27.

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