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A reactive local search-based algorithm for the disjunctively constrained knapsack problem

Author

Listed:
  • M Hifi

    (La RIA Université de Picardie Jules-Verne d'Amiens)

  • M Michrafy

    (La RIA Université de Picardie Jules-Verne d'Amiens)

Abstract

In this paper, we propose a reactive local search-based algorithm for the disjunctively constrained knapsack problem (DCKP). DCKP is a variant of the standard knapsack problem, an NP-hard combinatorial optimization problem, with special disjunctive constraints. A disjunctive constraint is a couple of items for which only one item is packed. The proposed algorithm is based upon a reactive local search, where an explicit check for the repetition of configurations is added to the search process. Initially, two complementary greedy procedures are applied in order to construct a starting solution. Second, a degrading procedure is introduced in order (i) to escape to local optima and (ii) to introduce a diversification in the search space. Finally, a memory list is added in order to forbid the repetition of configurations. The performance of two versions of the algorithm has been evaluated on several problem instances and compared to the results obtained by running the Cplex solver. Encouraging results have been obtained.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:57:y:2006:i:6:d:10.1057_palgrave.jors.2602046
    DOI: 10.1057/palgrave.jors.2602046
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    References listed on IDEAS

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    1. P. C. Gilmore & R. E. Gomory, 1966. "The Theory and Computation of Knapsack Functions," Operations Research, INFORMS, vol. 14(6), pages 1045-1074, December.
    2. Pisinger, David, 1995. "A minimal algorithm for the multiple-choice knapsack problem," European Journal of Operational Research, Elsevier, vol. 83(2), pages 394-410, June.
    3. 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.
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    Cited by:

    1. Andrea Bettinelli & Valentina Cacchiani & Enrico Malaguti, 2017. "A Branch-and-Bound Algorithm for the Knapsack Problem with Conflict Graph," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 457-473, August.
    2. Wei, Zequn & Hao, Jin-Kao & Ren, Jintong & Glover, Fred, 2023. "Responsive strategic oscillation for solving the disjunctively constrained knapsack problem," European Journal of Operational Research, Elsevier, vol. 309(3), pages 993-1009.
    3. Coniglio, Stefano & Furini, Fabio & San Segundo, Pablo, 2021. "A new combinatorial branch-and-bound algorithm for the Knapsack Problem with Conflicts," European Journal of Operational Research, Elsevier, vol. 289(2), pages 435-455.
    4. Isma Dahmani & Mhand Hifi, 2021. "A modified descent method-based heuristic for binary quadratic knapsack problems with conflict graphs," Annals of Operations Research, Springer, vol. 298(1), pages 125-147, March.
    5. Fatma-Zohra Baatout & Mhand Hifi, 2023. "A two-phase hybrid evolutionary algorithm for solving the bi-objective scheduling multiprocessor tasks on two dedicated processors," Journal of Heuristics, Springer, vol. 29(2), pages 229-267, June.
    6. Caserta, Marco & Voß, Stefan, 2019. "The robust multiple-choice multidimensional knapsack problem," Omega, Elsevier, vol. 86(C), pages 16-27.
    7. Thekra Al-douri & Mhand Hifi & Vassilis Zissimopoulos, 2021. "An iterative algorithm for the Max-Min knapsack problem with multiple scenarios," Operational Research, Springer, vol. 21(2), pages 1355-1392, June.
    8. Hifi, Mhand & Yousef, Labib, 2019. "A local search-based method for sphere packing problems," European Journal of Operational Research, Elsevier, vol. 274(2), pages 482-500.

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