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An algorithm for the disjunctively constrained knapsack problem

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  • Mhand Hifi
  • Nabil Otmani

Abstract

This paper proposes an adaptation of the scatter search (SS) meta-heuristic for approximately solving the disjunctively constrained knapsack problem (DCKP). The DCKP can be viewed as a variant of the standard knapsack problem with special disjunctive constraints. Two versions of SS are presented which are organised following the usual structure of SS. The method is analysed computationally on a set of problem instances of the literature and compared to the results provided by the Cplex solver and other algorithms of the literature. For these instances, most of which cannot be solved to proven optimality in a reasonable time, the proposed method provides results of high quality within reasonable computational time.

Suggested Citation

  • Mhand Hifi & Nabil Otmani, 2012. "An algorithm for the disjunctively constrained knapsack problem," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 13(1), pages 22-43.
    • Handle: RePEc:ids:ijores:v:13:y:2012:i:1:p:22-43
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    Citations

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    Cited by:

    1. Fabio Caldarola & Gianfranco d’Atri & Enrico Zanardo, 2022. "Neural Fairness Blockchain Protocol Using an Elliptic Curves Lottery," Mathematics, MDPI, vol. 10(17), pages 1-20, August.
    2. Daniel Kowalczyk & Roel Leus, 2017. "An exact algorithm for parallel machine scheduling with conflicts," Journal of Scheduling, Springer, vol. 20(4), pages 355-372, August.
    3. 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.
    4. 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.
    5. Ulrich Pferschy & Joachim Schauer, 2017. "Approximation of knapsack problems with conflict and forcing graphs," Journal of Combinatorial Optimization, Springer, vol. 33(4), pages 1300-1323, May.
    6. 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.

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