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An integrated ILS-VND strategy for solving the knapsack problem with forfeits

Author

Listed:
  • Matheus M. Vieira

    (Universidade Federal de Alagoas)

  • Bruno Nogueira

    (Universidade Federal de Alagoas
    Universidade de Pernambuco)

  • Rian G. S. Pinheiro

    (Universidade Federal de Alagoas)

Abstract

This work address a variant of the knapsack problem, known as the knapsack problem with forfeits, which has numerous applications. In this variant, a set of items and a conflict graph are given, and the objective is to identify a collection of items that adhere to the knapsack’s capacity while maximizing the total value of the items minus the penalties for conflicting items. We propose a novel heuristic for this problem based on the concepts of iterated local search, variable neighborhood descent, and tabu search. Our heuristic takes into account four neighborhood structures, and we introduce efficient data structures to explore them. Experimental results demonstrate that our approach outperforms the state-of-the-art algorithms in the literature. In particular, it delivers superior solutions within significantly shorter computation times across all benchmark instances. Additionally, this study includes an analysis of how the proposed data structures have influenced both the quality of the solutions and the execution time of the method.

Suggested Citation

  • Matheus M. Vieira & Bruno Nogueira & Rian G. S. Pinheiro, 2024. "An integrated ILS-VND strategy for solving the knapsack problem with forfeits," Journal of Heuristics, Springer, vol. 30(5), pages 399-420, December.
    • Handle: RePEc:spr:joheur:v:30:y:2024:i:5:d:10.1007_s10732-024-09532-3
    DOI: 10.1007/s10732-024-09532-3
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
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