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A modified descent method-based heuristic for binary quadratic knapsack problems with conflict graphs

Author

Listed:
  • Isma Dahmani

    (EPROAD EA4669, Université de Picardie Jules Verne
    USTHB)

  • Mhand Hifi

    (EPROAD EA4669, Université de Picardie Jules Verne)

Abstract

The knapsack problem arises in a variety of real world applications, including flexible manufacturing systems, railway stations, hydrological studies and others. In this paper, we propose a descent method-based heuristic for tackling a special knapsack problem: the binary quadratic knapsack with conflict graphs. The proposed method combines (i) an intensification search with a descent method for enhancing the accuracy of the solutions and (ii) a diversification strategy which is used for enlarging the search space. The method uses degrading and re-optimization strategies in order to reach a series of diversified solutions. The performance of the proposed method is evaluated on benchmark instances taken from the literature, where its achieved results are compared to those reached by both GLPK solver and the best method available in the literature. The method seems very competitive, where it is able to achieve 37 new lower bounds.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:298:y:2021:i:1:d:10.1007_s10479-019-03290-3
    DOI: 10.1007/s10479-019-03290-3
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    References listed on IDEAS

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    1. George B. Dantzig, 1957. "Discrete-Variable Extremum Problems," Operations Research, INFORMS, vol. 5(2), pages 266-288, April.
    2. Hifi, M. & Sadfi, S. & Sbihi, A., 2000. "Efficient Algorithms for the Knapsack Sharing Problem," Papiers d'Economie Mathématique et Applications 2000.122, Université Panthéon-Sorbonne (Paris 1).
    3. 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.
    4. Xiaochuan Shi & Lei Wu & Xiaoliang Meng, 2017. "A New Optimization Model for the Sustainable Development: Quadratic Knapsack Problem with Conflict Graphs," Sustainability, MDPI, vol. 9(2), pages 1-10, February.
    5. Silvano Martello & David Pisinger & Paolo Toth, 1999. "Dynamic Programming and Strong Bounds for the 0-1 Knapsack Problem," Management Science, INFORMS, vol. 45(3), pages 414-424, March.
    6. Billionnet, Alain & Soutif, Eric, 2004. "An exact method based on Lagrangian decomposition for the 0-1 quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 157(3), pages 565-575, September.
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