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A Branch-and-Bound Algorithm for the Knapsack Problem with Conflict Graph

Author

Listed:
  • Andrea Bettinelli

    (OPTIT Srl, 40026 Imola (BO), Italy)

  • Valentina Cacchiani

    (Department of Electrical, Electronic, and Information Engineering “Guglielmo Marconi,” Università di Bologna, 40136 Bologna, Italy)

  • Enrico Malaguti

    (Department of Electrical, Electronic, and Information Engineering “Guglielmo Marconi,” Università di Bologna, 40136 Bologna, Italy)

Abstract

We study the knapsack problem with conflict graph (KPCG), an extension of the 0-1 knapsack problem, in which a conflict graph describing incompatibilities between items is given. The goal of the KPCG is to select the maximum profit set of compatible items while satisfying the knapsack capacity constraint. We present a new branch-and-bound approach to derive optimal solutions to the KPCG in short computing times. Extensive computational experiments are reported showing that, for instances with graph density of 10% and larger, the proposed method outperforms a state-of-the-art approach and mixed-integer programming formulations tackled through a general purpose solver.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:orijoc:v:29:y:2017:i:3:p:457-473
    DOI: 10.1287/ijoc.2016.0742
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    References listed on IDEAS

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    1. Ruslan Sadykov & François Vanderbeck, 2013. "Bin Packing with Conflicts: A Generic Branch-and-Price Algorithm," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 244-255, May.
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    4. Albert E. Fernandes Muritiba & Manuel Iori & Enrico Malaguti & Paolo Toth, 2010. "Algorithms for the Bin Packing Problem with Conflicts," INFORMS Journal on Computing, INFORMS, vol. 22(3), pages 401-415, August.
    5. 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.
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