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On the exact separation of cover inequalities of maximum-depth

Author

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  • Catanzaro, Daniele

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

  • Coniglio, Stefano
  • Furini, Fabio

Abstract

We investigate the problem of separating cover inequalities of maximum-depth exactly. We propose a pseudopolynomial-time dynamic-programming algorithm for its solution, thanks to which we show that this problem is weakly NP-hard (similarly to the problem of separating cover inequalities of maximum violation). We carry out extensive computational experiments on instances of the knapsack and the multi-dimensional knapsack problems with and without conflict constraints. The results show that, with a cutting-plane generation method based on the maximum-depth criterion, we can optimize over the cover-inequality closure by generating a number of cuts smaller than when adopting the standard maximum-violation criterion. We also introduce the Point-to-Hyperplane Distance Knapsack Problem (PHD-KP), a problem closely related to the separation problem for maximum-depth cover inequalities, and show how the proposed dynamic programming algorithm can be adapted for effectively solving the PHD-KP as well.

Suggested Citation

  • Catanzaro, Daniele & Coniglio, Stefano & Furini, Fabio, 2021. "On the exact separation of cover inequalities of maximum-depth," LIDAM Discussion Papers CORE 2021018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2021018
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    References listed on IDEAS

    as
    1. Amaldi, Edoardo & Coniglio, Stefano, 2013. "A distance-based point-reassignment heuristic for the k-hyperplane clustering problem," European Journal of Operational Research, Elsevier, vol. 227(1), pages 22-29.
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    3. Egon Balas & Sebastián Ceria & Gérard Cornuéjols, 1996. "Mixed 0-1 Programming by Lift-and-Project in a Branch-and-Cut Framework," Management Science, INFORMS, vol. 42(9), pages 1229-1246, September.
    4. Giuseppe Andreello & Alberto Caprara & Matteo Fischetti, 2007. "Embedding {0, ½}-Cuts in a Branch-and-Cut Framework: A Computational Study," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 229-238, May.
    5. 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.
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    Keywords

    Knapsack Problem ; Cover Inequalities ; Dynamic Programming ; Mixed Integer Nonlinear Programming ; Cutting Plane Generation;
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