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Two-row and two-column mixed-integer presolve using hashing-based pairing methods

Author

Listed:
  • Patrick Gemander

    (Friedrich-Alexander-Universität Erlangen-Nürnberg)

  • Wei-Kun Chen

    (Beijing Institute of Technology)

  • Dieter Weninger

    (Friedrich-Alexander-Universität Erlangen-Nürnberg)

  • Leona Gottwald

    (Zuse Institute Berlin)

  • Ambros Gleixner

    (Zuse Institute Berlin)

  • Alexander Martin

    (Friedrich-Alexander-Universität Erlangen-Nürnberg)

Abstract

In state-of-the-art mixed-integer programming solvers, a large array of reduction techniques are applied to simplify the problem and strengthen the model formulation before starting the actual branch-and-cut phase. Despite their mathematical simplicity, these methods can have significant impact on the solvability of a given problem. However, a crucial property for employing presolve techniques successfully is their speed. Hence, most methods inspect constraints or variables individually in order to guarantee linear complexity. In this paper, we present new hashing-based pairing mechanisms that help to overcome known performance limitations of more powerful presolve techniques that consider pairs of rows or columns. Additionally, we develop an enhancement to one of these presolve techniques by exploiting the presence of set-packing structures on binary variables in order to strengthen the resulting reductions without increasing runtime. We analyze the impact of these methods on the MIPLIB 2017 benchmark set based on an implementation in the MIP solver SCIP.

Suggested Citation

  • Patrick Gemander & Wei-Kun Chen & Dieter Weninger & Leona Gottwald & Ambros Gleixner & Alexander Martin, 2020. "Two-row and two-column mixed-integer presolve using hashing-based pairing methods," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(3), pages 205-240, October.
    • Handle: RePEc:spr:eurjco:v:8:y:2020:i:3:d:10.1007_s13675-020-00129-6
    DOI: 10.1007/s13675-020-00129-6
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    References listed on IDEAS

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    Cited by:

    1. Chen, Liang & Chen, Sheng-Jie & Chen, Wei-Kun & Dai, Yu-Hong & Quan, Tao & Chen, Juan, 2023. "Efficient presolving methods for solving maximal covering and partial set covering location problems," European Journal of Operational Research, Elsevier, vol. 311(1), pages 73-87.

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