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Presolve Reductions in Mixed Integer Programming

Author

Listed:
  • Tobias Achterberg

    (Gurobi GmbH, 10245 Berlin, Germany)

  • Robert E. Bixby

    (Gurobi Optimization, Beaverton, Oregon 97008)

  • Zonghao Gu

    (Gurobi Optimization, Beaverton, Oregon 97008)

  • Edward Rothberg

    (Gurobi Optimization, Beaverton, Oregon 97008)

  • Dieter Weninger

    (University Erlangen-Nürnberg, 91054 Erlangen, Germany)

Abstract

Mixed integer programming has become a very powerful tool for modeling and solving real-world planning and scheduling problems, with the breadth of applications appearing to be almost unlimited. A critical component in the solution of these mixed integer programs is a set of routines commonly referred to as presolve. Presolve can be viewed as a collection of preprocessing techniques that reduce the size of and, more importantly, improve the “strength” of the given model formulation, that is, the degree to which the constraints of the formulation accurately describe the underlying polyhedron of integer-feasible solutions. As our computational results will show, presolve is a key factor in the speed with which we can solve mixed integer programs and is often the difference between a model being intractable and solvable, in some cases easily solvable. In this paper we describe the presolve functionality in the Gurobi commercial mixed integer programming code. This includes an overview, or taxonomy of the different methods that are employed, as well as more-detailed descriptions of several of the techniques, with some of them appearing, to our knowledge, for the first time in the literature.

Suggested Citation

  • Tobias Achterberg & Robert E. Bixby & Zonghao Gu & Edward Rothberg & Dieter Weninger, 2020. "Presolve Reductions in Mixed Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 473-506, April.
    • Handle: RePEc:inm:orijoc:v:32:y:2020:i:2:p:473-506
    DOI: 10.1287/ijoc.2018.0857
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    References listed on IDEAS

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    Cited by:

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    3. 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.
    4. Yifu Chen & Christos T. Maravelias, 2022. "Variable Bound Tightening and Valid Constraints for Multiperiod Blending," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2073-2090, July.
    5. Veremyev, Alexander & Boginski, Vladimir & Pasiliao, Eduardo L. & Prokopyev, Oleg A., 2022. "On integer programming models for the maximum 2-club problem and its robust generalizations in sparse graphs," European Journal of Operational Research, Elsevier, vol. 297(1), pages 86-101.

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    Keywords

    mixed integer programming; presolving;

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