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Operations Research Proceedings 2017 pp 165–170Cite as

Measuring the Impact of Branching Rules for Mixed-Integer Programming

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Abstract

Branching rules are an integral component of the branch-and-bound algorithm typically used to solve mixed-integer programs and subject to intense research. Different approaches for branching are typically compared based on the solving time as well as the size of the branch-and-bound tree needed to prove optimality. The latter, however, has some flaws when it comes to sophisticated branching rules that do not only try to take a good branching decision, but have additional side-effects. We propose a new measure for the quality of a branching rule that distinguishes tree size reductions obtained by better branching decisions from those obtained by such side-effects. It is evaluated for common branching rules providing new insights in the importance of strong branching.

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Acknowledgements

The work for this article has been conducted within the Research Campus Modal funded by the German Federal Ministry of Education and Research (fund number 05M14ZAM).

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Authors and Affiliations

  1. Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany

    Gerald Gamrath & Christoph Schubert

Authors
  1. Gerald Gamrath
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  2. Christoph Schubert
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Corresponding author

Correspondence to Gerald Gamrath .

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Editors and Affiliations

  1. Department of Information Systems, Freie Universität Berlin, Berlin, Germany

    Natalia Kliewer

  2. Management Science Group, Otto-von-Guericke Universität Magdeburg, Magdeburg, Germany

    Jan Fabian Ehmke

  3. Department of Mathematics, Freie Universität Berlin, Berlin, Germany

    Ralf Borndörfer

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Gamrath, G., Schubert, C. (2018). Measuring the Impact of Branching Rules for Mixed-Integer Programming. In: Kliewer, N., Ehmke, J., Borndörfer, R. (eds) Operations Research Proceedings 2017. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-89920-6_23

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