Measuring the Impact of Branching Rules for Mixed-Integer Programming

  • Gerald GamrathEmail author
  • Christoph Schubert
Conference paper
Part of the Operations Research Proceedings book series (ORP)


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.


Mixed-integer programming Branch-and-bound Branching rule Strong branch 



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).


  1. 1.
    Achterberg, T. (2007). Constraint Integer Programming. Ph.D. thesis. Technische Universität, Berlin.Google Scholar
  2. 2.
    Achterberg, T., & Berthold, T. (2009). Hybrid Branching. In W. J. van Hoeve & J. N. Hooker (Eds.), CPAIOR 2009 (Vol. 5547, pp. 309–311). LNCS, Springer.CrossRefGoogle Scholar
  3. 3.
    Achterberg, T., Koch, T., & Martin, A. (2005). Branching rules revisited. Operations Research Letters, 33, 42–54.CrossRefGoogle Scholar
  4. 4.
    Benichou, M., et al. (1971). Experiments in mixed-integer linear programming. Mathematical Programming, 1, 76–94.CrossRefGoogle Scholar
  5. 5.
    COR@L MIP Instances. Accessed June 2017.
  6. 6.
    Gamrath, G. (2014). Improving strong branching by domain propagation. EURO Journal on Computational Optimization, 2(3), 99–122.CrossRefGoogle Scholar
  7. 7.
    Gauthier, J. -M., & Ribière, G. (1977). Experiments in mixed-integer linear programmingusing pseudo-costs. Math Prog, 12(1), 26–47.CrossRefGoogle Scholar
  8. 8.
    Koch, T., et al. (2011). MIPLIB 2010. Mathematical Programming Computation, 3(2), 103–163.CrossRefGoogle Scholar
  9. 9.
    Land, A. H., & Doig, A. G. (1960). An automatic method of solving discrete programming problems. Econometrica, 28(3), 497–520.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Zuse Institute BerlinBerlinGermany

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