Measuring the Impact of Branching Rules for Mixed-Integer Programming
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.
KeywordsMixed-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.Achterberg, T. (2007). Constraint Integer Programming. Ph.D. thesis. Technische Universität, Berlin.Google Scholar
- 5.COR@L MIP Instances. Accessed June 2017. http://coral.ise.lehigh.edu/data-sets/mixedinteger-instances/.