Improving strong branching by domain propagation

Please always quote using this URN: urn:nbn:de:0297-zib-42546
  • One of the essential components of a branch-and-bound based mixed-integer linear programming (MIP) solver is the branching rule. Strong branching is a method used by many state-of-the-art branching rules to select the variable to branch on. It precomputes the dual bounds of potential child nodes by solving auxiliary linear programs (LPs) and thereby helps to take good branching decisions that lead to a small search tree. In this paper, we describe how these dual bound predictions can be improved by including domain propagation into strong branching. Domain propagation is a technique usually used at every node of the branch-and-bound tree to tighten the local domains of variables. Computational experiments on standard MIP instances indicate that our improved strong branching method significantly improves the quality of the predictions and causes almost no additional effort. For a full strong branching rule, we are able to obtain substantial reductions of the branch-and-bound tree size as well as the solving time. Moreover, also the state-of-the-art hybrid branching rule can be improved this way. This paper extends previous work by the author published in the proceedings of the CPAIOR 2013.

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Author:Gerald Gamrath
Document Type:ZIB-Report
Tag:branch-and-bound; branching rule; domain propagation; mixed-integer programming; strong branching; variable selection
MSC-Classification:90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90-08 Computational methods
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Bxx Operations research and management science / 90B40 Search theory
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C10 Integer programming
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C11 Mixed integer programming
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
CCS-Classification:G. Mathematics of Computing / G.4 MATHEMATICAL SOFTWARE
Date of first Publication:2013/09/23
Series (Serial Number):ZIB-Report (13-47)
ISSN:1438-0064
Published in:EURO Journal on Computational Optimization
DOI:https://doi.org/10.1007/s13675-014-0021-8