## Branching on multi-aggregated variables

Please always quote using this URN: urn:nbn:de:0297-zib-53829

- In mixed-integer programming, the branching rule is a key component to a fast convergence of the branch-and-bound algorithm. The most common strategy is to branch on simple disjunctions that split the domain of a single integer variable into two disjoint intervals. Multi-aggregation is a presolving step that replaces variables by an affine linear sum of other variables, thereby reducing the problem size. While this simplification typically improves the performance of MIP solvers, it also restricts the degree of freedom in variable-based branching rules. We present a novel branching scheme that tries to overcome the above drawback by considering general disjunctions defined by multi-aggregated variables in addition to the standard disjunctions based on single variables. This natural idea results in a hybrid between variable- and constraint-based branching rules. Our implementation within the constraint integer programming framework SCIP incorporates this into a full strong branching rule and reduces the number of branch-and-bound nodes on a general test set of publicly available benchmark instances. For a specific class of problems, we show that the solving time decreases significantly.

Author: | Gerald Gamrath, Anna Melchiori, Timo Berthold, Ambros M. Gleixner, Domenico Salvagnin |
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Document Type: | ZIB-Report |

Tag: | mixed-integer programming, branch-and-bound, branching rule, strong branching |

MSC-Classification: | 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 | |

Date of first Publication: | 2015/03/09 |

Series (Serial Number): | ZIB-Report (15-10) |

ISSN: | 1438-0064 |

Published in: | Integration of AI and OR Techniques in Constraint Programming |

Preprint: | urn:nbn:de:0297-zib-53829 |

DOI: | http://dx.doi.org/10.1007/978-3-319-18008-3_10 |