## The MCF-Separator -- Detecting and Exploiting Multi-Commodity Flow Structures in MIPs

Please always quote using this URN: urn:nbn:de:0297-zib-11592

- Given a general mixed integer program (MIP), we automatically detect block structures in the constraint matrix together with the coupling by capacity constraints arising from multi-commodity-flow formulations. We identify the underlying graph and generate cutting planes based on cuts in the detected network. Our implementation adds a separator to the branch-and-cut libraries of SCIP and CPLEX. We make use of the complemented mixed integer rounding framework (cMIR) but provide a special purpose aggregation heuristic that exploits the network structure. Our separation scheme speeds-up the computation for a large set of MIPs coming from network design problems by a factor of two on average.

Author: | Tobias Achterberg, Christian Raack |
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Document Type: | ZIB-Report |

Tag: | cplex; cut-based inequalities; mixed integer programming; network detection; scip |

MSC-Classification: | 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] / 90C35 Programming involving graphs or networks [See also 90C27] | |

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: | 2009/11/30 |

Series (Serial Number): | ZIB-Report (09-38) |

ISSN: | 1438-0064 |