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

Please always quote using this URN:urn:nbn:de:0296-matheon-6699
  • 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.

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Metadaten
Author:Tobias Achterberg, Christian Raack
URN:urn:nbn:de:0296-matheon-6699
Referee:Andreas Bley
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2009/12/15
Release Date:2009/11/30
Tag:
Institute:Zuse Institute Berlin (ZIB)
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
Preprint Number:677
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