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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| 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 |
