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The Mcf-separator: detecting and exploiting multi-commodity flow structures in MIPs

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Abstract

Given a general mixed integer program, 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 but provide a special purpose aggregation heuristic that exploits the network structure. Our separation scheme speeds-up the computation for a large set of mixed integer programs coming from network design problems by a factor two on average. We show that almost 10% of the instances in general testsets contain consistent embedded networks. For these instances the computation time is decreased by 18% on average.

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Authors and Affiliations

  1. IBM Schoenaicher, Str. 220, 71003, Boeblingen, Germany

    Tobias Achterberg

  2. Zuse Institute Berlin (ZIB), Takustr. 7, 14195, Berlin, Germany

    Christian Raack

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  1. Tobias Achterberg
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  2. Christian Raack
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Correspondence to Christian Raack.

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This research has been supported by the DFG research Center Matheon.

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Achterberg, T., Raack, C. The Mcf-separator: detecting and exploiting multi-commodity flow structures in MIPs. Math. Prog. Comp. 2, 125–165 (2010). https://doi.org/10.1007/s12532-010-0015-3

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