The <Emphasis Type="SmallCaps">Mcf</Emphasis>-separator: detecting and exploiting multi-commodity flow structures in MIPs |
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Authors: | Tobias Achterberg Christian Raack |
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Institution: | 1.IBM Schoenaicher,Boeblingen,Germany;2.Zuse Institute Berlin (ZIB),Berlin,Germany |
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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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