## 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.

$Rev: 13581$