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

Tobias Achterberg(achterberg***at***de.ibm.com)
Christian Raack(raack***at***zib.de)

Abstract: 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 (c-MIR) 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.

Keywords: mixed integer programming, network detection, cut-based inequalities, separator, Cplex, Scip

Category 1: Integer Programming (Cutting Plane Approaches )

Category 2: Combinatorial Optimization (Branch and Cut Algorithms )

Category 3: Network Optimization

Citation: ZIB Report ZR-09-38, November 2009, Zuse Institute Berlin, Takustr. 7, 14195 Berlin

Download: [Postscript][PDF]

Entry Submitted: 11/28/2009
Entry Accepted: 11/28/2009
Entry Last Modified: 11/28/2009

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