Authors
Tobias Achterberg, Christian Raack
Publication date
2010/6/1
Journal
Mathematical Programming Computation
Volume
2
Issue
2
Pages
125-165
Publisher
Springer Berlin/Heidelberg
Description
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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