@misc{RaackKosterWessaely, author = {Raack, Christian and Koster, Arie M.C.A. and Wess{\"a}ly, Roland}, title = {On the strength of cut-based inequalities for capacitated network design polyhedra}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9512}, number = {07-08}, abstract = {In this paper we study capacitated network design problems, differentiating directed, bidirected and undirected link capacity models. We complement existing polyhedral results for the three variants by new classes of facet-defining valid inequalities and unified lifting results. For this, we study the restriction of the problems to a cut of the network. First, we show that facets of the resulting cutset polyhedra translate into facets of the original network design polyhedra if the two subgraphs defined by the network cut are (strongly) connected. Second, we provide an analysis of the facial structure of cutset polyhedra, elaborating the differences caused by the three different types of capacity constraints. We present flow-cutset inequalities for all three models and show under which conditions these are facet-defining. We also state a new class of facets for the bidirected and undirected case and it is shown how to handle multiple capacity modules by Mixed Integer Rounding (MIR).}, language = {en} } @misc{AchterbergRaack, author = {Achterberg, Tobias and Raack, Christian}, title = {The MCF-Separator -- Detecting and Exploiting Multi-Commodity Flow Structures in MIPs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11592}, number = {09-38}, 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 (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.}, language = {en} }