@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{RaackKosterOrlowskietal., author = {Raack, Christian and Koster, Arie M.C.A. and Orlowski, Sebastian and Wess{\"a}ly, Roland}, title = {Capacitated network design using general flow-cutset inequalities}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9576}, number = {07-14}, abstract = {This paper deals with directed, bidirected, and undirected capacitated network design problems. Using mixed integer rounding (MIR), we generalize flow-cutset inequalities to these three link types and to an arbitrary modular link capacity structure, and propose a generic separation algorithm. In an extensive computational study on 54 instances from the Survivable Network Design Library (SNDlib), we show that the performance of cplex can significantly be enhanced by this class of cutting planes. The computations reveal the particular importance of the subclass of cutset-inequalities.}, language = {en} } @misc{IdzikowskiOrlowskiRaacketal., author = {Idzikowski, Filip and Orlowski, Sebastian and Raack, Christian and Woesner, Hagen and Wolisz, Adam}, title = {Dynamic routing at different layers in IP-over-WDM networks -- Maximizing energy savings}, organization = {Zuse Institute Berlin}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11692}, number = {10-07}, abstract = {We estimate potential energy savings in IP-over-WDM networks achieved by switching off router line cards in low-demand hours. We compare three approaches to react on dynamics in the IP traffic over time, FUFL, DUFL and DUDL. They provide different levels of freedom in adjusting the routing of lightpaths in the WDM layer and the routing of demands in the IP layer. Using MILP models based on three realistic network topologies as well as realistic demands, power, and cost values, we show that already a simple monitoring of the lightpath utilization in order to deactivate empty line cards (FUFL) brings substantial benefits. The most significant savings, however, are achieved by rerouting traffic in the IP layer (DUFL), which allows emptying and deactivating lightpaths together with the corresponding line cards. A sophisticated reoptimization of the virtual topologies and the routing in the optical domain for every demand scenario (DUDL) yields nearly no additional profits in the considered networks. These results are independent of the ratio between the demand and capacity granularities, the time scale and the network topology, and show little dependency on the demand structure.}, 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} }