@article{RaackRaymondSchlechteetal.2013, author = {Raack, Christian and Raymond, Annie and Schlechte, Thomas and Werner, Axel}, title = {Standings in sports competitions using integer programming}, volume = {10}, journal = {Journal of Quantitative Analysis in Sports}, number = {2}, publisher = {De Gruyter}, doi = {10.1515/jqas-2013-0111}, pages = {131 -- 137}, year = {2013}, language = {en} } @phdthesis{Raack2012, author = {Raack, Christian}, title = {Capacitated Network Design - Multi-Commodity Flow Formulations, Cutting Planes, and Demand Uncertainty}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:83-opus-36167}, school = {Technische Universit{\"a}t Berlin}, year = {2012}, abstract = {In this thesis, we develop methods in mathematical optimization to dimension networks at minimal cost. Given hardware and cost models, the challenge is to provide network topologies and efficient capacity plans that meet the demand for network traffic (data, passengers, freight). We incorporate crucial aspects of practical interest such as the discrete structure of available capacities as well as the uncertainty of demand forecasts. The considered planning problems typically arise in the strategic design of telecommunication or public transport networks and also in logistics. One of the essential aspects studied in this work is the use of cutting planes to enhance solution approaches based on multi-commodity flow formulations. Providing theoretical and computational evidence for the efficacy of inequalities based on network cuts, we extend existing theory and algorithmic work in different directions. First, we prove that special-purpose techniques, originally designed to solve capacitated network design problems, can be successfully integrated into general-purpose mixed integer programming (MIP) solvers. Our approach relies on an automatic detection of network structure within the constraint matrix of general mixed in teger programs. More precisely, we identify multi-commodity (MCF) network sub-matrices and resolve the isomorphisms of the commodity blocks as well as the original graph structure. In the subsequent separation framework, we guide the constraint aggregation of available cutting plane procedures (e. g. based on mixed integer rounding) to produce strong cutting planes that reflect the structure of the constructed network. The new MCF-separator integrates network design specific methodology into general optimization tools which is of particular importance for practitioners that tend to use MIP solvers as black boxes. Extensive computational tests show that our network detection procedure operates accurately and reliably. Moreover, due to the generated cutting planes, we achieve an average speed-up of a factor of two for pure network design problems with general MIP solvers. Many of these instances can only be solved to optimality in reasonable time if the new MCF-separator is active. In 9 \% of the instances of general MIP test sets we find consistent embedded networks and generate violated inequalities. In this case the computation time decreases by 18 \% on average with almost no degradation for unaffected instances. Second, we generalize concepts, models, and cutting planes from deterministic network design to robust network design, incorporating the uncertainty of traffic demands. We enhance and compare strategies that are able to handle a polyhedral set of different traffic scenarios. In particular, we consider two correlated solution methods, based on separating extreme demand scenarios and dualizing the linear description of the demand polytope, respectively. We consider robust network design as two-stage robust optimization with recourse. First stage capacity decisions are fixed for all scenarios while the second stage flow depends on the realized demands. In order to reroute the traffic as a function of the demand dynamics, we consider three alternative recourse actions, namely, static, affine, and dynamic routing. We analyze properties of the new affine routing and show that it combines advantages of the well-known static and dynamic models. Using the concept of robust cut-set polyhedra and the corresponding lifting theorems, we develop several classes of facet-defining inequalities based on network cuts that can be used to further accelerate solution strategies for robust network design. Among them are the well-known (flow) cut-set inequalities, which we generalize to general demand polytopes, but also new classes of potential cutting planes, so-called envelope inequalities. The practical importance of the developed cutting planes is revealed by a series of computational tests. Similar to the results for the MCF-separator we achieve speed-ups of two and more using the generalized classes of strong inequalities. To evaluate the robustness of solutions that are computed with our framework we use real-life measurements of traffic dynamics from different existing telecommunication networks, among them data from the German and the European research network. Our results indicate that traffic peaks do not necessarily occur all simultaneously with respect to different source-destination pairs, which is of practical importance for the design of uncertainty sets. It is, in particular, not necessary to dimension networks for a scenario that assumes all source-destination traffic is at its peak simultaneously. With our solutions we save up to 20 \% of the corresponding solution cost compared to this artificial scenario and achieve comparable levels of robustness.}, language = {en} } @article{GroetschelRaackWerner2013, author = {Gr{\"o}tschel, Martin and Raack, Christian and Werner, Axel}, title = {Towards optimizing the deployment of optical access networks}, volume = {2}, journal = {EURO Journal on Computational Optimization}, publisher = {Springer}, doi = {10.1007/s13675-013-0016-x}, pages = {17 -- 53}, year = {2013}, language = {en} } @article{BetkerKosiankowskiLangeetal.2014, author = {Betker, Andreas and Kosiankowski, Dirk and Lange, Christoph and Pfeuffer, Frank and Raack, Christian and Werner, Axel}, title = {Energy efficiency in extensive IP-over-WDM networks with protection}, journal = {Operations Research Proceedings 2012}, editor = {Helber, Stefan and Breitner, Michael and R{\"o}sch, Daniel and Sch{\"o}n, Cornelia and Graf von der Schulenburg, Johann-Matthias and Sibbertsen, Philipp and Steinbach, Marc and Weber, Stefan and Wolter, Anja}, publisher = {Springer}, doi = {10.1007/978-3-319-00795-3_14}, pages = {93 -- 99}, year = {2014}, language = {en} } @article{PossRaack2013, author = {Poss, Michael and Raack, Christian}, title = {Affine recourse for the robust network design problem: Between static and dynamic routing}, volume = {61}, journal = {Networks - Special Issue: INOC 2011 Conference, June 13-16, 2011, Hamburg, Germany}, number = {2}, doi = {10.1002/net.21482}, pages = {180 -- 198}, year = {2013}, abstract = {Affinely-Adjustable Robust Counterparts provide tractable alternatives to (two-stage) robust programs with arbitrary recourse. We apply them to robust network design with polyhedral demand uncertainty, introducing the affine routing principle. We compare the affine routing to the well-studied static and dynamic routing schemes for robust network design. All three schemes are embedded into the general framework of two-stage network design with recourse. It is shown that affine routing can be seen as a generalization of the widely used static routing still being tractable and providing cheaper solutions. We investigate properties on the demand polytope under which affine routings reduce to static routings and also develop conditions on the uncertainty set leading to dynamic routings being affine. We show however that affine routings suffer from the drawback that (even totally) dominated demand vectors are not necessarily supported by affine solutions. Uncertainty sets have to be designed accordingly. Finally, we present computational results on networks from SNDlib. We conclude that for these instances the optimal solutions based on affine routings tend to be as cheap as optimal network designs for dynamic routings. In this respect the affine routing principle can be used to approximate the cost for two-stage solutions with free recourse which are hard to compute.}, language = {en} } @inproceedings{MenneRaackWessaelyetal.2012, author = {Menne, Ulrich and Raack, Christian and Wess{\"a}ly, Roland and Kharitonov, Daniel}, title = {Optimal Degree of Optical Circuit Switching in IP-over-WDM Networks}, booktitle = {Optical Network Design and Modeling (ONDM), 2012 16th International Conference on}, doi = {10.1109/ONDM.2012.6210206}, pages = {1 -- 6}, year = {2012}, abstract = {In this paper, we study the influence of technology, traffic properties and price trends on optimized design of a reference IP-over-WDM network with rich underlying fiber topology. In each network node, we investigate the optimal degree of traffic switching in an optical (lambda) domain versus an electrical (packet) domain, also known as measure of \emph{node transparency}. This measure is studied in connection to changes in traffic volume, demand affinity, optical circuit speeds and equipment cost. By applying variable design constraints, we assess the relative roles of the two distinct equipment groups, IP routers and optical cross-connects, with respect to resulting changes in cost-sensitive network architectures.}, language = {en} } @misc{Raack2005, type = {Master Thesis}, author = {Raack, Christian}, title = {Employing Mixed-Integer Rounding in Telecommunication Network Design}, year = {2005}, language = {en} } @inproceedings{OrlowskiKosterRaacketal.2007, author = {Orlowski, Sebastian and Koster, Arie M.C.A. and Raack, Christian and Wess{\"a}ly, Roland}, title = {Two-layer Network Design by Branch-and-Cut featuring MIP-based Heuristics}, booktitle = {Proceedings of the INOC 2007, Spa, Belgium, also ZIB Report ZR-06-47}, publisher = {International Network Optimization Conference}, address = {Spa, Belgium}, year = {2007}, language = {en} } @inproceedings{RaackKosterOrlowskietal.2007, 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}, booktitle = {Proceedings of the INOC 2007, Spa, Belgium, also ZIB Report ZR-07-14}, publisher = {International Network Optimization Conference}, address = {Spa, Belgium}, year = {2007}, language = {en} } @incollection{KosterOrlowskiRaacketal.2008, author = {Koster, Arie M.C.A. and Orlowski, Sebastian and Raack, Christian and Baier, Georg and Engel, Thomas}, title = {Single-layer Cuts for Multi-Layer Network Design Problems}, booktitle = {Telecommunications Modeling Policy and Technology, also ZIB Report ZR-07-21}, publisher = {Springer}, address = {College Park, MD, U.S.A.}, pages = {1 -- 23}, year = {2008}, language = {en} }