@misc{HoeselKosterLeenseletal.2000, author = {Hoesel, Stan P.M. van and Koster, Arie M.C.A. and Leensel, Robert L.M.J. van de and Savelsbergh, Martin W.P.}, title = {Polyhedral Results for the Edge Capacity Polytope}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5907}, number = {00-22}, year = {2000}, abstract = {Network loading problems occur in the design of telecommunication networks, in many different settings. The polyhedral structure of this problem is important in developing solution methods for the problem. In this paper we investigate the polytope of the problem restricted to one edge of the network (the edge capacity problem). We describe classes of strong valid inequalities for the edge capacity polytope, and we derive conditions under which these constraints define facets. As the edge capacity problem is a relaxation of the network loading problem, their polytopes are intimately related. We, therefore, also give conditions under which the inequalities of the edge capacity polytope define facets of the network loading polytope. Furthermore, some structural properties are derived, such as the relation of the edge capacity polytope to the knapsack polytope. We conclude the theoretical part of this paper with some lifting theorems, where we show that this problem is polynomially solvable for most of our classes of valid inequalities. In a computational study the quality of the constraints is investigated. Here, we show that the valid inequalities of the edge capacity polytope are not only important for solving the edge capacity problem, but also for the network loading problem, showing that the edge capacity problem is an important subproblem.}, language = {en} } @misc{Groetschel2000, author = {Gr{\"o}tschel, Martin}, title = {Mathematik in der Industrie: interessante Branchen und zuk{\"u}nftige Einsatzfelder}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6125}, number = {00-44}, year = {2000}, abstract = {Dieser kurze Artikel hat keine umfassende {\"U}bersicht zum Ziel. Basierend auf eigenen Erfahrungen durch Projekte mit Industriefirmen m{\"o}chte ich einige Branchen erw{\"a}hnen, bei denen nach meiner Einsch{\"a}tzung Mathematik in Zukunft zunehmend Anwendung finden wird. Ich werde das anhand konkreter Beispiele erl{\"a}utern. Mathematik ersetzt in der Regel traditionelle Analyse-, Planungs- und Entwurfstechniken. Den (nicht leichten) Schritt zum Einsatz mathematischer Methoden macht ein Praktiker nur, wenn es sich f{\"u}r ihn ``lohnt''. Wann sich dies lohnt, ist schwer abzusch{\"a}tzen. Man kann aber einige Indikatoren daf{\"u}r finden, ob eine Branche f{\"u}r den Einsatz von Mathematik ``reif'' ist. Ob es dann dazu kommt, h{\"a}ngt von vielen Faktoren ab, nicht zuletzt von der Psychologie und dem sozialen Umfeld der beteiligten Personen sowie der Bereitschaft, sich auf ein so schwieriges Terrain zu begeben und Kompromisse einzugehen. Gerade letzteres f{\"a}llt Mathematikern gelegentlich schwer.}, language = {de} } @misc{AbboudGroetschelKoch2006, author = {Abboud, Nadine and Gr{\"o}tschel, Martin and Koch, Thorsten}, title = {Mathematical Methods for Physical Layout of Printed Circuit Boards: An Overview}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9231}, number = {06-29}, year = {2006}, abstract = {This article surveys mathematical models and methods used for physical PCB layout, i.e., component placement and wire routing. The main concepts are briefly described together with relevant references.}, language = {en} } @misc{HeinzSchlechteStephanetal.2011, author = {Heinz, Stefan and Schlechte, Thomas and Stephan, R{\"u}diger and Winkler, Michael}, title = {Solving steel mill slab design problems}, issn = {1438-0064}, doi = {10.1007/s10601-011-9113-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14089}, number = {11-38}, year = {2011}, abstract = {The steel mill slab design problem from the CSPLIB is a combinatorial optimization problem motivated by an application of the steel industry. It has been widely studied in the constraint programming community. Several methods were proposed to solve this problem. A steel mill slab library was created which contains 380 instances. A closely related binpacking problem called the multiple knapsack problem with color constraints, originated from the same industrial problem, was discussed in the integer programming community. In particular, a simple integer program for this problem has been given by Forrest et al. The aim of this paper is to bring these different studies together. Moreover, we adapt the model of Forrest et al. for the steel mill slab design problem. Using this model and a state-of-the-art integer program solver all instances of the steel mill slab library can be solved efficiently to optimality. We improved, thereby, the solution values of 76 instances compared to previous results. Finally, we consider a recently introduced variant of the steel mill slab design problem, where within all solutions which minimize the leftover one is interested in a solution which requires a minimum number of slabs. For that variant we introduce two approaches and solve all instances of the steel mill slab library with this slightly changed objective function to optimality.}, language = {en} } @misc{PossRaack2011, author = {Poss, Michael and Raack, Christian}, title = {Affine recourse for the robust network design problem: between static and dynamic routing}, doi = {10.1002/net.21482}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12122}, number = {11-03}, year = {2011}, 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} } @misc{BorndoerferHoangKarbsteinetal.2013, author = {Bornd{\"o}rfer, Ralf and Hoang, Nam-Dung and Karbstein, Marika and Koch, Thorsten and Martin, Alexander}, title = {How Many Steiner Terminals Can You Connect in 20 Years?}, issn = {1438-0064}, doi = {10.1007/978-3-642-38189-8_10}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42524}, year = {2013}, abstract = {Steiner trees are constructed to connect a set of terminal nodes in a graph. This basic version of the Steiner tree problem is idealized, but it can effectively guide the search for successful approaches to many relevant variants, from both a theoretical and a computational point of view. This article illustrates the theoretical and algorithmic progress on Steiner tree type problems on two examples, the Steiner connectivity and the Steiner tree packing problem.}, language = {en} } @misc{GamrathFischerGallyetal.2016, author = {Gamrath, Gerald and Fischer, Tobias and Gally, Tristan and Gleixner, Ambros and Hendel, Gregor and Koch, Thorsten and Maher, Stephen J. and Miltenberger, Matthias and M{\"u}ller, Benjamin and Pfetsch, Marc and Puchert, Christian and Rehfeldt, Daniel and Schenker, Sebastian and Schwarz, Robert and Serrano, Felipe and Shinano, Yuji and Vigerske, Stefan and Weninger, Dieter and Winkler, Michael and Witt, Jonas T. and Witzig, Jakob}, title = {The SCIP Optimization Suite 3.2}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57675}, year = {2016}, abstract = {The SCIP Optimization Suite is a software toolbox for generating and solving various classes of mathematical optimization problems. Its major components are the modeling language ZIMPL, the linear programming solver SoPlex, the constraint integer programming framework and mixed-integer linear and nonlinear programming solver SCIP, the UG framework for parallelization of branch-and-bound-based solvers, and the generic branch-cut-and-price solver GCG. It has been used in many applications from both academia and industry and is one of the leading non-commercial solvers. This paper highlights the new features of version 3.2 of the SCIP Optimization Suite. Version 3.2 was released in July 2015. This release comes with new presolving steps, primal heuristics, and branching rules within SCIP. In addition, version 3.2 includes a reoptimization feature and improved handling of quadratic constraints and special ordered sets. SoPlex can now solve LPs exactly over the rational number and performance improvements have been achieved by exploiting sparsity in more situations. UG has been tested successfully on 80,000 cores. A major new feature of UG is the functionality to parallelize a customized SCIP solver. GCG has been enhanced with a new separator, new primal heuristics, and improved column management. Finally, new and improved extensions of SCIP are presented, namely solvers for multi-criteria optimization, Steiner tree problems, and mixed-integer semidefinite programs.}, language = {en} } @misc{Schweiger2010, type = {Master Thesis}, author = {Schweiger, Jonas}, title = {Application of Multistage Stochastic Programming in Strategic Telecommunication Network Planning}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12206}, school = {Zuse Institute Berlin (ZIB)}, pages = {149}, year = {2010}, abstract = {Telecommunication is fundamental for the information society. In both, the private and the professional sector, mobile communication is nowadays taken for granted. Starting primarily as a service for speech communication, data service and mobile Internet access are now driving the evolution of network infrastructure. In the year 2009, 19 million users generated over 33 million GB of traffic using mobile data services. The 3rd generation networks (3G or UMTS) in Germany comprises over 39,000 base stations with some 120,000 cells. From 1998 to 2008, the four network operators in Germany invested over 33 billion Euros in their infrastructure. A careful allocation of the resources is thus crucial for the profitability for a network operator: a network should be dimensioned to match customers demand. As this demand evolves over time, the infrastructure has to evolve accordingly. The demand evolution is hard to predict and thus constitutes a strong source of uncertainty. Strategic network planning has to take this uncertainty into account, and the planned network evolution should adapt to changing market conditions. The application of superior planning methods under the consideration of uncertainty can improve the profitability of the network and creates a competitive advantage. Multistage stochastic programming is a suitable framework to model strategic telecommunication network planning. We present mathematical models and effective optimization procedures for strategic cellular network design. The demand evolution is modeled as a continuous stochastic process which is approximated by a discrete scenario tree. A tree-stage approach is used for the construction of non-uniform scenario trees that serve as input of the stochastic program. The model is calibrated by historical traffic observations. A realistic system model of UMTS radio cells is used that determines coverage areas and cell capacities and takes signal propagation and interferences into account. The network design problem is formulated as a multistage stochastic mixed integer linear program, which is solved using state-of-the-art commercial MIP solvers. Problem specific presolving is proposed to reduce the problem size. Computational results on realistic data is presented. Optimization for the expected profit and the conditional value at risk are performed and compared.}, language = {en} } @misc{EisenblaetterSchweiger2011, author = {Eisenbl{\"a}tter, Andreas and Schweiger, Jonas}, title = {Multistage Stochastic Programming in Strategic Telecommunication Network Planning}, doi = {10.1007/s10287-012-0143-5}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12232}, number = {11-06}, year = {2011}, abstract = {Mobile communication is nowadays taken for granted. Having started primarily as a service for speech communication, data service and mobile Internet access are now driving the evolution of network infrastructure. Operators are facing the challenge to match the demand by continuously expanding and upgrading the network infrastructure. However, the evolution of the customer's demand is uncertain. We introduce a novel (long-term) network planning approach based on multistage stochastic programming, where demand evolution is considered as a stochastic process and the network is extended as to maximize the expected profit. The approach proves capable of designing large-scale realistic UMTS networks with a time-horizon of several years. Our mathematical optimization model, the solution approach, and computational results are presented in this paper.}, language = {en} } @misc{GleixnerHeldHuangetal.2012, author = {Gleixner, Ambros and Held, Harald and Huang, Wei and Vigerske, Stefan}, title = {Towards globally optimal operation of water supply networks}, issn = {1438-0064}, doi = {10.3934/naco.2012.2.695}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-15603}, year = {2012}, abstract = {This paper is concerned with optimal operation of pressurized water supply networks at a fixed point in time. We use a mixed-integer nonlinear programming (MINLP) model incorporating both the nonlinear physical laws and the discrete decisions such as switching pumps on and off. We demonstrate that for instances from our industry partner, these stationary models can be solved to ε-global optimality within small running times using problem-specific presolving and state-of-the-art MINLP algorithms. In our modeling, we emphasize the importance of distinguishing between what we call real and imaginary flow, i.e., taking into account that the law of Darcy-Weisbach correlates pressure difference and flow along a pipe if and only if water is available at the high pressure end of a pipe. Our modeling solution extends to the dynamic operative planning problem.}, language = {en} }