@misc{BurgschweigerGnaedigSteinbach2005, author = {Burgschweiger, Jens and Gn{\"a}dig, Bernd and Steinbach, Marc}, title = {Nonlinear Programming Techniques for Operative Planning in Large Drinking Water Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8657}, number = {05-31}, year = {2005}, abstract = {Mathematical decision support for operative planning in water supply systems is highly desirable but leads to very difficult optimization problems. We propose a nonlinear programming approach that yields practically satisfactory operating schedules in acceptable computing time even for large networks. Based on a carefully designed model supporting gradient-based optimization algorithms, this approach employs a special initialization strategy for convergence acceleration, special minimum up and down time constraints together with pump aggregation to handle switching decisions, and several network reduction techniques for further speed-up. Results for selected application scenarios at Berliner Wasserbetriebe demonstrate the success of the approach.}, language = {en} } @misc{BurgschweigerGnaedigSteinbach2005, author = {Burgschweiger, Jens and Gn{\"a}dig, Bernd and Steinbach, Marc}, title = {Optimierte Tagesplanung im Berliner Trinkwassernetz}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8668}, number = {05-32}, year = {2005}, abstract = {Der Artikel beschreibt ein mathematisches Optimierungssystem zur Betriebsplanung in großen Wassernetzen, das bei den Berliner Wasserbetrieben eingesetzt wird. F{\"u}r das Berliner Versorgungsnetz werden Optimierungsergebnisse vorgestellt.}, language = {de} } @misc{BurgschweigerGnaedigSteinbach2004, author = {Burgschweiger, Jens and Gn{\"a}dig, Bernd and Steinbach, Marc}, title = {Optimization Models for Operative Planning in Drinking Water Networks}, doi = {10.1007/s11081-008-9040-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8237}, number = {04-48}, year = {2004}, abstract = {The topic of this paper is minimum cost operative planning of pressurized water supply networks over a finite horizon and under reliable demand forecast. Since this is a very hard problem, it is desirable to employ sophisticated mathematical algorithms, which in turn calls for carefully designed models with suitable properties. The paper develops a nonlinear mixed integer model and a nonlinear programming model with favorable properties for gradient-based optimization methods, based on smooth component models for the network elements. In combination with further nonlinear programming techniques (to be reported elsewhere), practically satisfactory near-optimum solutions even for large networks can be generated in acceptable time using standard optimization software on a PC workstation. Such an optimization system is in operation at Berliner Wasserbetriebe.}, language = {en} } @misc{KosterZymolka2004, author = {Koster, Arie M.C.A. and Zymolka, Adrian}, title = {Provably Good Solutions for Wavelength Assignment in Optical Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8155}, number = {04-40}, year = {2004}, abstract = {In this paper, we study the minimum converter wavelength assignment problem in optical networks. To benchmark the quality of solutions obtained by heuristics, we derive an integer programming formula tion by generalizing the formulation of Mehrotra and Trick (1996) for the vertex coloring problem. To handle the exponential number of variables, we propose a column generation approach. Computational experiments show that the value of the linear relaxation states a good lower bound and can often prove optimality of the best solution generated heuristically.}, language = {en} } @misc{KosterZymolka2004, author = {Koster, Arie M.C.A. and Zymolka, Adrian}, title = {Linear Programming Lower Bounds for Minimum Converter Wavelength Assignment in Optical Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8160}, number = {04-41}, year = {2004}, abstract = {In this paper, we study the conflict-free assignment of wavelengths to lightpaths in an optical network with the opportunity to place wavelength converters. To benchmark heuristics for the problem, we develop integer programming formulations and study their properties. Moreover, we study the computational performance of the column generation algorithm for solving the linear relaxation of the most promising formulation. In many cases, a non-zero lower bound on the number of required converters is generated this way. For several instances, we in fact prove optimality since the lower bound equals the best known solution value.}, language = {en} } @misc{KochWessaely2004, author = {Koch, Thorsten and Wess{\"a}ly, Roland}, title = {Hierarchical Infrastructure Planning in Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8174}, number = {04-42}, year = {2004}, abstract = {In this article, strategical infrastructure planning problems in the design of large-scale telecommunication networks are discussed based on experiences from three projects with industrial partners: The access network planning of the German Gigabit-Wissenschaftsnetz (G-WiN) for DFN (Verein zur F{\"o}rderung eines Deutschen Forschungsnetzes e.V.), the mobile network switching center location planning project for E-Plus Mobilfunk, and the fixed network switching center location planning project for TELEKOM AUSTRIA. We introduce a mathematical model for a hierarchical multi-commodity capacitated facility location problem, present adaptions of this basic model to the specific requirements within the different projects and discuss the individual peculiarities and model decisions made. Eventually, we present and discuss computational results of three associated case studies, illustrating '"how we did the job`` with mathematical methods.}, language = {en} } @misc{FroylandKochMegowetal.2006, author = {Froyland, Gary and Koch, Thorsten and Megow, Nicole and Duane, Emily and Wren, Howard}, title = {Optimizing the Landside Operation of a Container Terminal}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9004}, number = {06-06}, year = {2006}, abstract = {This paper concerns the problem of operating a landside container exchange area that is serviced by multiple semi-automated rail mounted gantry cranes (RMGs) that are moving on a single bi-directional traveling lane. Such a facility is being built by Patrick Corporation at the Port Botany terminal in Sydney. The gantry cranes are a scarce resource and handle the bulk of container movements. Thus, they require a sophisticated analysis to achieve near optimal utilization. We present a three stage algorithm to manage the container exchange facility, including the scheduling of cranes, the control of associated short-term container stacking, and the allocation of delivery locations for trucks and other container transporters. The key components of our approach are a time scale decomposition, whereby an integer program controls decisions across a long time horizon to produce a balanced plan that is fed to a series of short time scale online subproblems, and a highly efficient space-time divisioning of short term storage areas. A computational evaluation shows that our heuristic can find effective solutions for the planning problem; on real-world data it yields a solution at most~8\\% above a lower bound on optimal RMG utilization.}, language = {en} } @misc{GroetschelHinrichsSchroeeretal.2006, author = {Gr{\"o}tschel, Martin and Hinrichs, Hinrich and Schr{\"o}er, Klaus and Tuchscherer, Andreas}, title = {Ein gemischt-ganzzahliges lineares Optimierungsmodell f{\"u}r ein Laserschweißproblem im Karosseriebau}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9141}, number = {06-21}, year = {2006}, abstract = {Wir besch{\"a}ftigen uns mit dem Problem der Betriebsplanung von Laserschweißrobotern im Karosseriebau. Gegeben ist eine Menge von Schweißn{\"a}hten, die innerhalb einer Fertigungszelle an einem Karosserieteil gefertigt werden m{\"u}ssen. Die Schweißn{\"a}hte werden durch mehrere parallel betriebene Roboter bearbeitet. Die Aufgabe besteht darin, f{\"u}r jeden Roboter eine Reihenfolge und eine zeitliche Koordinierung seiner Bewegungen zu finden, so dass alle Schweißn{\"a}hte innerhalb der Taktzeit der Fertigungszelle bearbeitet werden und so wenig Laserquellen wie m{\"o}glich eingesetzt werden. Dabei m{\"u}ssen einige Nebenbedingungen ber{\"u}cksichtigt werden. F{\"u}r dieses spezielle Schweißproblem haben wir eine Formulierung als gemischt-ganzzahliges lineares Programm entwickelt, welches sich f{\"u}r die untersuchten praktischen F{\"a}lle sehr schnell l{\"o}sen l{\"a}sst.}, language = {de} } @misc{AscheuerGroetschelKrumkeetal.1998, author = {Ascheuer, Norbert and Gr{\"o}tschel, Martin and Krumke, Sven and Rambau, J{\"o}rg}, title = {Combinatorial Online Optimization}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3674}, number = {SC-98-24}, year = {1998}, abstract = {In ``classical'' optimization, all data of a problem instance are considered given. The standard theory and the usual algorithmic techniques apply to such cases only. Online optimization is different. Many decisions have to be made before all data are available. In addition, decisions once made cannot be changed. How should one act ``best'' in such an environment? In this paper we survey online problems coming up in combinatorial optimization. We first outline theoretical concepts, such as competitiveness against various adversaries, to analyze online problems and algorithms. The focus, however, lies on real-world applications. We report, in particular, on theoretical investigations and our practical experience with problems arising in transportation and the automatic handling of material.}, language = {en} } @misc{BleyGroetschelWessaely1998, author = {Bley, Andreas and Gr{\"o}tschel, Martin and Wess{\"a}ly, Roland}, title = {Design of Broadband Virtual Private Networks: Model and Heuristics for the B-WiN}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3565}, number = {SC-98-13}, year = {1998}, abstract = {We investigate the problem of designing survivable broadband virtual private networks that employ the Open Shortest Path First (OSPF) routing protocol to route the packages. The capacities available for the links of the network are a minimal capacity plus multiples of a unit capacity. Given the directed communication demands between all pairs of nodes, we wish to select the capacities in a such way, that even in case of a single node or a single link failure a specified percentage of each demand can be satisfied and the costs for these capacities are minimal. We present a mixed--integer linear programming formulation of this problem and several heuristics for its solution. Furthermore, we report on computational results with real-world data.}, language = {en} } @misc{HoangKoch2012, author = {Hoang, Nam-Dung and Koch, Thorsten}, title = {Steiner Tree Packing Revisited}, issn = {1438-0064}, doi = {10.1007/s00186-012-0391-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14625}, number = {12-02}, year = {2012}, abstract = {The Steiner tree packing problem (STPP) in graphs is a long studied problem in combinatorial optimization. In contrast to many other problems, where there have been tremendous advances in practical problem solving, STPP remains very difficult. Most heuristics schemes are ineffective and even finding feasible solutions is already NP-hard. What makes this problem special is that in order to reach the overall optimal solution non-optimal solutions to the underlying NP-hard Steiner tree problems must be used. Any non-global approach to the STPP is likely to fail. Integer programming is currently the best approach for computing optimal solutions. In this paper we review some "classical" STPP instances which model the underlying real world application only in a reduced form. Through improved modelling, including some new cutting planes, and by emplyoing recent advances in solver technology we are for the first time able to solve those instances in the original 3D grid graphs to optimimality.}, language = {en} } @misc{Gleixner2009, type = {Master Thesis}, author = {Gleixner, Ambros}, title = {Solving Large-scale Open Pit Mining Production Scheduling Problems by Integer Programming}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11389}, school = {Zuse Institute Berlin (ZIB)}, year = {2009}, abstract = {Since the initial application of mathematical optimisation methods to mine planning in 1965, the Lerchs-Grossmann algorithm for computing the ultimate pit limit, operations researchers have worked on a variety of challenging problems in the area of open pit mining. This thesis focuses on the open pit mining production scheduling problem: Given the discretisation of an orebody as a block model, determine the sequence in which the blocks should be removed from the pit, over the lifespan of the mine, such that the net present value of the mining operation is maximised. In practise, when some material has been removed from the pit, it must be processed further in order to extract the valuable elements contained therein. If the concentration of valuable elements is not sufficiently high, the material is discarded as waste or stockpiled. Realistically-sized block models can contain hundreds of thousands of blocks. A common approach to render these problem instances computationally tractable is the aggregation of blocks to larger scheduling units. The thrust of this thesis is the investigation of a new mixed-integer programming formulation for the open pit mining production scheduling problem, which allows for processing decisions to be made at block level, while the actual mining schedule is still computed at aggregate level. A drawback of this model in its full form is the large number of additional variables needed to model the processing decisions. One main result of this thesis shows how these processing variables can be aggregated efficiently to reduce the problem size significantly, while practically incurring no loss in net present value. The second focus is on the application of lagrangean relaxation to the resource constraints. Using a result of M{\"o}hring et al. (2003) for project scheduling, the lagrangean relaxation can be solved efficiently via minimum cut computations in a weighted digraph. Experiments with a bundle algorithm implementation by Helmberg showed how the lagrangean dual can be solved within a small fraction of the time required by standard linear programming algorithms, while yielding practically the same dual bound. Finally, several problem-specific heuristics are presented together with computational results: two greedy sub-MIP start heuristics and a large neighbourhood search heuristic. A combination of a lagrangean-based start heuristic followed by a large neighbourhood search proved to be effective in generating solutions with objective values within a 0.05\% gap of the optimum.}, language = {en} } @misc{BleyGleixnerKochetal.2009, author = {Bley, Andreas and Gleixner, Ambros and Koch, Thorsten and Vigerske, Stefan}, title = {Comparing MIQCP solvers to a specialised algorithm for mine production scheduling}, organization = {ZIB}, issn = {1438-0064}, doi = {10.1007/978-3-642-25707-0}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11507}, number = {09-32}, year = {2009}, abstract = {In this paper we investigate the performance of several out-of-the box solvers for mixed-integer quadratically constrained programmes (MIQCPs) on an open pit mine production scheduling problem with mixing constraints. We compare the solvers BARON, Couenne, SBB, and SCIP to a problem-specific algorithm on two different MIQCP formulations. The computational results presented show that general-purpose solvers with no particular knowledge of problem structure are able to nearly match the performance of a hand-crafted algorithm.}, language = {en} } @misc{VuLitzelKoch2025, author = {Vu, Thi Huong and Litzel, Ida and Koch, Thorsten}, title = {Similarity-based fuzzy clustering scientific articles: potentials and challenges from mathematical and computational perspectives}, arxiv = {http://arxiv.org/abs/2506.04045}, year = {2025}, abstract = {Fuzzy clustering, which allows an article to belong to multiple clusters with soft membership degrees, plays a vital role in analyzing publication data. This problem can be formulated as a constrained optimization model, where the goal is to minimize the discrepancy between the similarity observed from data and the similarity derived from a predicted distribution. While this approach benefits from leveraging state-of-the-art optimization algorithms, tailoring them to work with real, massive databases like OpenAlex or Web of Science -- containing about 70 million articles and a billion citations -- poses significant challenges. We analyze potentials and challenges of the approach from both mathematical and computational perspectives. Among other things, second-order optimality conditions are established, providing new theoretical insights, and practical solution methods are proposed by exploiting the problem's structure. Specifically, we accelerate the gradient projection method using GPU-based parallel computing to efficiently handle large-scale data.}, language = {en} } @misc{Bley2003, author = {Bley, Andreas}, title = {A Lagrangian Approach for Integrated Network Design and Routing in IP Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7515}, number = {03-29}, year = {2003}, abstract = {We consider the problem of designing a network that employs a non-bifurcated shortest path routing protocol. The network's nodes and the set of potential links are given together with a set of forecasted end-to-end traffic demands. All relevant hardware components installable at links or nodes are considered. The goal is to simultaneously choose the network's topology, to decide which hardware components to install on which links and nodes, and to find appropriate routing weights such that the overall network cost is minimized. In this paper, we present a mathematical optimization model for this problem and an algorithmic solution approach based on a Lagrangian relaxation. Computational results achieved with this approach for several real-world network planning problems are reported.}, language = {en} } @misc{EisenblaetterKosterWallbaumetal.2002, author = {Eisenbl{\"a}tter, Andreas and Koster, Arie M.C.A. and Wallbaum, Randolf and Wess{\"a}ly, Roland}, title = {Load Balancing in Signaling Transfer Points}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7179}, number = {02-50}, year = {2002}, abstract = {Signaling is crucial to the operation of modern telecommunication networks. A breakdown in the signaling infrastructure typically causes customer service failures, incurs revenue losses, and hampers the company image. Therefore, the signaling network has to be highest reliability and survivability. This in particular holds for the routers in such a network, called \textit{signaling transfer points\/} (STPs). The robustness of an STP can be improved by equally distributing the load over the internal processing units. Several constraints have to be taken into account. The load of the links connected to a processing unit changes over time introducing an imbalance of the load. In this paper, we show how integer linear programming can be applied to reduce the imbalance within an STP, while keeping the number of changes small. Two alternative models are presented. Computational experiments validate the integer programming approach in practice. The GSM network operator E-Plus saves substantial amounts of time and money by employing the proposed approach.}, language = {en} } @misc{ZymolkaKosterWessaely2002, author = {Zymolka, Adrian and Koster, Arie M.C.A. and Wess{\"a}ly, Roland}, title = {Transparent optical network design with sparse wavelength conversion}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7017}, number = {02-34}, year = {2002}, abstract = {We consider the design of transparent optical networks from a practical perspective. Network operators aim at satisfying the communication demands at minimum cost. Such an optimization involves three interdependent planning issues: the dimensioning of the physical topology, the routing of lightpaths, and the wavelength assignment. Further topics include the reliability of the configuration and sparse wavelength conversion for efficient use of the capacities. In this paper, we investigate this extensive optical network design task. Using a flexible device-based model, we present an integer programming formulation that supports greenfield planning as well as expansion planning on top of an existing network. As solution method, we propose a suitable decomposition approach that separates the wavelength assignment from the dimensioning and routing. Our method in particular provides a lower bound on the total cost which allows to rate the solution quality. Computational experiments on realistic networks approve the solution approach to be appropriate.}, language = {en} } @misc{BleyKoch2002, author = {Bley, Andreas and Koch, Thorsten}, title = {Integer programming approaches to access and backbone IP-network planning}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7081}, number = {02-41}, year = {2002}, abstract = {In this article we study the problem of designing a nation-wide communication network. Such networks usually consist of an access layer, a backbone layer, and maybe several intermediate layers. The nodes of each layer must be connected to those of the next layer in a tree-like fashion. The backbone layer has to satisfy certain survivability and routing constraints. Given the node locations, the demands between them, the possible connections and hardware configurations, and various other technical and administrational constraints, the goal is to decide, which node is assigned to which network level, how the nodes are connected, what hardware must be installed, and how traffic is routed in the backbone. Mixed integer linear programming models and solution methods are presented for both the access and the backbone network design problem. The focus is on the design of IP-over-SDH networks, but the access network design model and large parts of the backbone network design models are general and also applicable for other types of communication networks. Results obtained with these methods in the planning of the German research network are presented.}, language = {en} } @phdthesis{Koch2005, author = {Koch, Thorsten}, title = {Rapid Mathematical Programming}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8346}, number = {04-58}, year = {2005}, abstract = {The thesis deals with the implementation and application of out-of-the-box tools in linear and mixed integer programming. It documents the lessons learned and conclusions drawn from five years of implementing, maintaining, extending, and using several computer codes to solve real-life industrial problems. By means of several examples it is demonstrated how to apply algebraic modeling languages to rapidly devise mathematical models of real-world problems. It is shown that today's MIP solvers are capable of solving the resulting mixed integer programs, leading to an approach that delivers results very quickly. Even though, problems are tackled that not long ago required the implementation of specialized branch-and-cut algorithms. In the first part of the thesis the modeling language Zimpl is introduced. Chapter 2 contains a complete description of the language. In the subsequent chapter details of the implementation are described. Both theoretical and practical considerations are discussed. Aspects of software engineering, error prevention, and detection are addressed. In the second part several real-world projects are examined that employed the methodology and the tools developed in the first part. Chapter 4 presents three projects from the telecommunication industry dealing with facility location problems. Chapter 5 characterizes questions that arise in UMTS planning. Problems, models, and solutions are discussed. Special emphasis is put on the dependency of the precision of the input data and the results. Possible reasons for unexpected and undesirable solutions are explained. Finally, the Steiner tree packing problem in graphs, a well-known hard combinatorial problem, is revisited. A formerly known, but not yet used model is applied to combine switchbox wire routing and via minimization. All instances known from the literature are solved by this approach, as are some newly generated bigger problem instances.}, language = {en} } @misc{HelmbergRoehl2005, author = {Helmberg, Christoph and R{\"o}hl, Stefan}, title = {A Case Study of Joint Online Truck Scheduling and Inventory Management for Multiple Warehouses}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8454}, number = {05-11}, year = {2005}, abstract = {For a real world problem --- transporting pallets between warehouses in order to guarantee sufficient supply for known and additional stochastic demand --- we propose a solution approach via convex relaxation of an integer programming formulation, suitable for online optimization. The essential new element linking routing and inventory management is a convex piecewise linear cost function that is based on minimizing the expected number of pallets that still need transportation. For speed, the convex relaxation is solved approximately by a bundle approach yielding an online schedule in 5 to 12 minutes for up to 3 warehouses and 40000 articles; in contrast, computation times of state of the art LP-solvers are prohibitive for online application. In extensive numerical experiments on a real world data stream, the approximate solutions exhibit negligible loss in quality; in long term simulations the proposed method reduces the average number of pallets needing transportation due to short term demand to less than half the number observed in the data stream.}, language = {en} } @misc{Koster2005, author = {Koster, Arie M.C.A.}, title = {Wavelength Assignment in Multi-Fiber WDM Networks by Generalized Edge Coloring}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8478}, number = {05-13}, year = {2005}, abstract = {In this paper, we study wavelength assignment problems in multi-fiber WDM networks. We focus on the special case that all lightpaths have at most two links. This in particular holds in case the network topology is a star. As the links incident to a specific node in a meshed topology form a star subnetwork, results for stars are also of interest for general meshed topologies. We show that wavelength assignment with at most two links per lightpath can be modeled as a generalized edge coloring problem. By this relation, we show that for a network with an even number of fibers at all links and at most two links per lightpath, all lightpaths can be assigned a wavelength without conversion. Moreover, we derive a lower bound on the number of lightpaths to be converted for networks with arbitrary numbers of fibers at the links. A comparison with linear programming lower bounds reveals that the bounds coincide for problems with at most two links per lightpath. For meshed topologies, the cumulative lower bound over all star subnetworks equals the best known solution value for all realistic wavelength assignment instances available, by this proving optimality.}, language = {en} } @misc{BienstockBley2000, author = {Bienstock, Daniel and Bley, Andreas}, title = {Capacitated Network Design with Multicast Commodities}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5823}, number = {00-14}, year = {2000}, abstract = {This paper addresses the problem of designing a minimum cost network whose capacities are sufficiently large to allow a feasible routing of a given set of multicast commodities. A multicast commodity consists of a set of two or mo re terminals that need to be connected by a so called broadcast tree, which consumes on all of its edges a capacity as large as the demand value associated with that commodity. We model the network design problem with multicast commodities as the problem of packing capacitated Steiner trees in a graph. In the first part of the paper we present three mixed-integer programming formulations for this problem. The first natural formulation uses only one integer capacity variable for each edge and and one binary tree variable for each commodity-edge pair. Applying well-known techniques from the Steiner tree problem, we then develop a stronger directed and a multicommodity flow based mixed-integer programming formulation. In the second part of the paper we study the associated polyhedra and derive valid and even facet defining inequalities for the natural formulation. Finally, we describe separation algorithms for these inequalities and present computational results that demonstrate the strength of our extended formulations.}, language = {en} } @misc{Koster2000, author = {Koster, Arie M.C.A.}, title = {Re-Optimization of Signaling Transfer Points}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5863}, number = {00-18}, year = {2000}, abstract = {In this paper we describe the results of a computational study towards the (re)optimization of signaling transfer points (STPs) in telecommunication networks. The best performance of an STP is achieved whenever the traffic load is evenly distributed among the internal components. Due to the continuously changing traffic pattern, the load of the components has to be re-optimized on a regular basis. Besides the balancing objective also the number of rearrangements have to be taken into account. In this paper we present two alternative formulations to deal with both requirements. Computational results show that for both formulations (near) optimal solutions can be obtained within reasonable time limits.}, language = {en} } @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} } @misc{Bley2008, author = {Bley, Andreas}, title = {An Integer Programming Algorithm for Routing Optimization in IP Networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10814}, number = {08-30}, year = {2008}, abstract = {Most data networks nowadays use shortest path protocols to route the traffic. Given administrative routing lengths for the links of the network, all data packets are sent along shortest paths with respect to these lengths from their source to their destination. In this paper, we present an integer programming algorithm for the minimum congestion unsplittable shortest path routing problem, which arises in the operational planning of such networks. Given a capacitated directed graph and a set of communication demands, the goal is to find routing lengths that define a unique shortest path for each demand and minimize the maximum congestion over all links in the resulting routing. We illustrate the general decomposition approach our algorithm is based on, present the integer and linear programming models used to solve the master and the client problem, and discuss the most important implementational aspects. Finally, we report computational results for various benchmark problems, which demonstrate the efficiency of our algorithm.}, language = {en} } @phdthesis{Bley2007, author = {Bley, Andreas}, title = {Routing and Capacity Optimization for IP Networks}, isbn = {978-3-86727-281-0}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:83-opus-15530}, year = {2007}, abstract = {This thesis is concerned with dimensioning and routing optimization problems for communication networks that employ a shortest path routing protocol such as OSPF, IS-IS, or RIP. These protocols are widely used in the Internet. With these routing protocols, all end-to-end data streams are routed along shortest paths with respect to a metric of link lengths. The network administrator can configure the routing only by modifying this metric. In this thesis we consider the unsplittable shortest path routing variant, where each communication demand must be sent unsplit through the network. This requires that all shortest paths are uniquely determined. The major difficulties in planning such networks are that the routing can be controlled only indirectly via the routing metric and that all routing paths depend on the same routing metric. This leads to rather complicated and subtle interdependencies among the paths that comprise a valid routing. In contrast to most other routing schemes, the paths for different communication demands cannot be configured independent of each other. Part I of the thesis is dedicated to the relation between path sets and routing metrics and to the combinatorial properties of those path sets that comprise a valid unsplittable shortest path routing. Besides reviewing known approaches to find a compatible metric for a given path set (or to prove that none exists) and discussing some properties of valid path sets, we show that the problem of finding a compatible metric with integer lengths as small as possible and the problem of finding a smallest possible conflict in the given path set are both NP-hard to approximate within a constant factor. In Part II of the thesis we discuss the relation between unsplittable shortest path routing and several other routing schemes and we analyze the computational complexity of three basic unsplittable shortest path routing problems. We show that the lowest congestion that can be obtained with unsplittable shortest path routing may significantly exceed that achievable with other routing paradigms and we prove several non-approximability results for unsplittable shortest path routing problems that are stronger than those for the corresponding unsplittable flow problems. In addition, we derive various polynomial time approximation algorithms for general and special cases of these problems. In Part III of the thesis we finally develop an integer linear programming approach to solve these and more realistic unsplittable shortest path routing problems to optimality. We present alternative formulations for these problems, discuss their strength and computational complexity, and show how to derive strong valid inequalities. Eventually, we describe our implementation of this solution approach and report on the numerical results obtained for real-world problems that came up in the planning the German National Research and Education Networks G-WiN and X-WiN and for several benchmark instances.}, language = {en} } @phdthesis{Weider2007, author = {Weider, Steffen}, title = {Integration of Vehicle and Duty Scheduling in Public Transport}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:83-opus-16240}, year = {2007}, abstract = {This thesis describes the algorithm IS-OPT that integrates scheduling of vehicles and duties in public bus transit. IS-OPT is the first algorithm which solves integrated vehicle and duty scheduling problems arising in medium sized carriers such that its solutions can be used in daily operations without further adaptions. This thesis is structured as follows: The first chapter highlights mathematical models of the planning process of public transit companies and examines their potential for integrating them with other planning steps. It also introduces descriptions of the vehicle and the duty scheduling problem. Chapter 2 motivates why it can be useful to integrate vehicle and duty scheduling, explains approaches of the literature, and gives an outline of our algorithm IS-OPT. The following chapters go into the details of the most important techniques and methods of IS-OPT: In Chapter 3 we describe how we use Lagrangean relaxation in a column generation framework. Next, in Chapter 4, we describe a variant of the proximal bundle method (PBM) that is used to approximate linear programs occurring in the solution process. We introduce here a new variant of the PBM which is able to utilize inexact function evaluation and the use of epsilon-subgradients. We also show the convergence of this method under certain assumptions. Chapter 5 treats the generation of duties for the duty scheduling problem. This problem is modeled as a resourceconstraint- shortest-path-problem with non-linear side constraints and nearly linear objective function. It is solved in a two-stage approach. At first we calculate lower bounds on the reduced costs of duties using certain nodes by a new inexact label-setting algorithm. Then we use these bounds to speed up a depth-first-search algorithm that finds feasible duties. In Chapter 6 we present the primal heuristic of IS-OPT that solves the integrated problem to integrality. We introduce a new branch-and-bound based heuristic which we call rapid branching. Rapid branching uses the proximal bundle method to compute lower bounds, it introduces a heuristic node selection scheme, and it utilizes a new branching rule that fixes sets of many variables at once. The common approach to solve the problems occurring in IS-OPT is to trade inexactness of the solutions for speed of the algorithms. This enables, as we show in Chapter 7, to solve large real world integrated problems by IS-OPT. The scheduled produced by IS-OPT save up to 5\% of the vehicle and duty cost of existing schedules of regional and urban public transport companies.}, language = {en} } @misc{Bley2007, author = {Bley, Andreas}, title = {Routing and Capacity Optimization for IP networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10323}, number = {07-33}, year = {2007}, abstract = {This article describes the main concepts and techniques that have been developed during the last year at ZIB to solve dimensioning and routing optimization problems for IP networks. We discuss the problem of deciding if a given path set corresponds to an unsplittable shortest path routing, the fundamental properties of such path sets, and the computational complexity of some basic network planning problems for this routing type. Then we describe an integer-linear programming approach to solve such problems in practice. This approach has been used successfully in the planning of the German national education and research network for several years.}, language = {en} } @misc{HillerKochScheweetal.2018, author = {Hiller, Benjamin and Koch, Thorsten and Schewe, Lars and Schwarz, Robert and Schweiger, Jonas}, title = {A System to Evaluate Gas Network Capacities: Concepts and Implementation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-67438}, year = {2018}, abstract = {In 2005 the European Union liberalized the gas market with a disruptive change and decoupled trading of natural gas from its transport. The gas is now transported by independent so-called transmissions system operators or TSOs. The market model established by the European Union views the gas transmission network as a black box, providing shippers (gas traders and consumers) the opportunity to transport gas from any entry to any exit. TSOs are required to offer the maximum possible capacities at each entry and exit such that any resulting gas flow can be realized by the network. The revenue from selling these capacities more than one billion Euro in Germany alone, but overestimating the capacity might compromise the security of supply. Therefore, evaluating the available transport capacities is extremely important to the TSOs. This is a report on a large project in mathematical optimization, set out to develop a new toolset for evaluating gas network capacities. The goals and the challenges as they occurred in the project are described, as well as the developments and design decisions taken to meet the requirements.}, language = {en} } @phdthesis{Zymolka2007, author = {Zymolka, Adrian}, title = {Design of Survivable Optical Networks by Mathematical Optimization}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10408}, year = {2007}, abstract = {Abstract The cost-efficient design of survivable optical telecommunication networks is the topic of this thesis. In cooperation with network operators, we have developed suitable concepts and mathematical optimization methods to solve this comprehensive planning task in practice. Optical technology is more and more employed in modern telecommunication networks. Digital information is thereby transmitted as short light pulses through glass fibers. Moreover, the optical medium allows for simultaneous transmissions on a single fiber by use of different wavelengths. Recent optical switches enable a direct forwarding of optical channels in the network nodes without the previously required signal retransformation to electronics. Their integration creates ongoing optical connections,which are called lightpaths. We study the problem of finding cost-efficient configurations of optical networks which meet specified communication requirements. A configuration comprises the determination of all lightpaths to establish as well as the detailed allocation of all required devices and systems. We use a flexible modeling framework for a realistic representation of the networks and their composition. For different network architectures, we formulate integer linear programs which model the design task in detail. Moreover, network survivability is an important issue due to the immense bandwidths offered by optical technology. Operators therefore request for designs which perpetuate protected connections and guarantee for a defined minimum throughput in case of malfunctions. In order to achieve an effective realization of scalable protection, we present a novel survivability concept tailored to optical networks and integrate several variants into the models. Our solution approach is based on a suitable model decomposition into two subtasks which separates two individually hard subproblems and enables this way to compute cost-efficient designs with approved quality guarantee. The first subtask consists of routing the connections with corresponding dimensioning of capacities and constitutes a common core task in the area of network planning. Sophisticated methods for such problems have already been developed and are deployed by appropriate integration. The second subtask is characteristic for optical networks and seeks for a conflict-free assignment of available wavelengths to the lightpaths using a minimum number of involved wavelength converters. For this coloring-like task, we derive particular models and study methods to estimate the number of unavoidable conversions. As constructive approach, we develop heuristics and an exact branch-and-price algorithm. Finally, we carry out an extensive computational study on realistic data, provided by our industrial partners. As twofold purpose, we demonstrate the potential of our approach for computing good solutions with quality guarantee, and we exemplify its flexibility for application to network design and analysis.}, language = {en} } @misc{KochAchterbergAndersenetal.2010, author = {Koch, Thorsten and Achterberg, Tobias and Andersen, Erling and Bastert, Oliver and Berthold, Timo and Bixby, Robert E. and Danna, Emilie and Gamrath, Gerald and Gleixner, Ambros and Heinz, Stefan and Lodi, Andrea and Mittelmann, Hans and Ralphs, Ted and Salvagnin, Domenico and Steffy, Daniel and Wolter, Kati}, title = {MIPLIB 2010}, doi = {10.1007/s12532-011-0025-9}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12953}, number = {10-31}, year = {2010}, abstract = {This paper reports on the fifth version of the Mixed Integer Programming Library. The MIPLIB 2010 is the first MIPLIB release that has been assembled by a large group from academia and from industry, all of whom work in integer programming. There was mutual consent that the concept of the library had to be expanded in order to fulfill the needs of the community. The new version comprises 361 instances sorted into several groups. This includes the main benchmark test set of 87 instances, which are all solvable by today's codes, and also the challenge test set with 164 instances, many of which are currently unsolved. For the first time, we include scripts to run automated tests in a predefined way. Further, there is a solution checker to test the accuracy of provided solutions using exact arithmetic.}, language = {en} } @misc{FuegenschuhGeisslerGollmeretal.2013, author = {F{\"u}genschuh, Armin and Geißler, Bj{\"o}rn and Gollmer, Ralf and Hayn, Christine and Henrion, Rene and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Martin, Alexander and Mirkov, Radoslava and Morsi, Antonio and R{\"o}misch, Werner and R{\"o}vekamp, Jessica and Schewe, Lars and Schmidt, Martin and Schultz, R{\"u}diger and Schwarz, Robert and Schweiger, Jonas and Stangl, Claudia and Steinbach, Marc and Willert, Bernhard}, title = {Mathematical Optimization for Challenging Network Planning Problems in Unbundled Liberalized Gas Markets}, issn = {1438-0064}, doi = {10.1007/s12667-013-0099-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17821}, year = {2013}, abstract = {The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators. While previously network operator and gas vendor where united, they were forced to split up into independent companies. The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way. We show that these new paradigms lead to new and challenging mathematical optimization problems. In order to solve them and to provide meaningful results for practice, all aspects of the underlying problems, such as combinatorics, stochasticity, uncertainty, and nonlinearity, have to be addressed. With such special-tailored solvers, free network capacities and topological network extensions can, for instance, be determined.}, language = {en} } @misc{PfetschFuegenschuhGeissleretal.2012, author = {Pfetsch, Marc and F{\"u}genschuh, Armin and Geißler, Bj{\"o}rn and Geißler, Nina and Gollmer, Ralf and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Martin, Alexander and Morsi, Antonio and R{\"o}vekamp, Jessica and Schewe, Lars and Schmidt, Martin and Schultz, R{\"u}diger and Schwarz, Robert and Schweiger, Jonas and Stangl, Claudia and Steinbach, Marc and Vigerske, Stefan and Willert, Bernhard}, title = {Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions}, issn = {1438-0064}, doi = {10.1080/10556788.2014.888426}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-16531}, year = {2012}, abstract = {In this article we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: Given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints. We describe a two-stage approach to solve the resulting complex and numerically difficult mixed-integer non-convex nonlinear feasibility problem. The first phase consists of four distinct algorithms facilitating mixed-integer linear, mixed-integer nonlinear, reduced nonlinear, and complementarity constrained methods to compute possible settings for the discrete decisions. The second phase employs a precise continuous nonlinear programming model of the gas network. Using this setup, we are able to compute high quality solutions to real-world industrial instances whose size is significantly larger than networks that have appeared in the literature previously.}, language = {en} } @phdthesis{Schweiger2017, author = {Schweiger, Jonas}, title = {Exploiting structure in non-convex quadratic optimization and gas network planning under uncertainty}, pages = {411}, year = {2017}, abstract = {The amazing success of computational mathematical optimization over the last decades has been driven more by insights into mathematical structures than by the advance of computing technology. In this vein, we address applications, where nonconvexity in the model and uncertainty in the data pose principal difficulties. The first part of the thesis deals with non-convex quadratic programs. Branch\&Bound methods for this problem class depend on tight relaxations. We contribute in several ways: First, we establish a new way to handle missing linearization variables in the well-known Reformulation-Linearization-Technique (RLT). This is implemented into the commercial software CPLEX. Second, we study the optimization of a quadratic objective over the standard simplex or a knapsack constraint. These basic structures appear as part of many complex models. Exploiting connections to the maximum clique problem and RLT, we derive new valid inequalities. Using exact and heuristic separation methods, we demonstrate the impact of the new inequalities on the relaxation and the global optimization of these problems. Third, we strengthen the state-of-the-art relaxation for the pooling problem, a well-known non-convex quadratic problem, which is, for example, relevant in the petrochemical industry. We propose a novel relaxation that captures the essential non-convex structure of the problem but is small enough for an in-depth study. We provide a complete inner description in terms of the extreme points as well as an outer description in terms of inequalities defining its convex hull (which is not a polyhedron). We show that the resulting valid convex inequalities significantly strengthen the standard relaxation of the pooling problem. The second part of this thesis focuses on a common challenge in real world applications, namely, the uncertainty entailed in the input data. We study the extension of a gas transport network, e.g., from our project partner Open Grid Europe GmbH. For a single scenario this maps to a challenging non-convex MINLP. As the future transport patterns are highly uncertain, we propose a robust model to best prepare the network operator for an array of scenarios. We develop a custom decomposition approach that makes use of the hierarchical structure of network extensions and the loose coupling between the scenarios. The algorithm used the single-scenario problem as black-box subproblem allowing the generalization of our approach to problems with the same structure. The scenario-expanded version of this problem is out of reach for today's general-purpose MINLP solvers. Yet our approach provides primal and dual bounds for instances with up to 256 scenarios and solves many of them to optimality. Extensive computational studies show the impact of our work.}, language = {en} } @misc{HeinzStephanSchlechte2009, author = {Heinz, Stefan and Stephan, R{\"u}diger and Schlechte, Thomas}, title = {Solving Steel Mill Slab Problems with Branch and Price}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11260}, number = {09-14}, year = {2009}, abstract = {The steel mill slab design problem from the CSPLib is a binpacking problem that is motivated by an application of the steel industry and that has been widely studied in the constraint programming community. Recently, several people proposed new models and methods to solve this problem. A steel mill slab library was created which contains 380 instances. A closely related binpacking problem called multiple knapsack problem with color constraints, originated from the same industrial problem, were discussed in the integer programming community. In particular, a simple integer programming for this problem has been given by Forrest et al. [3]. The aim of this paper is to bring these different studies together. Moreover, we adopt the model of [3] for the steel mill slab problem. Using a state of the art integer program solver, this model is capable to solve all instances of the steel mill slab library, mostly in less than one second, to optimality. We improved, thereby, the solution value of 76 instances.}, language = {en} } @misc{HillerKlugTuchscherer2009, author = {Hiller, Benjamin and Klug, Torsten and Tuchscherer, Andreas}, title = {Improving the performance of elevator systems using exact reoptimization algorithms}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11155}, number = {09-05}, year = {2009}, abstract = {This extended abstract is about algorithms for controlling elevator systems employing destination hall calls, i.e. the passenger provides his destination floor when calling an elevator. We present the first exact algorithm for controlling a group of elevators and report on simulation results indicating that destination hall call systems outperform conventional systems.}, language = {en} } @misc{Tuchscherer2003, type = {Master Thesis}, author = {Tuchscherer, Andreas}, title = {Dynamical Configuration of Transparent Optical Telecommunication Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10214}, school = {Zuse Institute Berlin (ZIB)}, year = {2003}, abstract = {All-optical telecommunication networks allow for switching connections by lightpaths which can pass several network links without any opto-electronic conversion. Upon arrival of a connection request, it must be decided online, i.e., without knowledge of future requests, if it is accepted and in that case on which lightpaths the connection is routed. This online problem with the goal of maximizing the total profit gained by accepted requests is called Dynamic Singleclass Call Admission Problem (DSCA). We present existing and new algorithms for the DSCA as well as their theoretical and practical evaluation.}, language = {en} } @misc{BestuzhevaBesanconChenetal.2021, author = {Bestuzheva, Ksenia and Besan{\c{c}}on, Mathieu and Chen, Wei-Kun and Chmiela, Antonia and Donkiewicz, Tim and van Doornmalen, Jasper and Eifler, Leon and Gaul, Oliver and Gamrath, Gerald and Gleixner, Ambros and Gottwald, Leona and Graczyk, Christoph and Halbig, Katrin and Hoen, Alexander and Hojny, Christopher and van der Hulst, Rolf and Koch, Thorsten and L{\"u}bbecke, Marco and Maher, Stephen J. and Matter, Frederic and M{\"u}hmer, Erik and M{\"u}ller, Benjamin and Pfetsch, Marc E. and Rehfeldt, Daniel and Schlein, Steffan and Schl{\"o}sser, Franziska and Serrano, Felipe and Shinano, Yuji and Sofranac, Boro and Turner, Mark and Vigerske, Stefan and Wegscheider, Fabian and Wellner, Philipp and Weninger, Dieter and Witzig, Jakob}, title = {The SCIP Optimization Suite 8.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-85309}, year = {2021}, abstract = {The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type for cut selection, and a complete rework of the way nonlinear constraints are handled. Additionally, SCIP 8.0 now supports interfaces for Julia as well as Matlab. Further, UG now includes a unified framework to parallelize all solvers, a utility to analyze computational experiments has been added to GCG, dual solutions can be postsolved by PaPILO, new heuristics and presolving methods were added to SCIP-SDP, and additional problem classes and major performance improvements are available in SCIP-Jack.}, language = {en} } @misc{BolusaniBesanconBestuzhevaetal.2024, author = {Bolusani, Suresh and Besan{\c{c}}on, Mathieu and Bestuzheva, Ksenia and Chmiela, Antonia and Dion{\´i}sio, Jo{\~a}o and Donkiewicz, Tim and van Doornmalen, Jasper and Eifler, Leon and Ghannam, Mohammed and Gleixner, Ambros and Graczyk, Christoph and Halbig, Katrin and Hedtke, Ivo and Hoen, Alexander and Hojny, Christopher and van der Hulst, Rolf and Kamp, Dominik and Koch, Thorsten and Kofler, Kevin and Lentz, Jurgen and Manns, Julian and Mexi, Gioni and M{\"u}hmer, Erik and E. Pfetsch, Marc and Schl{\"o}sser, Franziska and Serrano, Felipe and Shinano, Yuji and Turner, Mark and Vigerske, Stefan and Weninger, Dieter and Xu, Liding}, title = {The SCIP Optimization Suite 9.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-95528}, year = {2024}, abstract = {The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming framework SCIP. This report discusses the enhancements and extensions included in the SCIP Optimization Suite 9.0. The updates in SCIP 9.0 include improved symmetry handling, additions and improvements of nonlinear handlers and primal heuristics, a new cut generator and two new cut selection schemes, a new branching rule, a new LP interface, and several bug fixes. The SCIP Optimization Suite 9.0 also features new Rust and C++ interfaces for SCIP, new Python interface for SoPlex, along with enhancements to existing interfaces. The SCIP Optimization Suite 9.0 also includes new and improved features in the LP solver SoPlex, the presolving library PaPILO, the parallel framework UG, the decomposition framework GCG, and the SCIP extension SCIP-SDP. These additions and enhancements have resulted in an overall performance improvement of SCIP in terms of solving time, number of nodes in the branch-and-bound tree, as well as the reliability of the solver.}, language = {en} }