TY - GEN A1 - Eisenblätter, Andreas A1 - Fügenschuh, Armin A1 - Geerdes, Hans-Florian A1 - Koch, Thorsten A1 - Türke, Ulrich A1 - Meijerink, Ellen T1 - XML Data Specification and Documentation Y1 - 2003 PB - IST-2000-28088 MOMENTUM Technical Report ER - TY - CHAP A1 - Eisenblätter, Andreas A1 - Fügenschuh, Armin A1 - Geerdes, Hans-Florian A1 - Junglas, Daniel A1 - Koch, Thorsten A1 - Martin, Alexander T1 - Integer Programming Methods for UMTS Radio Network Planning T2 - Proceedings of the WiOpt’04, Cambridge, UK Y1 - 2004 ER - TY - GEN A1 - Shinano, Yuji A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten T1 - ParaSCIP - a parallel extension of SCIP N2 - Mixed integer programming (MIP) has become one of the most important techniques in Operations Research and Discrete Optimization. SCIP (Solving Constraint Integer Programs) is currently one of the fastest non-commercial MIP solvers. It is based on the branch-and-bound procedure in which the problem is recursively split into smaller subproblems, thereby creating a so-called branching tree. We present ParaSCIP, an extension of SCIP, which realizes a parallelization on a distributed memory computing environment. ParaSCIP uses SCIP solvers as independently running processes to solve subproblems (nodes of the branching tree) locally. This makes the parallelization development independent of the SCIP development. Thus, ParaSCIP directly profits from any algorithmic progress in future versions of SCIP. Using a first implementation of ParaSCIP, we were able to solve two previously unsolved instances from MIPLIB2003, a standard test set library for MIP solvers. For these computations, we used up to 2048 cores of the HLRN~II supercomputer. T3 - ZIB-Report - 10-27 KW - massive parallization KW - mixed integer programming KW - ParaSCIP KW - branch-and-cut KW - branch-and-bound Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11921 UR - http://www.springerlink.com/content/t2160206253v7661/ ER - TY - JOUR A1 - Pfetsch, Marc A1 - Fügenschuh, Armin A1 - Geißler, Björn A1 - Geißler, Nina A1 - Gollmer, Ralf A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Martin, Alexander A1 - Morsi, Antonio A1 - Rövekamp, Jessica A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schultz, Rüdiger A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Stangl, Claudia A1 - Steinbach, Marc A1 - Vigerske, Stefan A1 - Willert, Bernhard T1 - Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions JF - Optimization Methods and Software N2 - 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 feasibility problem. The first phase consists of four distinct algorithms applying linear, and methods for complementarity constraints to compute possible settings for the discrete decisions. The second phase employs a precise continuous programming model of the gas network. Using this setup, we are able to compute high quality solutions to real-world industrial instances that are significantly larger than networks that have appeared in the mathematical programming literature before. Y1 - 2014 U6 - https://doi.org/10.1080/10556788.2014.888426 PB - Taylor & Francis ER - TY - CHAP A1 - Fügenschuh, Armin A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Szabo, Jacint T1 - Gas Network Topology Optimization for Upcoming Market Requirements T2 - International Conference on the European Energy Market (EEM) N2 - Gas distribution networks are complex structures that consist of passive pipes, and active, controllable elements such as valves and compressors. Controlling such network means to find a suitable setting for all active components such that a nominated amount of gas can be transmitted from entries to exits through the network, without violating physical or operational constraints. The control of a large-scale gas network is a challenging task from a practical point of view. In most companies the actual controlling process is supported by means of computer software that is able to simulate the flow of the gas. However, the active settings have to be set manually within such simulation software. The solution quality thus depends on the experience of a human planner. When the gas network is insufficient for the transport then topology extensions come into play. Here a set of new pipes or active elements is determined such that the extended network admits a feasible control again. The question again is how to select these extensions and where to place them such that the total extension costs are minimal. Industrial practice is again to use the same simulation software, determine extensions by experience, add them to the virtual network, and then try to find a feasible control of the active elements. The validity of this approach now depends even more on the human planner. Another weakness of this manual simulation-based approach is that it cannot establish infeasibility of a certain gas nomination, unless all settings of the active elements are tried. Moreover, it is impossible to find a cost-optimal network extension in this way. In order to overcome these shortcomings of the manual planning approach we present a new approach, rigorously based on mathematical optimization. Hereto we describe a model for finding feasible controls and then extend this model such that topology extensions can additionally and simultaneously be covered. Numerical results for real-world instances are presented and discussed. Y1 - 2011 U6 - https://doi.org/10.1109/EEM.2011.5953035 SP - 346 EP - 351 ER - TY - CHAP A1 - Berthold, Timo A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Shinano, Yuji T1 - SCIP Optimization Suite を利用した 混合整数(線形/非線形) 計画問題の解法 T2 - Proceedings of the 24th RAMP symposium. The Operations Society of Japan, RAMP: Research Association of Mathematical Programming N2 - この論文ではソフトウェア・パッケージSCIP Optimization Suite を紹介し,その3つの構成要素:モデリン グ言語Zimpl, 線形計画(LP: linear programming) ソルバSoPlex, そして,制約整数計画(CIP: constraint integer programming) に対するソフトウェア・フレームワークSCIP, について述べる.本論文では,この3つの 構成要素を利用して,どのようにして挑戦的な混合整数線形計画問題(MIP: mixed integer linear optimization problems) や混合整数非線形計画問題(MINLP: mixed integer nonlinear optimization problems) をモデル化 し解くのかを説明する.SCIP は,現在,最も高速なMIP,MINLP ソルバの1つである.いくつかの例により, Zimpl, SCIP, SoPlex の利用方法を示すとともに,利用可能なインタフェースの概要を示す.最後に,将来の開 発計画の概要について述べる. N2 - This paper introduces the SCIP Optimization Suite and discusses the capabilities of its three components: the modeling language Zimpl, the linear programming solver SoPlex, and the constraint integer programming framework SCIP. We explain how in concert these can be used to model and solve challenging mixed integer linear and nonlinear optimization problems. SCIP is currently one of the fastest non-commercial MIP and MINLP solvers. We demonstrate the usage of Zimpl, SCIP, and SoPlex by selected examples, we give an overview over available interfaces, and outline plans for future development. Y1 - 2012 SP - 165 EP - 192 ER - TY - JOUR A1 - Fügenschuh, Armin A1 - Geißler, Björn A1 - Gollmer, Ralf A1 - Hayn, Christine A1 - Henrion, René A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Martin, Alexander A1 - Mirkov, Radoslava A1 - Morsi, Antonio A1 - Römisch, Werner A1 - Rövekamp, Jessica A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schultz, Rüdiger A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Stangl, Claudia A1 - Steinbach, Marc A1 - Willert, Bernhard T1 - Mathematical optimization for challenging network planning problems in unbundled liberalized gas markets JF - Energy Systems N2 - 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 were 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 discuss how these changing paradigms lead to new and challenging mathematical optimization problems. This includes the validation of nominations, that asks for the decision if the network’s capacity is sufficient to transport a specific amount of flow, the verification of booked capacities and the detection of available freely allocable capacities, and the topological extension of the network with new pipelines or compressors in order to increase its capacity. In order to solve each of these problems and to provide meaningful results for the practice, a mixture of different mathematical aspects have to be addressed, such as combinatorics, stochasticity, uncertainty, and nonlinearity. Currently, no numerical solver is available that can deal with such blended problems out-of-the-box. The main goal of our research is to develop such a solver, that moreover is able to solve instances of realistic size. In this article, we describe the main ingredients of our prototypical software implementations. Y1 - 2013 U6 - https://doi.org/10.1007/s12667-013-0099-8 VL - 5 IS - 3 SP - 449 EP - 473 PB - Springer Berlin Heidelberg CY - Berlin ER - TY - JOUR A1 - Hoang, Nam-Dung A1 - Koch, Thorsten T1 - Steiner tree packing revisited JF - Mathematical Methods of Operations Research N2 - 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. Y1 - 2012 U6 - https://doi.org/10.1007/s00186-012-0391-8 VL - 76 IS - 1 SP - 95 EP - 123 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Hoang, Nam-Dung A1 - Karbstein, Marika A1 - Koch, Thorsten A1 - Martin, Alexander ED - Jünger, Michael ED - Reinelt, Gerhard T1 - How many Steiner terminals can you connect in 20 years? T2 - Facets of Combinatorial Optimization; Festschrift for Martin Grötschel Y1 - 2013 U6 - https://doi.org/10.1007/978-3-642-38189-8_10 SP - 215 EP - 244 PB - Springer ER - TY - GEN A1 - Shinano, Yuji A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Winkler, Michael T1 - Solving hard MIPLIB2003 problems with ParaSCIP on Supercomputers: An update N2 - Contemporary supercomputers can easily provide years of CPU time per wall-clock hour. One challenge of today's software development is how to harness this wast computing power in order to solve really hard mixed integer programming instances. In 2010, two out of six open MIPLIB2003 instances could be solved by ParaSCIP in more than ten consecutive runs, restarting from checkpointing files. The contribution of this paper is threefold: For the first time, we present computational results of single runs for those two instances. Secondly, we provide new improved upper and lower bounds for all of the remaining four open MIPLIB2003 instances. Finally, we explain which new developments led to these results and discuss the current progress of ParaSCIP. Experiments were conducted on HLRNII, on HLRN III, and on the Titan supercomputer, using up to 35,200 cores. T3 - ZIB-Report - 13-66 KW - Mixed Integer Programming KW - MIPLIB2003 KW - ParaSCIP KW - Ubiquity Generator Framework KW - Supercomputer Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42888 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Hoang, Nam-Dung A1 - Karbstein, Marika A1 - Koch, Thorsten A1 - Martin, Alexander T1 - How Many Steiner Terminals Can You Connect in 20 Years? N2 - 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. T3 - ZIB-Report - 13-57 KW - Steiner tree KW - Steiner connectivity KW - Steiner tree packing Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42524 SN - 1438-0064 ER - TY - JOUR A1 - Humpola, Jesco A1 - Fügenschuh, Armin A1 - Koch, Thorsten T1 - Valid inequalities for the topology optimization problem in gas network design JF - OR Spectrum N2 - One quarter of Europe's energy demand is provided by natural gas distributed through a vast pipeline network covering the whole of Europe. At a cost of 1 million Euro per km extending the European pipeline network is already a multi-billion Euro business. Therefore, automatic planning tools that support the decision process are desired. Unfortunately, current mathematical methods are not capable of solving the arising network design problems due to their size and complexity. In this article, we will show how to apply optimization methods that can converge to a proven global optimal solution. By introducing a new class of valid inequalities that improve the relaxation of our mixed-integer nonlinear programming model, we are able to speed up the necessary computations substantially. Y1 - 2016 U6 - https://doi.org/https://doi.org/10.1007/s00291-015-0390-2 VL - 38 IS - 3 SP - 597 EP - 631 PB - Springer CY - Berlin Heidelberg ER - TY - GEN A1 - Maher, Stephen J. A1 - Fischer, Tobias A1 - Gally, Tristan A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Gottwald, Robert Lion A1 - Hendel, Gregor A1 - Koch, Thorsten A1 - Lübbecke, Marco A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schenker, Sebastian A1 - Schwarz, Robert A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Weninger, Dieter A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 4.0 N2 - The SCIP Optimization Suite is a powerful collection of optimization software that consists of the branch-cut-and-price framework and mixed-integer programming solver SCIP, the linear programming solver SoPlex, the modeling language Zimpl, the parallelization framework UG, and the generic branch-cut-and-price solver GCG. Additionally, it features the extensions SCIP-Jack for solving Steiner tree problems, PolySCIP for solving multi-objective problems, and SCIP-SDP for solving mixed-integer semidefinite programs. The SCIP Optimization Suite has been continuously developed and has now reached version 4.0. The goal of this report is to present the recent changes to the collection. We not only describe the theoretical basis, but focus on implementation aspects and their computational consequences. T3 - ZIB-Report - 17-12 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62170 SN - 1438-0064 ER - TY - CHAP A1 - Koch, Thorsten A1 - Pfetsch, Marc A1 - Rövekamp, Jessica T1 - Introduction T2 - Evaluating Gas Network Capacities Y1 - 2015 SN - 9781611973686 SP - 3 EP - 16 PB - Society for Industrial and Applied Mathematics ER - TY - GEN A1 - Gamrath, Gerald A1 - Fischer, Tobias A1 - Gally, Tristan A1 - Gleixner, Ambros A1 - Hendel, Gregor A1 - Koch, Thorsten A1 - Maher, Stephen J. A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schenker, Sebastian A1 - Schwarz, Robert A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Vigerske, Stefan A1 - Weninger, Dieter A1 - Winkler, Michael A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 3.2 N2 - 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. T3 - ZIB-Report - 15-60 KW - mixed-integer linear and nonlinear programming KW - MIP solver KW - MINLP solver KW - linear programming KW - LP solver KW - simplex method KW - modeling KW - parallel branch-and-bound KW - branch-cut-and-price framework KW - generic column generation KW - Steiner tree solver KW - multi-criteria optimization KW - mixed-integer semidefinite programming Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57675 SN - 1438-0064 ER - TY - JOUR A1 - Eisenblätter, Andreas A1 - Fügenschuh, Armin A1 - Fledderus, E. A1 - Geerdes, Hans-Florian A1 - Heideck, B. A1 - Junglas, Daniel A1 - Koch, Thorsten A1 - Kürner, T. A1 - Martin, Alexander ED - Martin, Alexander T1 - Mathematical Methods for Automatic Optimization of UMTS Radio Networks Y1 - 2003 UR - http://momentum.zib.de/paper/momentum-d43.pdf IS - D4.3 PB - IST-2000-28088 MOMENTUM ER - TY - JOUR A1 - Eisenblätter, Andreas A1 - Geerdes, Hans-Florian A1 - Junglas, Daniel A1 - Koch, Thorsten A1 - Kürner, T. A1 - Martin, Alexander T1 - Final Report on Automatic Planning and Optimisation Y1 - 2003 UR - http://momentum.zib.de/paper/momentum-d47.pdf IS - D4.7 PB - IST-2000-28088 MOMENTUM ER - TY - GEN A1 - Koch, Thorsten ED - Achterberg, Tobias ED - Beck, J. Christopher T1 - Which mixed integer programs could a million CPUs solve? T2 - CPAIOR 2011 – Late Breaking Abstracts Y1 - 2011 UR - http://opus4.kobv.de/opus4-zib/files/1294/ZR-11-20.pdf IS - 11-20 SP - 17 EP - 18 PB - Zuse Institute Berlin CY - Takustr. 7, Berlin ER - TY - CHAP A1 - Shinano, Yuji A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten ED - Bischof, Christian ED - Hegering, Heinz-Gerd ED - Nagel, Wolfgang ED - Wittum, Gabriel T1 - ParaSCIP: a parallel extension of SCIP T2 - Competence in High Performance Computing 2010 Y1 - 2012 U6 - https://doi.org/10.1007/978-3-642-24025-6_12 SP - 135 EP - 148 PB - Springer ER - TY - JOUR A1 - Koch, Thorsten A1 - Ralphs, Ted A1 - Shinano, Yuji T1 - Could we use a million cores to solve an integer program? JF - Mathematical Methods of Operations Research Y1 - 2012 U6 - https://doi.org/10.1007/s00186-012-0390-9 VL - 76 IS - 1 SP - 67 EP - 93 ER - TY - CHAP A1 - Dorndorf, Ulrich A1 - Droste, Stefan A1 - Koch, Thorsten ED - Kallrath, Josef T1 - Using ZIMPL for Modeling Production Planning Problems T2 - Algebraic Modeling Systems Y1 - 2012 U6 - https://doi.org/10.1007/978-3-642-23592-4 SP - 145 EP - 158 PB - Springer ER - TY - CHAP A1 - Martin, Alexander A1 - Geißler, Björn A1 - Heyn, Christine A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Morsi, Antonio A1 - Pfetsch, Marc A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schultz, Rüdiger A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Steinbach, Marc A1 - Willert, Bernhard T1 - Optimierung Technischer Kapazitäten in Gasnetzen T2 - Optimierung in der Energiewirtschaft Y1 - 2011 SP - 105 EP - 114 PB - VDI-Verlag, Düsseldorf ER - TY - CHAP A1 - Koch, Thorsten A1 - Leövey, Hernan A1 - Mirkov, Radoslava A1 - Römisch, Werner A1 - Wegner-Specht, Isabel T1 - Szenariogenerierung zur Modellierung der stochastischen Ausspeiselasten in einem Gastransportnetz T2 - Optimierung in der Energiewirtschaft Y1 - 2011 UR - http://www2.mathematik.hu-berlin.de/%7Eromisch/papers/SzengenVDI11.pdf SP - 115 EP - 125 PB - VDI-Verlag, Düsseldorf ER - TY - CHAP A1 - Cook, William A1 - Koch, Thorsten A1 - Steffy, Daniel A1 - Wolter, Kati ED - Günlük, Oktay ED - Woeginger, Gerhard T1 - An Exact Rational Mixed-Integer Programming Solver T2 - IPCO 2011 Y1 - 2011 U6 - https://doi.org/10.1007/978-3-642-20807-2_9 VL - 6655 SP - 104 EP - 116 ER - TY - GEN A1 - Shinano, Yuji A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Vigerske, Stefan A1 - Winkler, Michael T1 - 制約整数計画ソルバ SCIP の並列化 T1 - Parallelizing the Constraint Integer Programming Solver SCIP N2 - 制約整数計画(CIP: Constraint Integer Programming)は,制約プログラミング(CP: Constraint Programming),混合整数計画(MIP: Mixed Integer Programming), 充足可能性問題(SAT: Satisfiability Problems)の研究分野におけるモデリング技術と解法を統合している.その結果,制約整数計画は,広いクラスの最適化問題を扱うことができる.SCIP (Solving Constraint Integer Programs)は,CIPを解くソルバとして実装され,Zuse Institute Berlin (ZIB)の研究者を中心として継続的に拡張が続けられている.本論文では,著者らによって開発されたSCIP に対する2種類の並列化拡張を紹介する. 一つは,複数計算ノード間で大規模に並列動作するParaSCIP である. もう一つは,複数コアと共有メモリを持つ1台の計算機上で(スレッド)並列で動作するFiberSCIP である. ParaSCIP は,HLRN IIスーパーコンピュータ上で, 一つのインスタンスを解くために最大7,168 コアを利用した動作実績がある.また,統計数理研究所のFujitsu PRIMERGY RX200S5上でも,最大512コアを利用した動作実績がある.統計数理研究所のFujitsu PRIMERGY RX200S5上 では,これまでに最適解が得られていなかったMIPLIB2010のインスタンスであるdg012142に最適解を与えた. N2 - The paradigm of Constraint Integer Programming (CIP) combines modeling and solving techniques from the fields of Constraint Programming (CP), Mixed Integer Programming (MIP) and Satisfiability Problems (SAT). The paradigm allows us to address a wide range of optimization problems. SCIP is an implementation of the idea of CIP and is now continuously extended by a group of researchers centered at Zuse Institute Berlin (ZIB). This paper introduces two parallel extensions of SCIP. One is ParaSCIP, which is intended to run on a large scale distributed memory computing environment, and the other is FiberSCIP, intended to run on shared memory computing environments. ParaSCIP has successfully been run on the HLRN II supercomputer utilizing up to 7,168 cores to solve a single difficult MIP. It has also been tested on an ISM supercomputer (Fujitsu PRIMERGY RX200S5 using up to 512 cores). The previously unsolved instance dg012142 from MIPLIB2010 was solved by using the ISM supercomputer. T2 - Parallelizing the Constraint Integer Programming Solver SCIP T3 - ZIB-Report - 13-22 KW - Mixed Integer Programming KW - Constraint Integer Programming KW - Parallel Computing KW - Distributed Memory Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-18130 SN - 1438-0064 ER - TY - GEN A1 - Cook, William A1 - Koch, Thorsten A1 - Steffy, Daniel A1 - Wolter, Kati T1 - A Hybrid Branch-and-Bound Approach for Exact Rational Mixed-Integer Programming N2 - We present an exact rational solver for mixed-integer linear programming that avoids the numerical inaccuracies inherent in the floating-point computations used by existing software. This allows the solver to be used for establishing theoretical results and in applications where correct solutions are critical due to legal and financial consequences. Our solver is a hybrid symbolic/numeric implementation of LP-based branch-and-bound, using numerically-safe methods for all binding computations in the search tree. Computing provably accurate solutions by dynamically choosing the fastest of several safe dual bounding methods depending on the structure of the instance, our exact solver is only moderately slower than an inexact floating-point branch-and-bound solver. The software is incorporated into the SCIP optimization framework, using the exact LP solver QSopt_ex and the GMP arithmetic library. Computational results are presented for a suite of test instances taken from the MIPLIB and Mittelmann libraries and for a new collection of numerically difficult instances. T3 - ZIB-Report - 12-49 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17171 SN - 1438-0064 ER - TY - GEN A1 - Cook, William A1 - Koch, Thorsten A1 - Steffy, Daniel A1 - Wolter, Kati T1 - An Exact Rational Mixed-Integer Programming Solver N2 - We present an exact rational solver for mixed-integer linear programming that avoids the numerical inaccuracies inherent in the floating-point computations used by existing software. This allows the solver to be used for establishing theoretical results and in applications where correct solutions are critical due to legal and financial consequences. Our solver is a hybrid symbolic/numeric implementation of LP-based branch-and-bound, using numerically-safe methods for all binding computations in the search tree. Computing provably accurate solutions by dynamically choosing the fastest of several safe dual bounding methods depending on the structure of the instance, our exact solver is only moderately slower than an inexact floating-point branch-and-bound solver. The software is incorporated into the SCIP optimization framework, using the exact LP solver QSopt_ex and the GMP arithmetic library. Computational results are presented for a suite of test instances taken from the MIPLIB and Mittelmann collections. T3 - ZIB-Report - 11-07 KW - mixed integer programming KW - branch-and-bound KW - exact computation Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12329 ER - TY - JOUR A1 - Gamrath, Gerald A1 - Koch, Thorsten A1 - Maher, Stephen J. A1 - Rehfeldt, Daniel A1 - Shinano, Yuji T1 - SCIP-Jack – A solver for STP and variants with parallelization extensions JF - Mathematical Programming Computation N2 - The Steiner tree problem in graphs is a classical problem that commonly arises in practical applications as one of many variants. While often a strong relationship between different Steiner tree problem variants can be observed, solution approaches employed so far have been prevalently problem-specific. In contrast, this paper introduces a general-purpose solver that can be used to solve both the classical Steiner tree problem and many of its variants without modification. This versatility is achieved by transforming various problem variants into a general form and solving them by using a state-of-the-art MIP-framework. The result is a high-performance solver that can be employed in massively parallel environments and is capable of solving previously unsolved instances. Y1 - 2017 U6 - https://doi.org/10.1007/s12532-016-0114-x VL - 9 IS - 2 SP - 231 EP - 296 ER - TY - BOOK A1 - Greuel, Martin A1 - Koch, Thorsten A1 - Paule, Peter A1 - Sommese, Andrew T1 - Mathematical Software - ICMS 2016, 5th Int. Conf. Berlin, Germany, July 11-14, 2016, Proceedings T3 - Lecture Notes in Computer Science (LNCS) Y1 - 2016 SN - 978-3-319-42431-6 U6 - https://doi.org/10.1007/978-3-319-42432-3 VL - 9725 PB - Springer ER - TY - JOUR A1 - Hiller, Benjamin A1 - Koch, Thorsten A1 - Schewe, Lars A1 - Schwarz, Robert A1 - Schweiger, Jonas T1 - A System to Evaluate Gas Network Capacities: Concepts and Implementation JF - European Journal of Operational Research N2 - 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 trans- ported 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. Y1 - 2018 VL - 270 IS - 3 SP - 797 EP - 808 ER - TY - GEN A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Koch, Thorsten A1 - Miltenberger, Matthias A1 - Kniasew, Dimitri A1 - Schlögel, Dominik A1 - Martin, Alexander A1 - Weninger, Dieter T1 - Tackling Industrial-Scale Supply Chain Problems by Mixed-Integer Programming N2 - SAP's decision support systems for optimized supply network planning rely on mixed-integer programming as the core engine to compute optimal or near-optimal solutions. The modeling flexibility and the optimality guarantees provided by mixed-integer programming greatly aid the design of a robust and future-proof decision support system for a large and diverse customer base. In this paper we describe our coordinated efforts to ensure that the performance of the underlying solution algorithms matches the complexity of the large supply chain problems and tight time limits encountered in practice. T3 - ZIB-Report - 16-45 KW - supply chain management, supply network optimization, mixed-integer linear programming, primal heuristics, numerical stability, large-scale optimization Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61107 SN - 1438-0064 ER - TY - GEN A1 - Gamrath, Gerald A1 - Koch, Thorsten A1 - Maher, Stephen J. A1 - Rehfeldt, Daniel A1 - Shinano, Yuji T1 - SCIP-Jack - A solver for STP and variants with parallelization extensions N2 - The Steiner tree problem in graphs is a classical problem that commonly arises in practical applications as one of many variants. While often a strong relationship between different Steiner tree problem variants can be observed, solution approaches employed so far have been prevalently problem specific. In contrast, this paper introduces a general purpose solver that can be used to solve both the classical Steiner tree problem and many of its variants without modification. This is achieved by transforming various problem variants into a general form and solving them using a state-of-the-art MIP-framework. The result is a high-performance solver that can be employed in massively parallel environments and is capable of solving previously unsolved instances. T3 - ZIB-Report - 15-27 Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-54648 SN - 1438-0064 N1 - A revised version is provided here: http://nbn-resolving.de/urn:nbn:de:0297-zib-60170. ER - TY - CHAP A1 - Hayn, Christine A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Schewe, Lars A1 - Schweiger, Jonas A1 - Spreckelsen, Klaus T1 - Perspectives T2 - Evaluating Gas Network Capacities N2 - After we discussed approaches to validate nominations and to verify bookings, we consider possible future research paths. This includes determining technical capacities and planning of network extensions. Y1 - 2015 SN - 9781611973686 VL - SIAM-MOS series on Optimization ER - TY - GEN A1 - Berthold, Timo A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Shinano, Yuji T1 - SCIP Optimization Suite を利用した 混合整数(線形/非線形) 計画問題の解法 T1 - Solving mixed integer linear and nonlinear problems using the SCIP Optimization Suite N2 - この論文ではソフトウェア・パッケージSCIP Optimization Suite を紹介し,その3つの構成要素:モデリン グ言語Zimpl, 線形計画(LP: linear programming) ソルバSoPlex, そして,制約整数計画(CIP: constraint integer programming) に対するソフトウェア・フレームワークSCIP, について述べる.本論文では,この3つの 構成要素を利用して,どのようにして挑戦的な混合整数線形計画問題(MIP: mixed integer linear optimization problems) や混合整数非線形計画問題(MINLP: mixed integer nonlinear optimization problems) をモデル化 し解くのかを説明する.SCIP は,現在,最も高速なMIP,MINLP ソルバの1つである.いくつかの例により, Zimpl, SCIP, SoPlex の利用方法を示すとともに,利用可能なインタフェースの概要を示す.最後に,将来の開 発計画の概要について述べる. N2 - This paper introduces the SCIP Optimization Suite and discusses the capabilities of its three components: the modeling language Zimpl, the linear programming solver SoPlex, and the constraint integer programming framework SCIP. We explain how in concert these can be used to model and solve challenging mixed integer linear and nonlinear optimization problems. SCIP is currently one of the fastest non-commercial MIP and MINLP solvers. We demonstrate the usage of Zimpl, SCIP, and SoPlex by selected examples, we give an overview over available interfaces, and outline plans for future development. T3 - ZIB-Report - 12-24 KW - SCIP, MIP, MINLP, CIP, LP, modeling, optimization Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15598 SN - 1438-0064 ER - TY - GEN A1 - Martin, Alexander A1 - Geißler, Björn A1 - Hayn, Christine A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Morsi, Antonio A1 - Pfetsch, Marc A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schultz, Rüdiger A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Steinbach, Marc A1 - Willert, Bernhard T1 - Optimierung Technischer Kapazitäten in Gasnetzen N2 - Die mittel- und längerfristige Planung für den Gastransport hat sich durch Änderungen in den regulatorischen Rahmenbedingungen stark verkompliziert. Kernpunkt ist die Trennung von Gashandel und -transport. Dieser Artikel diskutiert die hieraus resultierenden mathematischen Planungsprobleme, welche als Validierung von Nominierungen und Buchungen, Bestimmung der technischen Kapazität und Topologieplanung bezeichnet werden. Diese mathematischen Optimierungsprobleme werden vorgestellt und Lösungsansätze skizziert. T3 - ZIB-Report - 11-56 KW - Gasnetzplanung KW - Technische Kapazitäten KW - Nominierungsvalidierung KW - Buchungsvalidierung KW - Topologieplanung Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15121 SN - 1438-0064 ER - TY - GEN A1 - Achterberg, Tobias A1 - Koch, Thorsten A1 - Tuchscherer, Andreas T1 - On the Effects of Minor Changes in Model Formulations N2 - Starting with the description of the Traveling Salesmen Problem formulation as given by van Vyve and Wolsey in the article Approximate extended formulations'', we investigate the effects of small variations onto the performance of contemporary mixed integer programming solvers. We will show that even minor changes in the formulation of the model can result in performance difference of more than a factor of 1000. As the results show it is not obvious which changes will result in performance improvements and which not. T3 - ZIB-Report - 08-29 Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10808 SN - 1438-0064 ER - TY - GEN A1 - Achterberg, Tobias A1 - Heinz, Stefan A1 - Koch, Thorsten T1 - Counting solutions of integer programs using unrestricted subtree detection N2 - In the recent years there has been tremendous progress in the development of algorithms to find optimal solutions for integer programs. In many applications it is, however, desirable (or even necessary) to generate all feasible solutions. Examples arise in the areas of hardware and software verification and discrete geometry. In this paper, we investigate how to extend branch-and-cut integer programming frameworks to support the generation of all solutions. We propose a method to detect so-called unrestricted subtrees, which allows us to prune the integer program search tree and to collect several solutions simultaneously. We present computational results of this branch-and-count paradigm which show the potential of the unrestricted subtree detection. T3 - ZIB-Report - 08-09 KW - Zählen KW - ganzzahlige Programme KW - IP KW - counting KW - integer programming KW - IP Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10632 SN - 1438-0064 ER - TY - GEN A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Koch, Thorsten A1 - Wolter, Kati T1 - Constraint Integer Programming: a New Approach to Integrate CP and MIP N2 - This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques from SAT solving. SCIP is available in source code and free for non-commercial use. We demonstrate the usefulness of CIP on two tasks. First, we apply the constraint integer programming approach to pure mixed integer programs. Computational experiments show that SCIP is almost competitive to current state-of-the-art commercial MIP solvers. Second, we employ the CIP framework to solve chip design verification problems, which involve some highly non-linear constraint types that are very hard to handle by pure MIP solvers. The CIP approach is very effective here: it can apply the full sophisticated MIP machinery to the linear part of the problem, while dealing with the non-linear constraints by employing constraint programming techniques. T3 - ZIB-Report - 08-01 KW - Constraint Programming KW - Ganzzahlige Programmierung KW - Branch-And-Cut KW - Optimierungssoftware KW - Chipverifikation KW - constraint programming KW - mixed integer programming KW - branch-and-cut KW - optimization software KW - chip verification Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10520 SN - 1438-0064 ER - TY - GEN A1 - Hiller, Benjamin A1 - Koch, Thorsten A1 - Schewe, Lars A1 - Schwarz, Robert A1 - Schweiger, Jonas T1 - A System to Evaluate Gas Network Capacities: Concepts and Implementation N2 - 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. T3 - ZIB-Report - 18-11 Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-67438 SN - 1438-0064 N1 - An earlier version of this report is available as ZR 17-03 at https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6193. ER - TY - GEN A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Generalized preprocessing techniques for Steiner tree and maximum-weight connected subgraph problems N2 - This article introduces new preprocessing techniques for the Steiner tree problem in graphs and one of its most popular relatives, the maximum-weight connected subgraph problem. Several of the techniques generalize previous results from the literature. The correctness of the new methods is shown, but also their NP-hardness is demonstrated. Despite this pessimistic worst-case complexity, several relaxations are discussed that are expected to allow for a strong practical efficiency of these techniques in strengthening both exact and heuristic solving approaches. T3 - ZIB-Report - 17-57 KW - Steiner tree KW - maximum-weight connected subgraph Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65439 SN - 1438-0064 ER - TY - CHAP A1 - Shinano, Yuji A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Winkler, Michael T1 - Solving Open MIP Instances with ParaSCIP on Supercomputers using up to 80,000 Cores T2 - Proc. of 30th IEEE International Parallel & Distributed Processing Symposium N2 - This paper describes how we solved 12 previously unsolved mixed-integer program- ming (MIP) instances from the MIPLIB benchmark sets. To achieve these results we used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP computation: up to 80,000 cores in parallel on the Titan supercomputer. In this paper we describe the basic parallelization mechanism of ParaSCIP, improvements of the dynamic load balancing and novel techniques to exploit the power of parallelization for MIP solving. We give a detailed overview of computing times and statistics for solving open MIPLIB instances. Y1 - 2016 U6 - https://doi.org/10.1109/IPDPS.2016.56 ER - TY - CHAP A1 - Bargmann, Dagmar A1 - Ebbers, Mirko A1 - Heinecke, Nina A1 - Koch, Thorsten A1 - Kühl, Veronika A1 - Pelzer, Antje A1 - Pfetsch, Marc A1 - Rövekamp, Jessica A1 - Spreckelsen, Klaus T1 - State-of-the-art in evaluating gas network capacities T2 - Evaluating Gas Network Capacities Y1 - 2015 SN - 9781611973686 SP - 65 EP - 84 PB - Society for Industrial and Applied Mathematics ER - TY - CHAP A1 - Schewe, Lars A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Pfetsch, Marc T1 - Mathematical optimization for evaluating gas network capacities T2 - Evaluating Gas Network Capacities Y1 - 2015 SN - 9781611973686 SP - 87 EP - 102 PB - Society for Industrial and Applied Mathematics ER - TY - CHAP A1 - Humpola, Jesco A1 - Fügenschuh, Armin A1 - Hiller, Benjamin A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Lenz, Ralf A1 - Schwarz, Robert A1 - Schweiger, Jonas T1 - The Specialized MINLP Approach T2 - Evaluating Gas Network Capacities N2 - We propose an approach to solve the validation of nominations problem using mixed-integer nonlinear programming (MINLP) methods. Our approach handles both the discrete settings and the nonlinear aspects of gas physics. Our main contribution is an innovative coupling of mixed-integer (linear) programming (MILP) methods with nonlinear programming (NLP) that exploits the special structure of a suitable approximation of gas physics, resulting in a global optimization method for this type of problem. Y1 - 2015 SN - 9781611973686 VL - SIAM-MOS series on Optimization ER - TY - BOOK A1 - Koch, Thorsten A1 - Hiller, Benjamin A1 - Pfetsch, Marc A1 - Schewe, Lars T1 - Evaluating Gas Network Capacities Y1 - 2015 SN - 978-1-611973-68-6 PB - SIAM ER - TY - GEN A1 - Rehfeldt, Daniel A1 - Koch, Thorsten A1 - Maher, Stephen J. T1 - Reduction Techniques for the Prize-Collecting Steiner Tree Problem and the Maximum-Weight Connected Subgraph Problem N2 - The concept of reduction has frequently distinguished itself as a pivotal ingredient of exact solving approaches for the Steiner tree problem in graphs. In this paper we broaden the focus and consider reduction techniques for three Steiner problem variants that have been extensively discussed in the literature and entail various practical applications: The prize-collecting Steiner tree problem, the rooted prize-collecting Steiner tree problem and the maximum-weight connected subgraph problem. By introducing and subsequently deploying numerous new reduction methods, we are able to drastically decrease the size of a large number of benchmark instances, already solving more than 90 percent of them to optimality. Furthermore, we demonstrate the impact of these techniques on exact solving, using the example of the state-of-the-art Steiner problem solver SCIP-Jack. T3 - ZIB-Report - 16-47 KW - Steiner tree problems KW - reduction techniques KW - prize-collecting Steiner tree problem KW - maximum-weight connected subgraph problem Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-60420 SN - 1438-0064 ER - TY - THES A1 - Koch, Thorsten T1 - Progress in computational integer programming Y1 - 2013 ER - TY - GEN A1 - Koch, Thorsten A1 - Ralphs, Ted A1 - Shinano, Yuji T1 - What could a million CPUs do to solve Integer Programs? N2 - Given the steady increase in cores per CPU, it is only a matter of time until supercomputers will have a million or more cores. In this article, we investigate the opportunities and challenges that will arise when trying to utilize this vast computing power to solve a single integer linear optimization problem. We also raise the question of whether best practices in sequential solution of ILPs will be effective in massively parallel environments. T3 - ZIB-Report - 11-40 Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14222 SN - 1438-0064 ER - TY - GEN A1 - Koch, Thorsten A1 - Achterberg, Tobias A1 - Andersen, Erling A1 - Bastert, Oliver A1 - Berthold, Timo A1 - Bixby, Robert E. A1 - Danna, Emilie A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Lodi, Andrea A1 - Mittelmann, Hans A1 - Ralphs, Ted A1 - Salvagnin, Domenico A1 - Steffy, Daniel A1 - Wolter, Kati T1 - MIPLIB 2010 N2 - 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. T3 - ZIB-Report - 10-31 KW - Mixed Integer Programming KW - Problem Instances KW - IP KW - MIP KW - MIPLIB Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12953 ER - TY - GEN A1 - Fügenschuh, Armin A1 - Geißler, Björn A1 - Gollmer, Ralf A1 - Hayn, Christine A1 - Henrion, Rene A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Martin, Alexander A1 - Mirkov, Radoslava A1 - Morsi, Antonio A1 - Römisch, Werner A1 - Rövekamp, Jessica A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schultz, Rüdiger A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Stangl, Claudia A1 - Steinbach, Marc A1 - Willert, Bernhard T1 - Mathematical Optimization for Challenging Network Planning Problems in Unbundled Liberalized Gas Markets N2 - 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. T3 - ZIB-Report - 13-13 KW - Gas Market Liberalization KW - Entry-Exit Model KW - Gas Network Access Regulation KW - Mixed-Integer Nonlinear Nonconvex Stochastic Optimization Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17821 SN - 1438-0064 ER - TY - GEN A1 - Pfetsch, Marc A1 - Fügenschuh, Armin A1 - Geißler, Björn A1 - Geißler, Nina A1 - Gollmer, Ralf A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Martin, Alexander A1 - Morsi, Antonio A1 - Rövekamp, Jessica A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schultz, Rüdiger A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Stangl, Claudia A1 - Steinbach, Marc A1 - Vigerske, Stefan A1 - Willert, Bernhard T1 - Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions N2 - 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. T3 - ZIB-Report - 12-41 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16531 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Shinano, Yuji T1 - Solving mixed integer linear and nonlinear problems using the SCIP Optimization Suite N2 - This paper introduces the SCIP Optimization Suite and discusses the capabilities of its three components: the modeling language Zimpl, the linear programming solver SoPlex, and the constraint integer programming framework SCIP. We explain how these can be used in concert to model and solve challenging mixed integer linear and nonlinear optimization problems. SCIP is currently one of the fastest non-commercial MIP and MINLP solvers. We demonstrate the usage of Zimpl, SCIP, and SoPlex by selected examples, we give an overview of available interfaces, and outline plans for future development. T3 - ZIB-Report - 12-27 KW - LP, MIP, CIP, MINLP, modeling, optimization, SCIP, SoPlex, Zimpl Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15654 SN - 1438-0064 ER -