@misc{KochRalphsShinano2011, author = {Koch, Thorsten and Ralphs, Ted and Shinano, Yuji}, title = {What could a million CPUs do to solve Integer Programs?}, issn = {1438-0064}, doi = {10.1007/s00186-012-0390-9}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14222}, number = {11-40}, year = {2011}, abstract = {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.}, 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} } @misc{BertholdGamrathGleixneretal.2012, author = {Berthold, Timo and Gamrath, Gerald and Gleixner, Ambros and Heinz, Stefan and Koch, Thorsten and Shinano, Yuji}, title = {Solving mixed integer linear and nonlinear problems using the SCIP Optimization Suite}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-15654}, year = {2012}, abstract = {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.}, language = {en} } @misc{GamrathKochMaheretal.2016, author = {Gamrath, Gerald and Koch, Thorsten and Maher, Stephen J. and Rehfeldt, Daniel and Shinano, Yuji}, title = {SCIP-Jack - A solver for STP and variants with parallelization extensions}, issn = {1438-0064}, doi = {10.1007/s12532-016-0114-x}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60170}, year = {2016}, abstract = {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.}, language = {en} } @misc{RehfeldtKoch2016, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {Transformations for the Prize-Collecting Steiner Tree Problem and the Maximum-Weight Connected Subgraph Problem to SAP}, issn = {1438-0064}, doi = {10.4208/jcm.1709-m2017-0002}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59777}, year = {2016}, abstract = {Transformations of Steiner tree problem variants have been frequently discussed in the literature. Besides allowing to easily transfer complexity results, they constitute a central pillar of exact state-of-the-art solvers for well-known variants such as the Steiner tree problem in graphs. In this paper transformations for both the prize-collecting Steiner tree problem and the maximum-weight connected subgraph problem to the Steiner arborescence problem are introduced for the first time. Furthermore, we demonstrate the considerable implications for practical solving approaches, including the computation of strong upper and lower bounds.}, language = {en} } @incollection{GotzesHeineckeHilleretal.2015, author = {Gotzes, Uwe and Heinecke, Nina and Hiller, Benjamin and R{\"o}vekamp, Jessica and Koch, Thorsten}, title = {Regulatory rules for gas markets in Germany and other European countries}, booktitle = {Evaluating gas network capacities}, publisher = {Society for Industrial and Applied Mathematics}, isbn = {978-1-611973-68-6}, pages = {45 -- 64}, year = {2015}, language = {en} } @misc{BreuerBussieckCaoetal.2017, author = {Breuer, Thomas and Bussieck, Michael and Cao, Karl-Kien and Cebulla, Felix and Fiand, Frederik and Gils, Hans Christian and Gleixner, Ambros and Khabi, Dmitry and Koch, Thorsten and Rehfeldt, Daniel and Wetzel, Manuel}, title = {Optimizing Large-Scale Linear Energy System Problems with Block Diagonal Structure by Using Parallel Interior-Point Methods}, issn = {1438-0064}, doi = {10.1007/978-3-319-89920-6_85}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66183}, year = {2017}, abstract = {Current linear energy system models (ESM) acquiring to provide sufficient detail and reliability frequently bring along problems of both high intricacy and increasing scale. Unfortunately, the size and complexity of these problems often prove to be intractable even for commercial state-of-the-art linear programming solvers. This article describes an interdisciplinary approach to exploit the intrinsic structure of these large-scale linear problems to be able to solve them on massively parallel high-performance computers. A key aspect are extensions to the parallel interior-point solver PIPS-IPM originally developed for stochastic optimization problems. Furthermore, a newly developed GAMS interface to the solver as well as some GAMS language extensions to model block-structured problems will be described.}, language = {en} } @misc{RehfeldtKoch2018, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {SCIP-Jack—a solver for STP and variants with parallelization extensions: An update}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66416}, year = {2018}, abstract = {The Steiner tree problem in graphs is a classical problem that commonly arises in practical applications as one of many variants. Although the different Steiner tree problem variants are usually strongly related, solution approaches employed so far have been prevalently problem-specific. Against this backdrop, the solver SCIP-Jack was created as a general-purpose framework that can be used to solve the classical Steiner tree problem and 11 of its variants. 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. Furthermore, SCIP-Jack includes various newly developed algorithmic components such as preprocessing routines and heuristics. The result is a high-performance solver that can be employed in massively parallel environments and is capable of solving previously unsolved instances. After the introduction of SCIP-Jack at the 2014 DIMACS Challenge on Steiner problems, the overall performance of the solver has considerably improved. This article provides an overview on the current state.}, language = {en} } @article{BertholdHendelKoch2017, author = {Berthold, Timo and Hendel, Gregor and Koch, Thorsten}, title = {From feasibility to improvement to proof: three phases of solving mixed-integer programs}, volume = {33}, journal = {Optimization Methods and Software}, number = {3}, publisher = {Taylor \& Francis}, doi = {10.1080/10556788.2017.1392519}, pages = {499 -- 517}, year = {2017}, abstract = {Modern mixed-integer programming (MIP) solvers employ dozens of auxiliary algorithmic components to support the branch-and-bound search in finding and improving primal solutions and in strengthening the dual bound. Typically, all components are tuned to minimize the average running time to prove optimality. In this article, we take a different look at the run of a MIP solver. We argue that the solution process consists of three distinct phases, namely achieving feasibility, improving the incumbent solution, and proving optimality. We first show that the entire solving process can be improved by adapting the search strategy with respect to the phase-specific aims using different control tunings. Afterwards, we provide criteria to predict the transition between the individual phases and evaluate the performance impact of altering the algorithmic behaviour of the non-commercial MIP solver Scip at the predicted phase transition points.}, language = {en} } @article{SchmidtAssmannBurlacuetal.2017, author = {Schmidt, Martin and Assmann, Denis and Burlacu, Robert and Humpola, Jesco and Joormann, Imke and Kanelakis, Nikolaos and Koch, Thorsten and Oucherif, Djamal and Pfetsch, Marc and Schewe, Lars and Schwarz, Robert and Sirvent, Matthias}, title = {GasLib - A Library of Gas Network Instances}, volume = {2}, journal = {Data}, number = {4}, doi = {10.3390/data2040040}, year = {2017}, language = {en} } @article{Koch2017, author = {Koch, Thorsten}, title = {The ZIMPL modeling language}, volume = {103}, journal = {Optima}, pages = {8 -- 9}, year = {2017}, language = {en} } @misc{RehfeldtKoch2017, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {Combining NP-Hard Reduction Techniques and Strong Heuristics in an Exact Algorithm for the Maximum-Weight Connected Subgraph Problem}, issn = {1438-0064}, doi = {10.1137/17M1145963}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64699}, year = {2017}, abstract = {Borne out of a surprising variety of practical applications, the maximum-weight connected subgraph problem has attracted considerable interest during the past years. This interest has not only led to notable research on theoretical properties, but has also brought about several (exact) solvers-with steadily increasing performance. Continuing along this path, the following article introduces several new algorithms such as reduction techniques and heuristics and describes their integration into an exact solver. The new methods are evaluated with respect to both their theoretical and practical properties. Notably, the new exact framework allows to solve common problem instances from the literature faster than all previous approaches. Moreover, one large-scale benchmark instance from the 11th DIMACS Challenge can be solved for the first time to optimality and the primal-dual gap for two other ones can be significantly reduced.}, language = {en} } @article{RehfeldtKochMaher2019, author = {Rehfeldt, Daniel and Koch, Thorsten and Maher, Stephen J.}, title = {Reduction Techniques for the Prize-Collecting Steiner Tree Problem and the Maximum-Weight Connected Subgraph Problem}, volume = {73}, journal = {Networks}, edition = {2}, publisher = {Wiley}, doi = {10.1002/net.21857}, pages = {206 -- 233}, year = {2019}, abstract = {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.}, language = {en} } @article{RehfeldtKoch2018, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {Transformations for the Prize-Collecting Steiner Tree Problem and the Maximum-Weight Connected Subgraph Problem to SAP}, volume = {36}, journal = {Journal of Computational Mathematics}, number = {3}, doi = {10.4208/jcm.1709-m2017-0002}, pages = {459 -- 468}, year = {2018}, abstract = {Transformations of Steiner tree problem variants have been frequently discussed in the literature. Besides allowing to easily transfer complexity results, they constitute a central pillar of exact state-of-the-art solvers for well-known variants such as the Steiner tree problem in graphs. In this paper transformations for both the prize-collecting Steiner tree problem and the maximum-weight connected subgraph problem to the Steiner arborescence problem are introduced for the first time. Furthermore, we demonstrate the considerable implications for practical solving approaches, including the computation of strong upper and lower bounds.}, language = {en} } @misc{LuceDuintjerTebbensLiesenetal.2009, author = {Luce, Robert and Duintjer Tebbens, Jurjen and Liesen, J{\"o}rg and Nabben, Robert and Gr{\"o}tschel, Martin and Koch, Thorsten and Schenk, Olaf}, title = {On the Factorization of Simplex Basis Matrices}, organization = {TU Berlin, Zuse Institute Berlin, University of Basel}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11392}, number = {09-24}, year = {2009}, abstract = {In the simplex algorithm, solving linear systems with the basis matrix and its transpose accounts for a large part of the total computation time. We investigate various methods from modern numerical linear algebra to improve the computation speed of the basis updates arising in LPs. The experiments are executed on a large real-world test set. The most widely used solution technique is sparse LU factorization, paired with an updating scheme that allows to use the factors over several iterations. Clearly, small number of fill-in elements in the LU factors is critical for the overall performance. Using a wide range of LPs we show numerically that after a simple permutation the non-triangular part of the basis matrix is so small, that the whole matrix can be factorized with (relative) fill-in close to the optimum. This permutation has been exploited by simplex practitioners for many years. But to our knowledge no systematic numerical study has been published that demonstrates the effective reduction to a surprisingly small non-triangular problem, even for large scale LPs. For the factorization of the non-triangular part most existing simplex codes use some variant of dynamic Markowitz pivoting, which originated in the late 1950s. We also show numerically that, in terms of fill-in and in the simplex context, dynamic Markowitz is quite consistently superior to other, more recently developed techniques.}, language = {en} } @misc{AchterbergBertholdHeinzetal.2008, author = {Achterberg, Tobias and Berthold, Timo and Heinz, Stefan and Koch, Thorsten and Wolter, Kati}, title = {Constraint Integer Programming: Techniques and Applications}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10950}, number = {08-43}, year = {2008}, abstract = {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 for solving satisfiability problems. SCIP is available in source code and free for noncommercial use. We demonstrate the usefulness of CIP on three 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 demonstrate how to use CIP techniques to compute the number of optimal solutions of integer programs. Third, we employ the CIP framework to solve chip design verification problems, which involve some highly nonlinear 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 nonlinear constraints by employing constraint programming techniques.}, language = {en} } @misc{GamrathKochRehfeldtetal.2014, author = {Gamrath, Gerald and Koch, Thorsten and Rehfeldt, Daniel and Shinano, Yuji}, title = {SCIP-Jack - A massively parallel STP solver}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-52293}, year = {2014}, abstract = {In this article we describe the impact from embedding a 15 year old model for solving the Steiner tree problem in graphs in a state-of-the-art MIP-Framework, making the result run in a massively parallel environment and extending the model to solve as many variants as possible. We end up with a high-perfomance solver that is capable of solving previously unsolved instances and, in contrast to its predecessor, is freely available for academic research.}, language = {en} } @misc{KochMartinPfetsch2013, author = {Koch, Thorsten and Martin, Alexander and Pfetsch, Marc}, title = {Progress in Academic Computational Integer Programming}, journal = {Facets of Combinatorial Optimization}, editor = {J{\"u}nger, Michael and Reinelt, Gerhard}, publisher = {Springer}, doi = {10.1007/978-3-642-38189-8_19}, pages = {483 -- 506}, year = {2013}, language = {en} } @misc{ArnoldBertholdHeinzetal.2014, author = {Arnold, Thomas and Berthold, Timo and Heinz, Stefan and Vigerske, Stefan and Henrion, Ren{\´e} and Gr{\"o}tschel, Martin and Koch, Thorsten and Tischendorf, Caren and R{\"o}misch, Werner}, title = {A Jack of all Trades? Solving stochastic mixed-integer nonlinear constraint programs}, issn = {1438-0064}, doi = {10.4171/137}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-49947}, year = {2014}, abstract = {Natural gas is one of the most important energy sources in Germany and Europe. In recent years, political regulations have led to a strict separation of gas trading and gas transport, thereby assigning a central role in energy politics to the transportation and distribution of gas. These newly imposed political requirements influenced the technical processes of gas transport in such a way that the complex task of planning and operating gas networks has become even more intricate. Mathematically, the combination of discrete decisions on the configuration of a gas transport network, the nonlinear equations describing the physics of gas, and the uncertainty in demand and supply yield large-scale and highly complex stochastic mixed-integer nonlinear optimization problems. The Matheon project "Optimization of Gas Transport" takes the key role of making available the necessary core technology to solve the mathematical optimization problems which model the topology planning and the operation of gas networks. An important aspect of the academic impact is the free availability of our framework. As a result of several years of research and development, it is now possible to download a complete state-of-the-art framework for mixed-integer linear and nonlinear programming in source code at http://scip.zib.de}, language = {en} } @misc{ArnoldBertholdHeinzetal.2014, author = {Arnold, Thomas and Berthold, Timo and Heinz, Stefan and Vigerske, Stefan and Henrion, Ren{\´e} and Gr{\"o}tschel, Martin and Koch, Thorsten and Tischendorf, Caren and R{\"o}misch, Werner}, title = {A Jack of all Trades? Solving stochastic mixed-integer nonlinear constraint programs}, volume = {1}, journal = {MATHEON - Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, doi = {10.4171/137}, pages = {135 -- 146}, year = {2014}, abstract = {Natural gas is one of the most important energy sources in Germany and Europe. In recent years, political regulations have led to a strict separation of gas trading and gas transport, thereby assigning a central role in energy politics to the transportation and distribution of gas. These newly imposed political requirements influenced the technical processes of gas transport in such a way that the complex task of planning and operating gas networks has become even more intricate. Mathematically, the combination of discrete decisions on the configuration of a gas transport network, the nonlinear equations describing the physics of gas, and the uncertainty in demand and supply yield large-scale and highly complex stochastic mixed-integer nonlinear optimization problems. The Matheon project "Optimization of Gas Transport" takes the key role of making available the necessary core technology to solve the mathematical optimization problems which model the topology planning and the operation of gas networks. An important aspect of the academic impact is the free availability of our framework. As a result of several years of research and development, it is now possible to download a complete state-of-the-art framework for mixed-integer linear and nonlinear programming in source code at http://scip.zib.de}, language = {en} } @article{CookKochSteffyetal.2013, author = {Cook, William and Koch, Thorsten and Steffy, Daniel and Wolter, Kati}, title = {A hybrid branch-and-bound approach for exact rational mixed-integer programming}, volume = {5}, journal = {Mathematical Programming Computation}, number = {3}, doi = {10.1007/s12532-013-0055-6}, pages = {305 -- 344}, year = {2013}, abstract = {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.}, language = {en} }