TY - GEN A1 - Gamrath, Gerald A1 - Anderson, Daniel A1 - Bestuzheva, Ksenia A1 - Chen, Wei-Kun A1 - Eifler, Leon A1 - Gasse, Maxime A1 - Gemander, Patrick A1 - Gleixner, Ambros A1 - Gottwald, Leona A1 - Halbig, Katrin A1 - Hendel, Gregor A1 - Hojny, Christopher A1 - Koch, Thorsten A1 - Le Bodic, Pierre A1 - Maher, Stephen J. A1 - Matter, Frederic A1 - Miltenberger, Matthias A1 - Mühmer, Erik A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Tawfik, Christine A1 - Vigerske, Stefan A1 - Wegscheider, Fabian A1 - Weninger, Dieter A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 7.0 N2 - The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming frame- work SCIP. This paper discusses enhancements and extensions contained in version 7.0 of the SCIP Optimization Suite. The new version features the parallel presolving library PaPILO as a new addition to the suite. PaPILO 1.0 simplifies mixed-integer linear op- timization problems and can be used stand-alone or integrated into SCIP via a presolver plugin. SCIP 7.0 provides additional support for decomposition algorithms. Besides im- provements in the Benders’ decomposition solver of SCIP, user-defined decomposition structures can be read, which are used by the automated Benders’ decomposition solver and two primal heuristics. Additionally, SCIP 7.0 comes with a tree size estimation that is used to predict the completion of the overall solving process and potentially trigger restarts. Moreover, substantial performance improvements of the MIP core were achieved by new developments in presolving, primal heuristics, branching rules, conflict analysis, and symmetry handling. Last, not least, the report presents updates to other components and extensions of the SCIP Optimization Suite, in particular, the LP solver SoPlex and the mixed-integer semidefinite programming solver SCIP-SDP. T3 - ZIB-Report - 20-10 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78023 SN - 1438-0064 ER - TY - GEN A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - On the exact solution of prize-collecting Steiner tree problems T3 - ZIB-Report - 20-11 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78174 SN - 1438-0064 ER - TY - JOUR 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 JF - Journal of Computational Mathematics N2 - The modeling flexibility and the optimality guarantees provided by mixed-integer programming greatly aid the design of robust and future-proof decision support systems. The complexity of industrial-scale supply chain optimization, however, often poses limits to the application of general mixed-integer programming solvers. In this paper we describe algorithmic innovations that help to ensure that MIP solver performance matches the complexity of the large supply chain problems and tight time limits encountered in practice. Our computational evaluation is based on a diverse set, modeling real-world scenarios supplied by our industry partner SAP. Y1 - 2019 U6 - https://doi.org/10.4208/jcm.1905-m2019-0055 VL - 37 SP - 866 EP - 888 ER - TY - CHAP A1 - Grötschel, Martin A1 - Koch, Thorsten A1 - Hoang, Nam-Dung ED - Biermann, Katja ED - Grötschel, Martin ED - Lutz-Westphal, Brigitte T1 - Lagenwechsel minimieren – oder das Bohren von Löchern in Leiterplatten T2 - Besser als Mathe Y1 - 2010 U6 - https://doi.org/10.1007/978-3-658-01004-1_19 SP - 161 EP - 174 PB - Vieweg+Teubner ER - TY - GEN A1 - Chen, Ying A1 - Koch, Thorsten A1 - Xu, Xiaofei T1 - Regularized partially functional autoregressive model with application to high-resolution natural gas forecasting in Germany N2 - We propose a partially functional autoregressive model with exogenous variables (pFAR) to describe the dynamic evolution of the serially correlated functional data. It provides a unit� ed framework to model both the temporal dependence on multiple lagged functional covariates and the causal relation with ultrahigh-dimensional exogenous scalar covariates. Estimation is conducted under a two-layer sparsity assumption, where only a few groups and elements are supposed to be active, yet without knowing their number and location in advance. We establish asymptotic properties of the estimator and investigate its unite sample performance along with simulation studies. We demonstrate the application of pFAR with the high-resolution natural gas flows in Germany, where the pFAR model provides insightful interpretation as well as good out-of-sample forecast accuracy. T3 - ZIB-Report - 19-34 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-74880 SN - 1438-0064 ER - TY - JOUR A1 - Hennings, Felix A1 - Anderson, Lovis A1 - Hoppmann-Baum, Kai A1 - Turner, Mark A1 - Koch, Thorsten T1 - Controlling transient gas flow in real-world pipeline intersection areas JF - Optimization and Engineering N2 - Compressor stations are the heart of every high-pressure gas transport network. Located at intersection areas of the network they are contained in huge complex plants, where they are in combination with valves and regulators responsible for routing and pushing the gas through the network. Due to their complexity and lack of data compressor stations are usually dealt with in the scientific literature in a highly simplified and idealized manner. As part of an ongoing project with one of Germany's largest Transmission System Operators to develop a decision support system for their dispatching center, we investigated how to automatize control of compressor stations. Each station has to be in a particular configuration, leading in combination with the other nearby elements to a discrete set of up to 2000 possible feasible operation modes in the intersection area. Since the desired performance of the station changes over time, the configuration of the station has to adapt. Our goal is to minimize the necessary changes in the overall operation modes and related elements over time, while fulfilling a preset performance envelope or demand scenario. This article describes the chosen model and the implemented mixed integer programming based algorithms to tackle this challenge. By presenting extensive computational results on real world data we demonstrate the performance of our approach. Y1 - 2021 U6 - https://doi.org/https://doi.org/10.1007/s11081-020-09559-y VL - 22 SP - 687 EP - 734 PB - Springer Nature ET - 2 ER - TY - GEN A1 - Hoang, Nam-Dung A1 - Koch, Thorsten T1 - Steiner Tree Packing Revisited 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. T3 - ZIB-Report - 12-02 KW - Steiner tree packing KW - Integer Programming KW - grid graphs Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14625 SN - 1438-0064 ER - TY - JOUR A1 - Breuer, Thomas A1 - Bussieck, Michael A1 - Fiand, Frederik A1 - Cao, Karl-Kiên A1 - Gils, Hans Christian A1 - Wetzel, Manuel A1 - Gleixner, Ambros A1 - Koch, Thorsten A1 - Rehfeldt, Daniel A1 - Khabi, Dmitry T1 - BEAM-ME: Ein interdisziplinärer Beitrag zur Erreichung der Klimaziele JF - OR-News : das Magazin der GOR Y1 - 2019 IS - 66 SP - 6 EP - 8 ER - TY - CHAP A1 - Gleixner, Ambros A1 - Kempke, Nils-Christian A1 - Koch, Thorsten A1 - Rehfeldt, Daniel A1 - Uslu, Svenja T1 - First Experiments with Structure-Aware Presolving for a Parallel Interior-Point Method T2 - Operations Research Proceedings 2019 N2 - In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware implementations of presolving as part of a parallel interior-point method to solve linear programs with block-diagonal structure, including both linking variables and linking constraints. While presolving reductions are often mathematically simple, their implementation in a high-performance computing environment is a complex endeavor. We report results on impact, performance, and scalability of the resulting presolving routines on real-world energy system models with up to 700 million nonzero entries in the constraint matrix. KW - block structure KW - energy system models KW - interior-point method KW - high performance computing KW - linear programming KW - parallelization KW - presolving KW - preprocessing Y1 - 2020 U6 - https://doi.org/10.1007/978-3-030-48439-2_13 SP - 105 EP - 111 PB - Springer International Publishing ET - 1 ER - TY - CHAP A1 - Shinano, Yuji A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Building Optimal Steiner Trees on Supercomputers by Using up to 43,000 Cores T2 - Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2019 N2 - SCIP-JACK is a customized, branch-and-cut based solver for Steiner tree and related problems. ug [SCIP-JACK, MPI] extends SCIP-JACK to a massively parallel solver by using the Ubiquity Generator (UG) framework. ug [SCIP-JACK, MPI] was the only solver that could run on a distributed environment at the (latest) 11th DIMACS Challenge in 2014. Furthermore, it could solve three well-known open instances and updated 14 best-known solutions to instances from the benchmark libary STEINLIB. After the DIMACS Challenge, SCIP-JACK has been considerably improved. However, the improvements were not reflected on ug [SCIP- JACK, MPI]. This paper describes an updated version of ug [SCIP-JACK, MPI], especially branching on constrains and a customized racing ramp-up. Furthermore, the different stages of the solution process on a supercomputer are described in detail. We also show the latest results on open instances from the STEINLIB. Y1 - 2019 U6 - https://doi.org/10.1007/978-3-030-19212-9_35 VL - 11494 SP - 529 EP - 539 PB - Springer ER - TY - GEN A1 - Hoppmann, Kai A1 - Hennings, Felix A1 - Lenz, Ralf A1 - Gotzes, Uwe A1 - Heinecke, Nina A1 - Spreckelsen, Klaus A1 - Koch, Thorsten T1 - Optimal Operation of Transient Gas Transport Networks T3 - ZIB-Report - 19-23 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73639 SN - 1438-0064 ER - TY - GEN A1 - Hennings, Felix A1 - Anderson, Lovis A1 - Hoppmann, Kai A1 - Turner, Mark A1 - Koch, Thorsten T1 - Controlling transient gas flow in real-world pipeline intersection areas N2 - Compressor stations are the heart of every high-pressure gas transport network. Located at intersection areas of the network they are contained in huge complex plants, where they are in combination with valves and regulators responsible for routing and pushing the gas through the network. Due to their complexity and lack of data compressor stations are usually dealt with in the scientific literature in a highly simplified and idealized manner. As part of an ongoing project with one of Germany's largest Transmission System Operators to develop a decision support system for their dispatching center, we investigated how to automatize control of compressor stations. Each station has to be in a particular configuration, leading in combination with the other nearby elements to a discrete set of up to 2000 possible feasible operation modes in the intersection area. Since the desired performance of the station changes over time, the configuration of the station has to adapt. Our goal is to minimize the necessary changes in the overall operation modes and related elements over time, while fulfilling a preset performance envelope or demand scenario. This article describes the chosen model and the implemented mixed integer programming based algorithms to tackle this challenge. By presenting extensive computational results on real world data we demonstrate the performance of our approach. T3 - ZIB-Report - 19-24 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73645 SN - 1438-0064 ER - TY - JOUR A1 - Chen, Ying A1 - Chua, Wee Song A1 - Koch, Thorsten T1 - Forecasting day-ahead high-resolution natural-gas demand and supply in Germany JF - Applied Energy N2 - Forecasting natural gas demand and supply is essential for an efficient operation of the German gas distribution system and a basis for the operational decisions of the transmission system operators. The German gas market is moving towards more short-term planning, in particular, day-ahead contracts. This increases the difficulty that the operators in the dispatching centre are facing, as well as the necessity of accurate forecasts. This paper presents a novel predictive model that provides day-ahead forecasts of the high resolution gas flow by developing a Functional AutoRegressive model with eXogenous variables (FARX). The predictive model allows the dynamic patterns of hourly gas flows to be described in a wide range of historical profiles, while also taking the relevant determinants data into account. By taking into account a richer set of information, FARX provides stronger performance in real data analysis, with both accuracy and high computational efficiency. Compared to several alternative models in out-of-sample forecasts, the proposed model can improve forecast accuracy by at least 12% and up to 5-fold for one node, 3% to 2-fold and 2-fold to 4-fold for the other two nodes. The results show that lagged 1-day gas flow and nominations are important predictors, and with their presence in the forecast model, temperature becomes insignificant for short-term predictions. Y1 - 2018 U6 - https://doi.org/https://doi.org/10.1016/j.apenergy.2018.06.137 IS - Volume 228 SP - 1091 EP - 1110 ER - TY - CHAP A1 - Rehfeldt, Daniel A1 - Shinano, Yuji A1 - Koch, Thorsten T1 - SCIP-Jack: An exact high performance solver for Steiner tree problems in graphs and related problems BT - Proceedings of the 7th International Conference on High Performance Scientific Computing T2 - Modeling, Simulation and Optimization of Complex Processes HPSC 2018 N2 - The Steiner tree problem in graphs is one of the classic combinatorial optimization problems. Furthermore, many related problems, such as the rectilinear Steiner tree problem or the maximum-weight connected subgraph problem, have been described in the literature—with a wide range of practical applications. To embrace this wealth of problem classes, the solver SCIP-JACK has been developed as an exact framework for classic Steiner tree and 11 related problems. Moreover, the solver comes with both shared- and distributed memory extensions by means of the UG framework. Besides its versatility, SCIP-JACK is highly competitive for most of the 12 problem classes it can solve, as for instance demonstrated by its top ranking in the recent PACE 2018 Challenge. This article describes the current state of SCIP-JACK and provides up-to-date computational results, including several instances that can now be solved for the first time to optimality. Y1 - 2021 U6 - https://doi.org/10.1007/978-3-030-55240-4_10 PB - Springer ER - TY - GEN A1 - Rehfeldt, Daniel A1 - Hobbie, Hannes A1 - Schönheit, David A1 - Gleixner, Ambros A1 - Koch, Thorsten A1 - Möst, Dominik T1 - A massively parallel interior-point solver for linear energy system models with block structure N2 - Linear energy system models are often a crucial component of system design and operations, as well as energy policy consulting. Such models can lead to large-scale linear programs, which can be intractable even for state-of-the-art commercial solvers|already the available memory on a desktop machine might not be sufficient. Against this backdrop, this article introduces an interior-point solver that exploits common structures of linear energy system models to efficiently run in parallel on distributed memory systems. The solver is designed for linear programs with doubly bordered block-diagonal constraint matrix and makes use of a Schur complement based decomposition. Special effort has been put into handling large numbers of linking constraints and variables as commonly observed in energy system models. In order to handle this strong linkage, a distributed preconditioning of the Schur complement is used. In addition, the solver features a number of more generic techniques such as parallel matrix scaling and structure-preserving presolving. The implementation is based on the existing parallel interior-point solver PIPS-IPM. We evaluate the computational performance on energy system models with up to 700 million non-zero entries in the constraint matrix, and with more than 200 million columns and 250 million rows. This article mainly concentrates on the energy system model ELMOD, which is a linear optimization model representing the European electricity markets by the use of a nodal pricing market clearing. It has been widely applied in the literature on energy system analyses during the recent years. However, it will be demonstrated that the new solver is also applicable to other energy system models. T3 - ZIB-Report - 19-41 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-74321 SN - 1438-0064 N1 - In the meantime, this report got published as a journal article: https://opus4.kobv.de/opus4-zib/frontdoor/index/index/searchtype/authorsearch/author/Hannes+Hobbie/docId/8191/start/1/rows/10 Please use this journal reference when citing this work. ER - TY - GEN A1 - Gleixner, Ambros A1 - Kempke, Nils-Christian A1 - Koch, Thorsten A1 - Rehfeldt, Daniel A1 - Uslu, Svenja T1 - First Experiments with Structure-Aware Presolving for a Parallel Interior-Point Method N2 - In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware implementations of presolving as part of a parallel interior-point method to solve linear programs with block-diagonal structure, including both linking variables and linking constraints. While presolving reductions are often mathematically simple, their implementation in a high-performance computing environment is a complex endeavor. We report results on impact, performance, and scalability of the resulting presolving routines on real-world energy system models with up to 700 million nonzero entries in the constraint matrix. T3 - ZIB-Report - 19-39 KW - block structure KW - energy system models KW - interior-point method KW - high performance computing KW - linear programming KW - parallelization KW - presolving KW - preprocessing Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-74084 SN - 1438-0064 ER - TY - GEN A1 - Gleixner, Ambros A1 - Eifler, Leon A1 - Gally, Tristan A1 - Gamrath, Gerald A1 - Gemander, Patrick A1 - Gottwald, Robert Lion A1 - Hendel, Gregor A1 - Hojny, Christopher A1 - Koch, Thorsten A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Viernickel, Jan Merlin A1 - Vigerske, Stefan A1 - Weninger, Dieter A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 5.0 N2 - This article describes new features and enhanced algorithms made available in version 5.0 of the SCIP Optimization Suite. In its central component, the constraint integer programming solver SCIP, remarkable performance improvements have been achieved for solving mixed-integer linear and nonlinear programs. On MIPs, SCIP 5.0 is about 41 % faster than SCIP 4.0 and over twice as fast on instances that take at least 100 seconds to solve. For MINLP, SCIP 5.0 is about 17 % faster overall and 23 % faster on instances that take at least 100 seconds to solve. This boost is due to algorithmic advances in several parts of the solver such as cutting plane generation and management, a new adaptive coordination of large neighborhood search heuristics, symmetry handling, and strengthened McCormick relaxations for bilinear terms in MINLPs. Besides discussing the theoretical background and the implementational aspects of these developments, the report describes recent additions for the other software packages connected to SCIP, in particular for the LP solver SoPlex, the Steiner tree solver SCIP-Jack, the MISDP solver SCIP-SDP, and the parallelization framework UG. T3 - ZIB-Report - 17-61 KW - constraint integer programming KW - linear programming KW - mixed-integer linear programming KW - mixed-integer nonlinear programming KW - optimization solver KW - branch-and-cut KW - branch-and-price KW - column generation framework KW - parallelization KW - mixed-integer semidefinite programming KW - Steiner tree optimization Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66297 SN - 1438-0064 ER - TY - GEN 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 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. T3 - ZIB-Report - 15-53 KW - Mixed Integer Programming KW - Parallel processing KW - Node merging KW - Racing ParaSCIP KW - Ubiquity Generator Framework KW - MIPLIB Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-56404 SN - 1438-0064 ER - TY - GEN A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Reduction-based exact solution of prize-collecting Steiner tree problems T3 - ZIB-Report - 18-55 Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-70958 SN - 1438-0064 ER - TY - GEN A1 - Shinano, Yuji A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Building Optimal Steiner Trees on Supercomputers by using up to 43,000 Cores N2 - SCIP-JACK is a customized, branch-and-cut based solver for Steiner tree and related problems. ug [SCIP-JACK, MPI] extends SCIP-JACK to a massively par- allel solver by using the Ubiquity Generator (UG) framework. ug [SCIP-JACK, MPI] was the only solver that could run on a distributed environment at the (latest) 11th DIMACS Challenge in 2014. Furthermore, it could solve three well-known open instances and updated 14 best known solutions to instances from the bench- mark libary STEINLIB. After the DIMACS Challenge, SCIP-JACK has been con- siderably improved. However, the improvements were not reflected on ug [SCIP- JACK, MPI]. This paper describes an updated version of ug [SCIP-JACK, MPI], especially branching on constrains and a customized racing ramp-up. Furthermore, the different stages of the solution process on a supercomputer are described in detail. We also show the latest results on open instances from the STEINLIB. T3 - ZIB-Report - 18-58 Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-71118 SN - 1438-0064 ER - TY - JOUR A1 - Gleixner, Ambros A1 - Hendel, Gregor A1 - Gamrath, Gerald A1 - Achterberg, Tobias A1 - Bastubbe, Michael A1 - Berthold, Timo A1 - Christophel, Philipp M. A1 - Jarck, Kati A1 - Koch, Thorsten A1 - Linderoth, Jeff A1 - Lübbecke, Marco A1 - Mittelmann, Hans A1 - Ozyurt, Derya A1 - Ralphs, Ted A1 - Salvagnin, Domenico A1 - Shinano, Yuji T1 - MIPLIB 2017: Data-Driven Compilation of the 6th Mixed-Integer Programming Library JF - Mathematical Programming Computation N2 - We report on the selection process leading to the sixth version of the Mixed Integer Programming Library. Selected from an initial pool of over 5,000 instances, the new MIPLIB 2017 collection consists of 1,065 instances. A subset of 240 instances was specially selected for benchmarking solver performance. For the first time, the compilation of these sets was done using a data-driven selection process supported by the solution of a sequence of mixed integer optimization problems, which encoded requirements on diversity and balancedness with respect to instance features and performance data. Y1 - 2021 U6 - https://doi.org/10.1007/s12532-020-00194-3 VL - 13 IS - 3 SP - 443 EP - 490 ER - TY - CHAP A1 - Bley, Andreas A1 - Gleixner, Ambros A1 - Koch, Thorsten A1 - Vigerske, Stefan T1 - Comparing MIQCP Solvers to a Specialised Algorithm for Mine Production Scheduling T2 - Modeling, Simulation and Optimization of Complex Processes. Proceedings of the Fourth International Conference on High Performance Scientific Computing, March 2-6, 2009, Hanoi, Vietnam N2 - 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. Y1 - 2012 U6 - https://doi.org/10.1007/978-3-642-25707-0_3 SP - 25 EP - 39 ER - TY - GEN A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu A1 - Koch, Thorsten T1 - Cutting Plane Selection with Analytic Centers and Multiregression N2 - Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of a cut by quantifying the extent to which it separates relevant parts of the relaxed feasible set. For this purpose, we use the analytic centers of the relaxation polytope or of its optimal face, as well as alternative optimal solutions of the linear programming relaxation. We assess the impact of the choice of distance measure on root node performance and throughout the whole branch-and-bound tree, comparing our measures against those prevalent in the literature. Finally, by a multi-output regression, we predict the relative performance of each measure, using static features readily available before the separation process. Our results indicate that analytic center-based methods help to significantly reduce the number of branch-and-bound nodes needed to explore the search space and that our multiregression approach can further improve on any individual method. T3 - ZIB-Report - 22-28 KW - cut selection KW - anlalytic center KW - mixed-integer programming Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89065 SN - 1438-0064 ER - TY - GEN A1 - Bley, Andreas A1 - Gleixner, Ambros A1 - Koch, Thorsten A1 - Vigerske, Stefan T1 - Comparing MIQCP solvers to a specialised algorithm for mine production scheduling N2 - 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. T3 - ZIB-Report - 09-32 Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11507 SN - 1438-0064 ER - TY - JOUR A1 - Chen, Ying A1 - Xu, Xiuqin A1 - Koch, Thorsten T1 - Day-ahead high-resolution forecasting of natural gas demand and supply in Germany with a hybrid model JF - Applied Energy N2 - As the natural gas market is moving towards short-term planning, accurate and robust short-term forecasts of the demand and supply of natural gas is of fundamental importance for a stable energy supply, a natural gas control schedule, and transport operation on a daily basis. We propose a hybrid forecast model, Functional AutoRegressive and Convolutional Neural Network model, based on state-of-the-art statistical modeling and artificial neural networks. We conduct short-term forecasting of the hourly natural gas flows of 92 distribution nodes in the German high-pressure gas pipeline network, showing that the proposed model provides nice and stable accuracy for different types of nodes. It outperforms all the alternative models, with an improved relative accuracy up to twofold for plant nodes and up to fourfold for municipal nodes. For the border nodes with rather flat gas flows, it has an accuracy that is comparable to the best performing alternative model. KW - Natural gas flow forecasting KW - Neural network KW - Hybrid model KW - Functional autoregressive Y1 - 2020 U6 - https://doi.org/https://doi.org/10.1016/j.apenergy.2019.114486 VL - 262 IS - 114486 ER - TY - GEN A1 - Tjusila, Gennesaret A1 - Besancon, Mathieu A1 - Turner, Mark A1 - Koch, Thorsten T1 - How Many Clues To Give? A Bilevel Formulation For The Minimum Sudoku Clue Problem N2 - It has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in any puzzle whose unique solution is the given grid? We call this problem the Minimum Sudoku Clue Problem (MSCP). We formulate MSCP as a binary bilevel linear program, present a class of globally valid inequalities, and provide a computational study on 50 MSCP instances of 9 by 9 Sudoku grids. Using a general bilevel solver, we solve 95\% of instances to optimality, and show that the solution process benefits from the addition of a moderate amount of inequalities. Finally, we extend the proposed model to other combinatorial problems in which uniqueness of the solution is of interest. T3 - ZIB-Report - 23-15 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-90902 ER - TY - GEN A1 - Shinano, Yuji A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Winkler, Michael T1 - Solving Previously Unsolved MIP Instances with ParaSCIP on Supercomputers by using up to 80,000 Cores N2 - Mixed-integer programming (MIP) problem is arguably among the hardest classes of optimization problems. This paper describes how we solved 21 previously unsolved 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. T3 - ZIB-Report - 20-16 KW - Mixed Integer Programming, Parallel processing, Node merging, Racing, ParaSCIP, Ubiquity Generator Framework, MIPLIB Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78393 SN - 1438-0064 ER - TY - GEN A1 - Gamrath, Gerald A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Miltenberger, Matthias A1 - Weninger, Dieter T1 - Progress in Presolving for Mixed Integer Programming N2 - Presolving attempts to eliminate redundant information from the problem formulation and simultaneously tries to strengthen the formulation. It can be very effective and is often essential for solving instances. Especially for mixed integer programming problems, fast and effective presolving algorithms are very important. In this paper, we report on three new presolving techniques. The first method searches for singleton continuous columns and tries to fix the corresponding variables. Then we present a presolving technique which exploits a partial order of the variables to induce fixings. Finally, we show an approach based on connected components in graphs. Our computational results confirm the profitable use of the algorithms in practice. T3 - ZIB-Report - 13-48 KW - mixed-integer programming KW - presolving KW - preprocessing Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42530 SN - 1438-0064 ER - TY - JOUR A1 - Dell’Amico, M. A1 - Hadjidimitriou, Natalia Selini A1 - Koch, Thorsten A1 - Petkovic, Milena T1 - Forecasting Natural Gas Flows in Large Networks JF - Machine Learning, Optimization, and Big Data. MOD 2017. N2 - Natural gas is the cleanest fossil fuel since it emits the lowest amount of other remains after being burned. Over the years, natural gas usage has increased significantly. Accurate forecasting is crucial for maintaining gas supplies, transportation and network stability. This paper presents two methodologies to identify the optimal configuration o parameters of a Neural Network (NN) to forecast the next 24 h of gas flow for each node of a large gas network. In particular the first one applies a Design Of Experiments (DOE) to obtain a quick initial solution. An orthogonal design, consisting of 18 experiments selected among a total of 4.374 combinations of seven parameters (training algorithm, transfer function, regularization, learning rate, lags, and epochs), is used. The best result is selected as initial solution of an extended experiment for which the Simulated Annealing is run to find the optimal design among 89.100 possible combinations of parameters. The second technique is based on the application of Genetic Algorithm for the selection of the optimal parameters of a recurrent neural network for time series forecast. GA was applied with binary representation of potential solutions, where subsets of bits in the bit string represent different values for several parameters of the recurrent neural network. We tested these methods on three municipal nodes, using one year and half of hourly gas flow to train the network and 60 days for testing. Our results clearly show that the presented methodologies bring promising results in terms of optimal configuration of parameters and forecast error. Y1 - 2018 U6 - https://doi.org/https://doi.org/10.1007/978-3-319-72926-8_14 VL - Lecture Notes in Computer Science IS - vol 10710 SP - 158 EP - 171 ER - TY - JOUR A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Combining NP-Hard Reduction Techniques and Strong Heuristics in an Exact Algorithm for the Maximum-Weight Connected Subgraph Problem JF - SIAM Journal on Optimization N2 - 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. Y1 - 2019 U6 - https://doi.org/10.1137/17M1145963 VL - 29 IS - 1 SP - 369 EP - 398 PB - Society for Industrial and Applied Mathematics ER - TY - GEN A1 - Ralphs, Ted A1 - Shinano, Yuji A1 - Berthold, Timo A1 - Koch, Thorsten ED - Hamadi, Youssef T1 - Parallel Solvers for Mixed Integer Linear Optimization T2 - Handbook of Parallel Constraint Reasoning Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-63516-3_8 SP - 283 EP - 336 PB - Springer Nature ER - TY - CHAP A1 - Breuer, Thomas A1 - Bussieck, Michael A1 - Cao, Karl-Kien A1 - Cebulla, Felix A1 - Fiand, Frederik A1 - Gils, Hans Christian A1 - Gleixner, Ambros A1 - Khabi, Dmitry A1 - Koch, Thorsten A1 - Rehfeldt, Daniel A1 - Wetzel, Manuel T1 - Optimizing Large-Scale Linear Energy System Problems with Block Diagonal Structure by Using Parallel Interior-Point Methods T2 - Operations Research Proceedings 2017 N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-89920-6_85 SP - 641 EP - 647 PB - Springer International Publishing ER - TY - CHAP A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - SCIP-Jack—a solver for STP and variants with parallelization extensions: An update T2 - Operations Research Proceedings 2017 N2 - 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. Y1 - 2018 SP - 191 EP - 196 ER - TY - GEN A1 - Gleixner, Ambros A1 - Bastubbe, Michael A1 - Eifler, Leon A1 - Gally, Tristan A1 - Gamrath, Gerald A1 - Gottwald, Robert Lion A1 - Hendel, Gregor A1 - Hojny, Christopher A1 - Koch, Thorsten A1 - Lübbecke, Marco A1 - Maher, Stephen J. A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schlösser, Franziska A1 - Schubert, Christoph A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Viernickel, Jan Merlin A1 - Walter, Matthias A1 - Wegscheider, Fabian A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 6.0 N2 - 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 6.0 of the SCIP Optimization Suite. Besides performance improvements of the MIP and MINLP core achieved by new primal heuristics and a new selection criterion for cutting planes, one focus of this release are decomposition algorithms. Both SCIP and the automatic decomposition solver GCG now include advanced functionality for performing Benders’ decomposition in a generic framework. GCG’s detection loop for structured matrices and the coordination of pricing routines for Dantzig-Wolfe decomposition has been significantly revised for greater flexibility. Two SCIP extensions have been added to solve the recursive circle packing problem by a problem-specific column generation scheme and to demonstrate the use of the new Benders’ framework for stochastic capacitated facility location. Last, not least, the report presents updates and additions to the other components and extensions of the SCIP Optimization Suite: the LP solver SoPlex, the modeling language Zimpl, the parallelization framework UG, the Steiner tree solver SCIP-Jack, and the mixed-integer semidefinite programming solver SCIP-SDP. T3 - ZIB-Report - 18-26 KW - constraint integer programming KW - linear programming KW - mixed-integer linear programming KW - mixed-integer nonlinear programming KW - optimization solver KW - branch-and-cut KW - branch-and-price KW - column generation framework KW - parallelization KW - mixed-integer semidefinite programming KW - Steiner tree optimization Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-69361 SN - 1438-0064 ER - TY - JOUR 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 JF - Mathematical Programming Computation Y1 - 2011 UR - http://mpc.zib.de/index.php/MPC/article/view/56 U6 - https://doi.org/10.1007/s12532-011-0025-9 VL - 3 IS - 2 SP - 103 EP - 163 ER - TY - CHAP A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Koch, Thorsten A1 - Wolter, Kati ED - Perron, Laurent ED - Trick, Michael T1 - Constraint Integer Programming: A New Approach to Integrate CP and MIP T2 - Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 5th International Conference, CPAIOR 2008 Y1 - 2008 U6 - https://doi.org/10.1007/978-3-540-68155-7_4 VL - 5015 SP - 6 EP - 20 PB - Springer ER - TY - CHAP A1 - Bley, Andreas A1 - Koch, Thorsten T1 - Integer programming approaches to access and backbone IP-network planning T2 - Modeling, Simulation and Optimization of Complex Processes, Proceedings of the 3rd International Conference on High Performance Scientific Computing, March 6-10, Hanoi, Vietnam Y1 - 2008 UR - http://opus.kobv.de/zib/volltexte/2002/709/ SP - 87 EP - 110 PB - Springer ER - TY - JOUR A1 - Eisenblätter, Andreas A1 - Geerdes, Hans-Florian A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Wessäly, Roland T1 - UMTS Radio Network Evaluation and Optimization beyond Snapshots JF - Mathematical Methods of Operations Research Y1 - 2005 UR - http://opus.kobv.de/zib/volltexte/2004/791/ U6 - https://doi.org/10.1007/s00186-005-0002-z VL - 63 IS - 1 SP - 1 EP - 29 ER - TY - JOUR A1 - Bley, Andreas A1 - Koch, Thorsten T1 - Optimierung des G-WiN JF - DFN-Mitteilungen Y1 - 2000 UR - http://www.dfn.de/content/fileadmin/5Presse/DFNMitteilungen/heft54.pdf IS - 54 SP - 13 EP - 15 ER - TY - JOUR A1 - Abboud, Nadine A1 - Grötschel, Martin A1 - Koch, Thorsten T1 - Mathematical methods for physical layout of printed circuit boards: an overview JF - OR Spectrum Y1 - 2008 U6 - https://doi.org/10.1007/s00291-007-0080-9 VL - 30 IS - 3 SP - 453 EP - 468 ER - TY - JOUR A1 - Achterberg, Tobias A1 - Grötschel, Martin A1 - Koch, Thorsten T1 - Teaching MIP Modeling and Solving JF - OR/MS Today Y1 - 2006 UR - http://www.lionhrtpub.com/orms/orms-12-06/freducation.html VL - 33 IS - 6 SP - 14 EP - 15 ER - TY - GEN A1 - Fügenschuh, Armin A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Szabó, Jácint T1 - Gas Network Topology Optimization for Upcoming Market Requirements 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. T3 - ZIB-Report - 11-09 KW - Mathematical Optimization KW - Gas Distribution Networks KW - Topology Planning Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12348 ER - TY - GEN A1 - Bley, Andreas A1 - Koch, Thorsten A1 - Niu, Lingfeng T1 - Experiments with nonlinear extensions to SCIP N2 - This paper describes several experiments to explore the options for solving a class of mixed integer nonlinear programming problems that stem from a real-world mine production planning project. The only type of nonlinear constraints in these problems are bilinear equalities involving continuous variables, which enforce the ratios between elements in mixed material streams. A branch-and-bound algorithm to handle the integer variables has been tried in another project. However, this branch-and-bound algorithm is not effective for handling the nonlinear constraints. Therefore state-of-the-art nonlinear solvers are utilized to solve the resulting nonlinear subproblems in this work. The experiments were carried out using the NEOS server for optimization. After finding that current nonlinear programming solvers seem to lack suitable preprocessing capabilities, we preprocess the instances beforehand and use an heuristic approach to solve the nonlinear subproblems. In the appendix, we explain how to add a polynomial constraint handler that uses IPOPT as embedded nonlinear programming solver for the constraint programming framework SCIP. This is one of the crucial steps for implementing our algorithm in SCIP. We briefly described our approach and give an idea of the work involved. T3 - ZIB-Report - 08-28 Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8300 SN - 1438-0064 ER - TY - CHAP A1 - Eisenblätter, Andreas A1 - Fügenschuh, Armin A1 - Koch, Thorsten A1 - Koster, Arie M.C.A. A1 - Martin, Alexander A1 - Pfender, Tobias A1 - Wegel, Oliver A1 - Wessäly, Roland ED - G. Anandalingam, S. T1 - Mathematical Model of Feasible Network Configurations for UMTS T2 - Telecommunications network design and management Y1 - 2002 SP - 1 EP - 24 PB - Kluwer ER - 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 -