TY - GEN A1 - Witzig, Jakob A1 - Berthold, Timo T1 - Conflict-Free Learning for Mixed Integer Programming N2 - Conflict learning plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. A major step for MIP conflict learning is to aggregate the LP relaxation of an infeasible subproblem to a single globally valid constraint, the dual proof, that proves infeasibility within the local bounds. Among others, one way of learning is to add these constraints to the problem formulation for the remainder of the search. We suggest to not restrict this procedure to infeasible subproblems, but to also use global proof constraints from subproblems that are not (yet) infeasible, but can be expected to be pruned soon. As a special case, we also consider learning from integer feasible LP solutions. First experiments of this conflict-free learning strategy show promising results on the MIPLIB2017 benchmark set. T3 - ZIB-Report - 19-59 KW - mixed integer programming KW - conflict analysis KW - dual proof analysis KW - no-good learning KW - solution learning Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-75338 SN - 1438-0064 ER - TY - CHAP A1 - Witzig, Jakob A1 - Berthold, Timo T1 - Conflict-Free Learning for Mixed Integer Programming T2 - Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2020 N2 - Conflict learning plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. A major step for MIP conflict learning is to aggregate the LP relaxation of an infeasible subproblem to a single globally valid constraint, the dual proof, that proves infeasibility within the local bounds. Among others, one way of learning is to add these constraints to the problem formulation for the remainder of the search. We suggest to not restrict this procedure to infeasible subproblems, but to also use global proof constraints from subproblems that are not (yet) infeasible, but can be expected to be pruned soon. As a special case, we also consider learning from integer feasible LP solutions. First experiments of this conflict-free learning strategy show promising results on the MIPLIB2017 benchmark set. Y1 - 2020 U6 - https://doi.org/10.1007/978-3-030-58942-4_34 IS - 12296 SP - 521 EP - 530 PB - Springer, Cham. 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 - Rehfeldt, Daniel A1 - Hobbie, Hannes A1 - Schönheit, David A1 - Koch, Thorsten A1 - Möst, Dominik A1 - Gleixner, Ambros T1 - A massively parallel interior-point solver for LPs with generalized arrowhead structure, and applications to energy system models JF - European Journal of Operational Research N2 - Linear energy system models are a crucial component of energy system design and operations, as well as energy policy consulting. If detailed enough, such models lead to large-scale linear programs, which can be intractable even for the best state-of-the-art solvers. This article introduces an interior-point solver that exploits common structures of 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. In order to handle the large number of linking constraints and variables commonly observed in energy system models, a distributed Schur complement preconditioner 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 solver PIPS-IPM. We evaluate the computational performance on energy system models with up to four billion nonzero entries in the constraint matrix—and up to one billion columns and one billion 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 in recent years. However, it will be demonstrated that the new solver is also applicable to other energy system models. Y1 - 2022 U6 - https://doi.org/10.1016/j.ejor.2021.06.063 VL - 296 IS - 1 SP - 60 EP - 71 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 - GEN A1 - Shinano, Yuji A1 - Rehfeldt, Daniel A1 - Galley, Tristan T1 - An Easy Way to Build Parallel State-of-the-art Combinatorial Optimization Problem Solvers: A Computational Study on Solving Steiner Tree Problems and Mixed Integer Semidefinite Programs by using ug[SCIP-*,*]-libraries N2 - Branch-and-bound (B&B) is an algorithmic framework for solving NP-hard combinatorial optimization problems. Although several well-designed software frameworks for parallel B&B have been developed over the last two decades, there is very few literature about successfully solving previously intractable combinatorial optimization problem instances to optimality by using such frameworks.The main reason for this limited impact of parallel solvers is that the algorithmic improvements for specific problem types are significantly greater than performance gains obtained by parallelization in general. Therefore, in order to solve hard problem instances for the first time, one needs to accelerate state-of-the-art algorithm implementations. In this paper, we present a computational study for solving Steiner tree problems and mixed integer semidefinite programs in parallel. These state-of-the-art algorithm implementations are based on SCIP and were parallelized via the ug[SCIP-*,*]-libraries---by adding less than 200 lines of glue code. Despite the ease of their parallelization, these solvers have the potential to solve previously intractable instances. In this paper, we demonstrate the convenience of such a parallelization and present results for previously unsolvable instances from the well-known PUC benchmark set, widely regarded as the most difficult Steiner tree test set in the literature. T3 - ZIB-Report - 19-14 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-72804 SN - 1438-0064 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 - Witzig, Jakob A1 - Berthold, Timo A1 - Heinz, Stefan T1 - Computational Aspects of Infeasibility Analysis in Mixed Integer Programming N2 - The analysis of infeasible subproblems plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from infeasible subproblems. The first is to analyze the sequence of implications, obtained by domain propagation, that led to infeasibility. The result of this analysis is one or more sets of contradicting variable bounds from which so-called conflict constraints can be generated. This concept is called conflict graph analysis and has its origin in solving satisfiability problems and is similarly used in constraint programming. The second concept is to analyze infeasible linear programming (LP) relaxations. Every ray of the dual LP provides a set of multipliers that can be used to generate a single new globally valid linear constraint. This method is called dual proof analysis. The main contribution of this paper is twofold. Firstly, we present three enhancements of dual proof analysis: presolving via variable cancellation, strengthening by applying mixed integer rounding functions, and a filtering mechanism. Further, we provide an intense computational study evaluating the impact of every presented component regarding dual proof analysis. Secondly, this paper presents the first integrated approach to use both conflict graph and dual proof analysis simultaneously within a single MIP solution process. All experiments are carried out on general MIP instances from the standard public test set MIPLIB 2017; the presented algorithms have been implemented within the non-commercial MIP solver SCIP and the commercial MIP solver FICO Xpress. T3 - ZIB-Report - 19-54 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-74962 SN - 1438-0064 ER - TY - CHAP A1 - Shinano, Yuji A1 - Rehfeldt, Daniel A1 - Gally, Tristan T1 - An Easy Way to Build Parallel State-of-the-art Combinatorial Optimization Problem Solvers: A Computational Study on Solving Steiner Tree Problems and Mixed Integer Semidefinite Programs by using ug[SCIP-*,*]-libraries T2 - Proceedings of the 9th IEEE Workshop Parallel / Distributed Combinatorics and Optimization N2 - Branch-and-bound (B&B) is an algorithmic framework for solving NP-hard combinatorial optimization problems. Although several well-designed software frameworks for parallel B&B have been developed over the last two decades, there is very few literature about successfully solving previously intractable combinatorial optimization problem instances to optimality by using such frameworks.The main reason for this limited impact of parallel solvers is that the algorithmic improvements for specific problem types are significantly greater than performance gains obtained by parallelization in general. Therefore, in order to solve hard problem instances for the first time, one needs to accelerate state-of-the-art algorithm implementations. In this paper, we present a computational study for solving Steiner tree problems and mixed integer semidefinite programs in parallel. These state-of-the-art algorithm implementations are based on SCIP and were parallelized via the ug[SCIP-*,*]-libraries---by adding less than 200 lines of glue code. Despite the ease of their parallelization, these solvers have the potential to solve previously intractable instances. In this paper, we demonstrate the convenience of such a parallelization and present results for previously unsolvable instances from the well-known PUC benchmark set, widely regarded as the most difficult Steiner tree test set in the literature. Y1 - 2019 U6 - https://doi.org/10.1109/IPDPSW.2019.00095 SP - 530 EP - 541 PB - IEEE 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 - JOUR A1 - Munguia, Lluis-Miquel A1 - Oxberry, Geoffrey A1 - Rajan, Deepak A1 - Shinano, Yuji T1 - Parallel PIPS-SBB: Multi-Level Parallelism For Stochastic Mixed-Integer Programs JF - Computational Optimization and Applications N2 - PIPS-SBB is a distributed-memory parallel solver with a scalable data distribution paradigm. It is designed to solve MIPs with a dual-block angular structure, which is characteristic of deterministic-equivalent Stochastic Mixed-Integer Programs (SMIPs). In this paper, we present two different parallelizations of Branch & Bound (B&B), implementing both as extensions of PIPS-SBB, thus adding an additional layer of parallelism. In the first of the proposed frameworks, PIPS-PSBB, the coordination and load-balancing of the different optimization workers is done in a decentralized fashion. This new framework is designed to ensure all available cores are processing the most promising parts of the B&B tree. The second, ug[PIPS-SBB,MPI], is a parallel implementation using the Ubiquity Generator (UG), a universal framework for parallelizing B&B tree search that has been successfully applied to other MIP solvers. We show the effects of leveraging multiple levels of parallelism in potentially improving scaling performance beyond thousands of cores. Y1 - 2019 U6 - https://doi.org/10.1007/s10589-019-00074-0 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 - Munguia, Lluis-Miquel A1 - Oxberry, Geoffrey A1 - Rajan, Deepak A1 - Shinano, Yuji T1 - Parallel PIPS-SBB: Multi-Level Parallelism For Stochastic Mixed-Integer Programs N2 - PIPS-SBB is a distributed-memory parallel solver with a scalable data distribution paradigm. It is designed to solve MIPs with a dual-block angular structure, which is characteristic of deterministic-equivalent Stochastic Mixed-Integer Programs (SMIPs). In this paper, we present two different parallelizations of Branch & Bound (B&B), implementing both as extensions of PIPS-SBB, thus adding an additional layer of parallelism. In the first of the proposed frameworks, PIPS-PSBB, the coordination and load-balancing of the different optimization workers is done in a decentralized fashion. This new framework is designed to ensure all available cores are processing the most promising parts of the B&B tree. The second, ug[PIPS-SBB,MPI], is a parallel implementation using the Ubiquity Generator (UG), a universal framework for parallelizing B&B tree search that has been successfully applied to other MIP solvers. We show the effects of leveraging multiple levels of parallelism in potentially improving scaling performance beyond thousands of cores. T3 - ZIB-Report - 17-58 KW - PIPS-SBB, UG, Parallel Branch and Bound Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65517 SN - 1438-0064 IS - ZIB-Report 17-58 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 - Georges, Alexander A1 - Gleixner, Ambros A1 - Gojic, Gorana A1 - Gottwald, Robert Lion A1 - Haley, David A1 - Hendel, Gregor A1 - Matejczyk, Bartlomiej T1 - Feature-Based Algorithm Selection for Mixed Integer Programming N2 - Mixed integer programming is a versatile and valuable optimization tool. However, solving specific problem instances can be computationally demanding even for cutting-edge solvers. Such long running times are often significantly reduced by an appropriate change of the solver's parameters. In this paper we investigate "algorithm selection", the task of choosing among a set of algorithms the ones that are likely to perform best for a particular instance. In our case, we treat different parameter settings of the MIP solver SCIP as different algorithms to choose from. Two peculiarities of the MIP solving process have our special attention. We address the well-known problem of performance variability by using multiple random seeds. Besides solving time, primal dual integrals are recorded as a second performance measure in order to distinguish solvers that timed out. We collected feature and performance data for a large set of publicly available MIP instances. The algorithm selection problem is addressed by several popular, feature-based methods, which have been partly extended for our purpose. Finally, an analysis of the feature space and performance results of the selected algorithms are presented. T3 - ZIB-Report - 18-17 KW - algorithm selection KW - mixed integer programming Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-68362 SN - 1438-0064 ER - TY - CHAP A1 - Cao, Karl-Kiên A1 - Gleixner, Ambros A1 - Miltenberger, Matthias T1 - Methoden zur Reduktion der Rechenzeit linearer Optimierungsmodelle in der Energiewirtschaft - Eine Performance-Analyse T2 - EnInnov 2016: 14. Symposium Energieinnovation 2016 N2 - Dieser Beitrag stellt mögliche Ansätze zur Reduktion der Rechenzeit von linearen Optimierungsproblemen mit energiewirtschaftlichem Anwendungshintergrund vor. Diese Ansätze bilden im Allgemeinen die Grundlage für konzeptionelle Strategien zur Beschleunigung von Energiesystemmodellen. Zu den einfachsten Beschleunigungsstrategien zählt die Verkleinerung der Modelldimensionen, was beispielsweise durch Ändern der zeitlichen, räumlichen oder technologischen Auflösung eines Energiesystemmodells erreicht werden kann. Diese Strategien sind zwar häufig ein Teil der Methodik in der Energiesystemanalyse, systematische Benchmarks zur Bewertung ihrer Effektivität werden jedoch meist nicht durchgeführt. Die vorliegende Arbeit adressiert genau diesen Sachverhalt. Hierzu werden Modellinstanzen des Modells REMix in verschiedenen Größenordnungen mittels einer Performance-Benchmark-Analyse untersucht. Die Ergebnisse legen zum einen den Schluss nahe, dass verkürzte Betrachtungszeiträume das größte Potential unter den hier analysierten Strategien zur Reduktion von Rechenzeit bieten. Zum anderen empfiehlt sich die Verwendung des Barrier-Lösungsverfahrens mit multiplen Threads unter Vernachlässigung des Cross-Over. Y1 - 2016 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 - 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 - CHAP A1 - Breuer, Thomas A1 - Bussieck, Michael A1 - Cao, Karl-Kien A1 - Fiand, Fred A1 - Gils, Hans-Christian A1 - Gleixner, Ambros A1 - Khabi, Dmitry A1 - Kempke, Nils A1 - Koch, Thorsten A1 - Rehfeldt, Daniel A1 - Wetzel, Manuel T1 - BEAM-ME: Accelerating Linear Energy Systems Models by a Massively Parallel Interior Point Method T2 - NIC Symposium 2020 Y1 - 2020 VL - 50 SP - 345 EP - 352 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 - GEN A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Transformations for the Prize-Collecting Steiner Tree Problem and the Maximum-Weight Connected Subgraph Problem to SAP N2 - 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. T3 - ZIB-Report - 16-36 KW - graph transformation KW - Steiner tree problems 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-59777 SN - 1438-0064 ER - TY - GEN 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 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. T3 - ZIB-Report - 17-75 KW - energy system models KW - interior-point methods KW - high-performance computing Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66183 SN - 1438-0064 ER - TY - GEN A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - SCIP-Jack—a solver for STP and variants with parallelization extensions: An update 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. T3 - ZIB-Report - 18-05 Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66416 SN - 1438-0064 ER - TY - GEN 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 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. T3 - ZIB-Report - 17-45 KW - maximum-weight connected subgraph Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64699 SN - 1438-0064 ER - TY - JOUR 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 JF - Networks 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. Y1 - 2019 U6 - https://doi.org/10.1002/net.21857 VL - 73 SP - 206 EP - 233 PB - Wiley ET - 2 ER - TY - JOUR A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Transformations for the Prize-Collecting Steiner Tree Problem and the Maximum-Weight Connected Subgraph Problem to SAP JF - Journal of Computational Mathematics N2 - 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. Y1 - 2018 U6 - https://doi.org/10.4208/jcm.1709-m2017-0002 VL - 36 IS - 3 SP - 459 EP - 468 ER -