TY - THES A1 - Rehfeldt, Daniel T1 - A Generic Approach to Solving the Steiner Tree Problem and Variants N2 - Spawned by practical applications, numerous variations of the classical Steiner tree problem in graphs have been studied during the last decades. Despite the strong relationship between the different variants, solution approaches employed so far have been prevalently problem-specific. In contrast, we pursue a general-purpose strategy resulting in a solver able to solve both the classical Steiner tree problem and ten of its variants without modification. These variants include well-known problems such as the prize-collecting Steiner tree problem, the maximum-weight connected subgraph problem or the rectilinear minimum Steiner tree problem. Bolstered by a variety of new methods, most notably reduction techniques, our solver is not only of unprecedented versatility, but furthermore competitive or even superior to specialized state-of-the-art programs for several Steiner problem variants. KW - Steiner Tree Problem KW - Steiner Tree Problem Variants Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57817 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 - 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 - Sun, Yahui A1 - Rehfeldt, Daniel A1 - Brazil, Marcus A1 - Thomas, Doreen A1 - Halgamuge, Saman T1 - A Physarum-Inspired Algorithm for Minimum-Cost Relay Node Placement in Wireless Sensor Networks JF - IEEE/ACM Transactions on Networking Y1 - 2020 U6 - https://doi.org/10.1109/TNET.2020.2971770 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 - 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 - JOUR A1 - Pedersen, Jaap A1 - Weinand, Jann Michael A1 - Syranidou, Chloi A1 - Rehfeldt, Daniel T1 - An efficient solver for large-scale onshore wind farm siting including cable routing JF - European Journal of Operational Research N2 - Existing planning approaches for onshore wind farm siting and grid integration often do not meet minimum cost solutions or social and environmental considerations. In this paper, we develop an exact approach for the integrated layout and cable routing problem of onshore wind farm planning using the Quota Steiner tree problem. Applying a novel transformation on a known directed cut formulation, reduction techniques, and heuristics, we design an exact solver that makes large problem instances solvable and outperforms generic MIP solvers. In selected regions of Germany, the trade-offs between minimizing costs and landscape impact of onshore wind farm siting are investigated. Although our case studies show large trade-offs between the objective criteria of cost and landscape impact, small burdens on one criterion can significantly improve the other criteria. In addition, we demonstrate that contrary to many approaches for exclusive turbine siting, grid integration must be simultaneously optimized to avoid excessive costs or landscape impacts in the course of a wind farm project. Our novel problem formulation and the developed solver can assist planners in decision-making and help optimize wind farms in large regions in the future. Y1 - 2024 ER - TY - GEN A1 - Pedersen, Jaap A1 - Weinand, Jann Michael A1 - Syranidou, Chloi A1 - Rehfeldt, Daniel T1 - An efficient solver for multi-objective onshore wind farm siting and network integration N2 - Existing planning approaches for onshore wind farm siting and network integration often do not meet minimum cost solutions or social and environmental considerations. In this paper, we develop an approach for the multi-objective optimization of turbine locations and their network connection using a Quota Steiner tree problem. Applying a novel transformation on a known directed cut formulation, reduction techniques, and heuristics, we design an exact solver that makes large problem instances solvable and outperforms generic MIP solvers. Although our case studies in selected regions of Germany show large trade-offs between the objective criteria of cost and landscape impact, small burdens on one criterion can significantly improve the other criteria. In addition, we demonstrate that contrary to many approaches for exclusive turbine siting, network integration must be simultaneously optimized in order to avoid excessive costs or landscape impacts in the course of a wind farm project. Our novel problem formulation and the developed solver can assist planners in decision making and help optimize wind farms in large regions in the future. T3 - ZIB-Report - 23-10 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-90590 SN - 1438-0064 ER - TY - CHAP A1 - Koch, Thorsten A1 - Rehfeldt, Daniel A1 - Shinano, Yuji T1 - An exact high performance solver for Steiner tree problems in graphs and related problems T2 - Modeling, Simulation and Optimization of Complex Processes HPSC 2018 Y1 - 2020 PB - Springer 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 -