TY - JOUR A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Implications, Conflicts, and Reductions for Steiner Trees JF - Mathematical Programming Y1 - 2023 U6 - https://doi.org/10.1007/s10107-021-01757-5 VL - 197 SP - 903 EP - 966 PB - Springer 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 U6 - https://doi.org/10.1016/j.ejor.2024.04.026 VL - 317 IS - 2 SP - 616 EP - 630 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 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - On the exact solution of prize-collecting Steiner tree problems JF - INFORMS Journal on Computing Y1 - 2021 U6 - https://doi.org/10.1287/ijoc.2021.1087 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 - JOUR A1 - Rehfeldt, Daniel A1 - Franz, Henriette A1 - Koch, Thorsten T1 - Optimal Connected Subgraphs: Integer Programming Formulations and Polyhedra JF - Networks Y1 - 2022 U6 - https://doi.org/10.1002/net.22101 VL - 80 IS - 3 SP - 314 EP - 332 PB - Wiley 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 - JOUR A1 - Rehfeldt, Daniel A1 - Koch, Thorsten A1 - Shinano, Yuji T1 - Faster exact solution of sparse MaxCut and QUBO problems JF - Mathematical Programming Computation N2 - The maximum-cut problem is one of the fundamental problems in combinatorial optimization. With the advent of quantum computers, both the maximum-cut and the equivalent quadratic unconstrained binary optimization problem have experienced much interest in recent years. This article aims to advance the state of the art in the exact solution of both problems—by using mathematical programming techniques. The main focus lies on sparse problem instances, although also dense ones can be solved. We enhance several algorithmic components such as reduction techniques and cutting-plane separation algorithms, and combine them in an exact branch-and-cut solver. Furthermore, we provide a parallel implementation. The new solver is shown to significantly outperform existing state-of-the-art software for sparse maximum-cut and quadratic unconstrained binary optimization instances. Furthermore, we improve the best known bounds for several instances from the 7th DIMACS Challenge and the QPLIB, and solve some of them (for the first time) to optimality. Y1 - 2023 U6 - https://doi.org/10.1007/s12532-023-00236-6 VL - 15 SP - 445 EP - 470 ER - TY - JOUR A1 - Rehfeldt, Daniel T1 - Faster Algorithms for Steiner Tree and related Problems: From Theory to Practice JF - OR News: Das Magazin der GOR Y1 - 2022 ER - TY - JOUR A1 - Kempke, Nils-Christian A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - A Massively Parallel Interior-Point-Method for Arrowhead Linear Programs JF - SIAM Journal on Scientific Computing Y1 - 2025 ER -