@misc{ShinanoRehfeldtKoch2018, author = {Shinano, Yuji and Rehfeldt, Daniel and Koch, Thorsten}, title = {Building Optimal Steiner Trees on Supercomputers by using up to 43,000 Cores}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71118}, year = {2018}, abstract = {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.}, language = {en} } @article{SunRehfeldtBraziletal.2020, author = {Sun, Yahui and Rehfeldt, Daniel and Brazil, Marcus and Thomas, Doreen and Halgamuge, Saman}, title = {A Physarum-Inspired Algorithm for Minimum-Cost Relay Node Placement in Wireless Sensor Networks}, journal = {IEEE/ACM Transactions on Networking}, doi = {10.1109/TNET.2020.2971770}, year = {2020}, language = {en} } @article{RehfeldtKochShinano2023, author = {Rehfeldt, Daniel and Koch, Thorsten and Shinano, Yuji}, title = {Faster exact solution of sparse MaxCut and QUBO problems}, volume = {15}, journal = {Mathematical Programming Computation}, doi = {10.1007/s12532-023-00236-6}, pages = {445 -- 470}, year = {2023}, abstract = {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.}, language = {en} } @inproceedings{Rehfeldt2022, author = {Rehfeldt, Daniel}, title = {Faster Algorithms for Steiner Tree and related Problems: From Theory to Practice}, booktitle = {Operations Research Proceedings 2022}, year = {2022}, language = {en} } @article{Rehfeldt2022, author = {Rehfeldt, Daniel}, title = {Faster Algorithms for Steiner Tree and related Problems: From Theory to Practice}, journal = {OR News: Das Magazin der GOR}, year = {2022}, language = {en} } @misc{RehfeldtFujisawaKochetal.2022, author = {Rehfeldt, Daniel and Fujisawa, Katsuki and Koch, Thorsten and Nakao, Masahiro and Shinano, Yuji}, title = {Computing single-source shortest paths on graphs with over 8 trillion edges}, issn = {1438-0064}, doi = {10.12752/8818}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-88180}, year = {2022}, abstract = {This paper introduces an implementation for solving the single-source shortest path problem on distributed-memory machines. It is tailored to power-law graphs and scales to trillions of edges. The new implementation reached 2nd and 10th place in the latest Graph500 benchmark in June 2022 and handled the largest and second-largest graphs among all participants.}, language = {en} } @article{KempkeRehfeldtKoch2025, author = {Kempke, Nils-Christian and Rehfeldt, Daniel and Koch, Thorsten}, title = {A Massively Parallel Interior-Point-Method for Arrowhead Linear Programs}, journal = {SIAM Journal on Scientific Computing}, arxiv = {http://arxiv.org/abs/2412.07731}, year = {2025}, language = {en} } @misc{PedersenLindnerRehfeldtetal.2025, author = {Pedersen, Jaap and Lindner, Niels and Rehfeldt, Daniel and Koch, Thorsten}, title = {Integrated Wind Farm Design: Optimizing Turbine Placement and Cable Routing with Wake Effects}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-99218}, year = {2025}, abstract = {An accelerated deployment of renewable energy sources is crucial for a successful transformation of the current energy system, with wind energy playing a key role in this transition. This study addresses the integrated wind farm layout and cable routing problem, a challenging nonlinear optimization problem. We model this problem as an extended version of the Quota Steiner Tree Problem (QSTP), optimizing turbine placement and network connectivity simultaneously to meet specified expansion targets. Our proposed approach accounts for the wake effect - a region of reduced wind speed induced by each installed turbine - and enforces minimum spacing between turbines. We introduce an exact solution framework in terms of the novel Quota Steiner Tree Problem with interference (QSTPI). By leveraging an interference-based splitting strategy, we develop an advanced solver capable of tackling large-scale problem instances. The presented approach outperforms generic state-of-the-art mixed integer programming solvers on our dataset by up to two orders of magnitude. Moreover, we demonstrate that our integrated method significantly reduces the costs in contrast to a sequential approach. Thus, we provide a planning tool that enhances existing planning methodologies for supporting a faster and cost-efficient expansion of wind energy.}, language = {en} } @misc{PedersenWeinandSyranidouetal.2023, author = {Pedersen, Jaap and Weinand, Jann Michael and Syranidou, Chloi and Rehfeldt, Daniel}, title = {An efficient solver for multi-objective onshore wind farm siting and network integration}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-90590}, year = {2023}, abstract = {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.}, language = {en} } @incollection{KochRehfeldtShinano2020, author = {Koch, Thorsten and Rehfeldt, Daniel and Shinano, Yuji}, title = {An exact high performance solver for Steiner tree problems in graphs and related problems}, booktitle = {Modeling, Simulation and Optimization of Complex Processes HPSC 2018}, publisher = {Springer}, year = {2020}, language = {en} } @misc{RehfeldtKoch2020, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {Implications, conflicts, and reductions for Steiner trees}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-80039}, year = {2020}, language = {en} }