TY - GEN A1 - Anderson, Lovis A1 - Hiller, Benjamin T1 - A Sweep-Plane Algorithm for the Computation of the Volume of a Union of Polytopes N2 - Optimization models often feature disjunctions of polytopes as submodels. Such a disjunctive set is initially (at best) relaxed to its convex hull, which is then refined by branching. To measure the error of the convex relaxation, the (relative) difference between the volume of the convex hull and the volume of the disjunctive set may be used. This requires a method to compute the volume of the disjunctive set. Naively, this can be done via inclusion/exclusion and leveraging the existing code for the volume of polytopes. However, this is often inefficient. We propose a revised variant of an old algorithm by Bieri and Nef (1983) for this purpose. The algorithm uses a sweep-plane to incrementally calculate the volume of the disjunctive set as a function of the offset parameter of the sweep-plane. T3 - ZIB-Report - 18-37 KW - Disjunctive Programming KW - Volume Algorithm KW - Union of Polytopes Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-69489 SN - 1438-0064 ER - TY - GEN A1 - Hiller, Benjamin A1 - Saitenmacher, René A1 - Walther, Tom T1 - Analysis of operating modes of complex compressor stations N2 - We consider the modeling of operation modes for complex compressor stations (i.e., ones with several in- or outlets) in gas networks. In particular, we propose a refined model that allows to precompute tighter relaxations for each operation mode. These relaxations may be used to strengthen the compressor station submodels in gas network optimization problems. We provide a procedure to obtain the refined model from the input data for the original model. This procedure is based on a nontrivial reduction of the graph representing the gas flow through the compressor station in an operation mode. T3 - ZIB-Report - 17-65 KW - bound tightening KW - flow patterns KW - model reformulation KW - multi-way compressor station Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-68179 SN - 1438-0064 ER - TY - GEN A1 - Witzig, Jakob A1 - Gamrath, Gerald A1 - Hiller, Benjamin T1 - Reoptimization Techniques in MIP Solvers N2 - Recently, there have been many successful applications of optimization algorithms that solve a sequence of quite similar mixed-integer programs (MIPs) as subproblems. Traditionally, each problem in the sequence is solved from scratch. In this paper we consider reoptimization techniques that try to benefit from information obtained by solving previous problems of the sequence. We focus on the case that subsequent MIPs differ only in the objective function or that the feasible region is reduced. We propose extensions of the very complex branch-and-bound algorithms employed by general MIP solvers based on the idea to ``warmstart'' using the final search frontier of the preceding solver run. We extend the academic MIP solver SCIP by these techniques to obtain a reoptimizing branch-and-bound solver and report computational results which show the effectiveness of the approach. T3 - ZIB-Report - 15-24 Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-54375 SN - 1438-0064 ER - TY - JOUR A1 - Domschke, Pia A1 - Groß, Martin A1 - Hante, Falk M. A1 - Hiller, Benjamin A1 - Schewe, Lars A1 - Schmidt, Martin T1 - Mathematische Modellierung, Simulation und Optimierung von Gastransportnetzwerken JF - gwf - Gas+Energie Y1 - 2015 VL - 156 IS - 11 SP - 880 EP - 885 ER - TY - GEN A1 - Hiller, Benjamin A1 - Saitenmacher, René A1 - Walther, Tom T1 - Analysis of operating modes of complex compressor stations N2 - We consider the modeling of operation modes for complex compressor stations (i.e., ones with several in- or outlets) in gas networks. In particular, we propose a refined model that allows to precompute tighter relaxations for each operation mode. These relaxations may be used to strengthen the compressor station submodels in gas network optimization problems. We provide a procedure to obtain the refined model from the input data for the original model. T3 - ZIB-Report - 16-61 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61092 SN - 1438-0064 ER - TY - GEN A1 - Hiller, Benjamin A1 - Walther, Tom T1 - Improving branching for disjunctive polyhedral models using approximate convex decompositions N2 - Disjunctive sets arise in a variety of optimization models and much esearch has been devoted to obtain strong relaxations for them. This paper focuses on the evaluation of the relaxation during the branch-and-bound search process. We argue that the branching possibilities (\ie binary variables) of the usual formulations are unsuitable to obtain strong bounds early in the search process as they do not capture the overall shape of the the entire disjunctive set. To analyze and exploit the shape of the disjunctive set we propose to compute a hierarchy of approximate convex decompositions and show how to extend the known formulations to obtain improved branching behavior. T3 - ZIB-Report - 17-68 KW - approximate convex decomposition KW - branch-and-bound KW - convex hull reformulation KW - disjunctive set Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-67462 SN - 1438-0064 ER - TY - JOUR A1 - Hiller, Benjamin A1 - Koch, Thorsten A1 - Schewe, Lars A1 - Schwarz, Robert A1 - Schweiger, Jonas T1 - A System to Evaluate Gas Network Capacities: Concepts and Implementation JF - European Journal of Operational Research N2 - In 2005 the European Union liberalized the gas market with a disruptive change and decoupled trading of natural gas from its transport. The gas is now trans- ported by independent so-called transmissions system operators or TSOs. The market model established by the European Union views the gas transmission network as a black box, providing shippers (gas traders and consumers) the opportunity to transport gas from any entry to any exit. TSOs are required to offer the maximum possible capacities at each entry and exit such that any resulting gas flow can be realized by the network. The revenue from selling these capacities more than one billion Euro in Germany alone, but overestimating the capacity might compromise the security of supply. Therefore, evaluating the available transport capacities is extremely important to the TSOs. This is a report on a large project in mathematical optimization, set out to develop a new toolset for evaluating gas network capacities. The goals and the challenges as they occurred in the project are described, as well as the developments and design decisions taken to meet the requirements. Y1 - 2018 VL - 270 IS - 3 SP - 797 EP - 808 ER - TY - GEN A1 - Hiller, Benjamin A1 - Koch, Thorsten A1 - Schewe, Lars A1 - Schwarz, Robert A1 - Schweiger, Jonas T1 - A System to Evaluate Gas Network Capacities: Concepts and Implementation N2 - In 2005 the European Union liberalized the gas market with a disruptive change and decoupled trading of natural gas from its transport. The gas is now transported by independent so-called transmissions system operators or TSOs. The market model established by the European Union views the gas transmission network as a black box, providing shippers (gas traders and consumers) the opportunity to transport gas from any entry to any exit. TSOs are required to offer the maximum possible capacities at each entry and exit such that any resulting gas flow can be realized by the network. The revenue from selling these capacities more than one billion Euro in Germany alone, but overestimating the capacity might compromise the security of supply. Therefore, evaluating the available transport capacities is extremely important to the TSOs. This is a report on a large project in mathematical optimization, set out to develop a new toolset for evaluating gas network capacities. The goals and the challenges as they occurred in the project are described, as well as the developments and design decisions taken to meet the requirements. T3 - ZIB-Report - 18-11 Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-67438 SN - 1438-0064 N1 - An earlier version of this report is available as ZR 17-03 at https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6193. ER - TY - CHAP A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Lehmann, Thomas A1 - Lenz, Ralf A1 - Morsi, Antonio A1 - Pfetsch, Marc A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Stangl, Claudia A1 - Willert, Bernhard T1 - Computational results for validation of nominations T2 - Evaluating Gas Network Capacities N2 - The different approaches to solve the validation of nomination problem presented in the previous chapters are evaluated computationally in this chapter. Each approach is analyzed individually, as well as the complete solvers for these problems. We demonstrate that the presented approaches can successfully solve large-scale real-world instances. Y1 - 2015 SN - 9781611973686 VL - SIAM-MOS series on Optimization ER - TY - CHAP A1 - Humpola, Jesco A1 - Fügenschuh, Armin A1 - Hiller, Benjamin A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Lenz, Ralf A1 - Schwarz, Robert A1 - Schweiger, Jonas T1 - The Specialized MINLP Approach T2 - Evaluating Gas Network Capacities N2 - We propose an approach to solve the validation of nominations problem using mixed-integer nonlinear programming (MINLP) methods. Our approach handles both the discrete settings and the nonlinear aspects of gas physics. Our main contribution is an innovative coupling of mixed-integer (linear) programming (MILP) methods with nonlinear programming (NLP) that exploits the special structure of a suitable approximation of gas physics, resulting in a global optimization method for this type of problem. Y1 - 2015 SN - 9781611973686 VL - SIAM-MOS series on Optimization ER - TY - BOOK A1 - Koch, Thorsten A1 - Hiller, Benjamin A1 - Pfetsch, Marc A1 - Schewe, Lars T1 - Evaluating Gas Network Capacities Y1 - 2015 SN - 978-1-611973-68-6 PB - SIAM ER -