The transition towards a more reliable, efficient, safe and financeable energy supply is currently in the midst of public interest in Germany as well as in many other industrial nations. At the same time and in order to reduce the dependency on nuclear energy, climate- and eco-friendly energy generation becomes more and more important. In this context, gas will play a significant role over the coming decades. However, there are many challenges with respect to transport, network technology, market regulatory conditions and the combination with other energy sources that need to be addressed. The SFB/TRR 154 project is trying to find answers to these challenges by means of mathematical modelling, simulation and optimization and to provide new-level solutions. The goal of subproject A04 is to develop algorithmic fundamentals for the efficient treatment of switching decisions in gas networks. In particular, this involves the modelling and algorithmics of the switching operations in compressor stations, since these pose a significant source of modelling and runtime complexity. The set of feasible work points of a compressor station in general is non-convex, in some circumstances even non-connected, but can be well approximated by the union of convex polyhedra. Hence, the treatment of such structures in MIPs and MINLPs will be the main focus of research in this subproject. While being motivated by the optimization of gas networks, the methods to be developed will be relevant in a much broader field of vision. Known techniques for modelling unions of polyhedra as the feasible set of a MIP rely on the description of the single polyhedra using inequalities. In contrast to this, another approach adapted to the geometric properties of the overall set can be considered. More precisely, the goal is to find and analyze a hierarchical description of a non-convex set that provides an as good as possible polyhedral relaxation on each level. This hierarchy can then be used in the branch-and-bound procedure for solving MINLPs together with suitable branching decisions. In the long term, this subproject of SFB/TRR 154 is aiming at the development of real-time capable methods for combinatorial decisions. Furthermore, since the transient control of gas networks requires the successive solving of many similar MIPs/MINLPs, reoptimization techniques come into view that use known information from previous optimization problems in order to reduce running time. For these, a detailed analysis of the problem structure and a deeper understanding of the complex MIP/MINLP solving process will be an essential topic of research.

Publications

2021
CINDy: Conditional gradient-based Identification of Non-linear Dynamics – Noise-robust recovery Journal of Computational and Applied Mathematics, 2021 (under review) Alejandro Carderera, Sebastian Pokutta, Christof Schütte, Martin Weiser BibTeX
arXiv
Combinatorial Switching for Routing Gas Flows
2018
A Sweep-Plane Algorithm for the Computation of the Volume of a Union of Polytopes ZIB-Report 18-37 Lovis Anderson, Benjamin Hiller PDF
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Combinatorial Switching for Routing Gas Flows
A System to Evaluate Gas Network Capacities: Concepts and Implementation European Journal of Operational Research, 270(3), pp. 797-808, 2018 (preprint available as ZIB-Report 18-11) Benjamin Hiller, Thorsten Koch, Lars Schewe, Robert Schwarz, Jonas Schweiger PDF (ZIB-Report)
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Combinatorial Switching for Routing Gas Flows
Analysis of operating modes of complex compressor stations ZIB-Report 17-65 Benjamin Hiller, René Saitenmacher, Tom Walther PDF
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Combinatorial Switching for Routing Gas Flows
Improving branching for disjunctive polyhedral models using approximate convex decompositions ZIB-Report 17-68 Benjamin Hiller, Tom Walther PDF
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Combinatorial Switching for Routing Gas Flows
Modelling compressor stations in gas networks ZIB-Report 17-67 Benjamin Hiller, Tom Walther PDF
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Combinatorial Switching for Routing Gas Flows
The Computation of the Volume of the Union of Polytopes via a Sweep-Plane Algorithm Master's thesis, Technische Universität Berlin, Thorsten Koch (Advisor), 2018 Lovis Anderson PDF
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Combinatorial Switching for Routing Gas Flows
2017
A System to Evaluate Gas Network Capacities: Concepts and Implementation ZIB-Report 17-03 Benjamin Hiller, Thorsten Koch, Lars Schewe, Robert Schwarz, Jonas Schweiger PDF
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Combinatorial Switching for Routing Gas Flows
Analysis of operating modes of complex compressor stations Proceedings of Operations Research 2016, pp. 251-257, 2017 (preprint available as ZIB-Report 16-61) Benjamin Hiller, René Saitenmacher, Tom Walther PDF (ZIB-Report)
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DOI
Combinatorial Switching for Routing Gas Flows
GasLib – A Library of Gas Network Instances Data, 2(4), 2017 Martin Schmidt, Denis Assmann, Robert Burlacu, Jesco Humpola, Imke Joormann, Nikolaos Kanelakis, Thorsten Koch, Djamal Oucherif, Marc Pfetsch, Lars Schewe, Robert Schwarz, Matthias Sirvent BibTeX
DOI
Combinatorial Switching for Routing Gas Flows
Polyhedral 3D Models for compressors in gas networks ZIB-Report 17-66 Tom Walther, Benjamin Hiller, René Saitenmacher PDF
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Combinatorial Switching for Routing Gas Flows
2016
Combinatorial Models of Compressor Stations in Gas Networks Bachelor's thesis, Freie Universität Berlin, Ralf Borndörfer, Benjamin Hiller (Advisors), 2016 René Saitenmacher PDF
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Combinatorial Switching for Routing Gas Flows
2015
Computational results for validation of nominations Evaluating Gas Network Capacities, 2015, ISBN: 9781611973686 Benjamin Hiller, Jesco Humpola, Thomas Lehmann, Ralf Lenz, Antonio Morsi, Marc Pfetsch, Lars Schewe, Martin Schmidt, Robert Schwarz, Jonas Schweiger, Claudia Stangl, Bernhard Willert BibTeX
Combinatorial Switching for Routing Gas Flows
Evaluating Gas Network Capacities SIAM, 2015, ISBN: 978-1-611973-68-6 Thorsten Koch, Benjamin Hiller, Marc Pfetsch, Lars Schewe BibTeX
Combinatorial Switching for Routing Gas Flows
Mathematische Modellierung, Simulation und Optimierung von Gastransportnetzwerken gwf - Gas+Energie, 156(11), pp. 880-885, 2015 Pia Domschke, Martin Groß, Falk M. Hante, Benjamin Hiller, Lars Schewe, Martin Schmidt BibTeX
Combinatorial Switching for Routing Gas Flows
Methods for verifying booked capacities Evaluating gas network capacities, Society for Industrial and Applied Mathematics, pp. 291-315, 2015 Benjamin Hiller, Christine Hayn, Holger Heitsch, René Henrion, Hernan Leövey, Andris Möller, Werner Römisch BibTeX
Combinatorial Switching for Routing Gas Flows
Regulatory rules for gas markets in Germany and other European countries Evaluating gas network capacities, Society for Industrial and Applied Mathematics, pp. 45-64, 2015, ISBN: 978-1-611973-68-6 Uwe Gotzes, Nina Heinecke, Benjamin Hiller, Jessica Rövekamp, Thorsten Koch BibTeX
Combinatorial Switching for Routing Gas Flows
Reoptimization Techniques in MIP Solvers pp. 181-192, Vol.9125, Experimental Algorithms, Lecture Notes in Computer Science, 2015, ISBN: 978-3-319-20086-6 (preprint available as ZIB-Report 15-24) Gerald Gamrath, Benjamin Hiller, Jakob Witzig PDF (ZIB-Report)
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Combinatorial Switching for Routing Gas Flows
The Specialized MINLP Approach Evaluating Gas Network Capacities, 2015, ISBN: 9781611973686 Jesco Humpola, Armin Fügenschuh, Benjamin Hiller, Thorsten Koch, Thomas Lehmann, Ralf Lenz, Robert Schwarz, Jonas Schweiger BibTeX
Combinatorial Switching for Routing Gas Flows