@article{LenzBecker2022, author = {Lenz, Ralf and Becker, Kai-Helge}, title = {Optimization of Capacity Expansion in Potential-driven Networks including Multiple Looping - A comparison of modelling approaches}, volume = {44}, journal = {OR Spectrum}, doi = {https://doi.org/10.1007/s00291-021-00648-7}, pages = {179 -- 224}, year = {2022}, abstract = {In commodity transport networks such as natural gas, hydrogen and water networks, flows arise from nonlinear potential differences between the nodes, which can be represented by so-called "potential-driven" network models. When operators of these networks face increasing demand or the need to handle more diverse transport situations, they regularly seek to expand the capacity of their network by building new pipelines parallel to existing ones ("looping"). The paper introduces a new mixed-integer non-linear programming (MINLP) model and a new non-linear programming (NLP) model and compares these with existing models for the looping problem and related problems in the literature, both theoretically and experimentally. On this basis, we give recommendations about the circumstances under which a certain model should be used. In particular, it turns out that one of our novel models outperforms the existing models. Moreover, the paper is the first to include the practically relevant option that a particular pipeline may be looped several times.}, language = {en} } @article{HoppmannBaum2021, author = {Hoppmann-Baum, Kai}, title = {On the Complexity of Computing Maximum and Minimum Min-Cost-Flows}, journal = {Networks}, doi = {10.1002/net.22060}, year = {2021}, abstract = {Consider a flow network, i.e., a directed graph where each arc has a nonnegative capacity value and an associated length, together with nonempty supply intervals for the sources and nonempty demand intervals for the sinks. The Maximum Min-Cost-Flow Problem (MaxMCF) is to find fixed supply and demand values within these intervals such that the optimal objective value of the induced Min-Cost-Flow Problem (MCF) is maximized. In this paper, we show that MaxMCF as well as its uncapacitated variant, the Maximum Transportation Problem (MaxTP), are NP-hard. Further, we prove that MaxMCF is APX-hard if a connectedness-condition regarding the sources and the sinks of the flow network is dropped. Finally, we show how the Minimum Min-Cost-Flow Problem (MinMCF) can be solved in polynomial time.}, language = {en} } @article{AndersonTurnerKoch2022, author = {Anderson, Lovis and Turner, Mark and Koch, Thorsten}, title = {Generative deep learning for decision making in gas networks}, volume = {95}, journal = {Mathematical Methods of Operations Research}, publisher = {Springer Nature}, doi = {10.1007/s00186-022-00777-x}, pages = {503 -- 532}, year = {2022}, abstract = {A decision support system relies on frequent re-solving of similar problem instances. While the general structure remains the same in corresponding applications, the input parameters are updated on a regular basis. We propose a generative neural network design for learning integer decision variables of mixed-integer linear programming (MILP) formulations of these problems. We utilise a deep neural network discriminator and a MILP solver as our oracle to train our generative neural network. In this article, we present the results of our design applied to the transient gas optimisation problem. With the trained network we produce a feasible solution in 2.5s, use it as a warm-start solution, and thereby decrease global optimal solution solve time by 60.5\%.}, language = {en} } @misc{ChenKochXu2019, author = {Chen, Ying and Koch, Thorsten and Xu, Xiaofei}, title = {Regularized partially functional autoregressive model with application to high-resolution natural gas forecasting in Germany}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74880}, year = {2019}, abstract = {We propose a partially functional autoregressive model with exogenous variables (pFAR) to describe the dynamic evolution of the serially correlated functional data. It provides a unit� ed framework to model both the temporal dependence on multiple lagged functional covariates and the causal relation with ultrahigh-dimensional exogenous scalar covariates. Estimation is conducted under a two-layer sparsity assumption, where only a few groups and elements are supposed to be active, yet without knowing their number and location in advance. We establish asymptotic properties of the estimator and investigate its unite sample performance along with simulation studies. We demonstrate the application of pFAR with the high-resolution natural gas flows in Germany, where the pFAR model provides insightful interpretation as well as good out-of-sample forecast accuracy.}, language = {en} } @article{HenningsAndersonHoppmannBaumetal.2021, author = {Hennings, Felix and Anderson, Lovis and Hoppmann-Baum, Kai and Turner, Mark and Koch, Thorsten}, title = {Controlling transient gas flow in real-world pipeline intersection areas}, volume = {22}, journal = {Optimization and Engineering}, edition = {2}, publisher = {Springer Nature}, doi = {https://doi.org/10.1007/s11081-020-09559-y}, pages = {687 -- 734}, year = {2021}, abstract = {Compressor stations are the heart of every high-pressure gas transport network. Located at intersection areas of the network they are contained in huge complex plants, where they are in combination with valves and regulators responsible for routing and pushing the gas through the network. Due to their complexity and lack of data compressor stations are usually dealt with in the scientific literature in a highly simplified and idealized manner. As part of an ongoing project with one of Germany's largest Transmission System Operators to develop a decision support system for their dispatching center, we investigated how to automatize control of compressor stations. Each station has to be in a particular configuration, leading in combination with the other nearby elements to a discrete set of up to 2000 possible feasible operation modes in the intersection area. Since the desired performance of the station changes over time, the configuration of the station has to adapt. Our goal is to minimize the necessary changes in the overall operation modes and related elements over time, while fulfilling a preset performance envelope or demand scenario. This article describes the chosen model and the implemented mixed integer programming based algorithms to tackle this challenge. By presenting extensive computational results on real world data we demonstrate the performance of our approach.}, language = {en} } @article{RoessigPetkovic2020, author = {R{\"o}ssig, Ansgar and Petkovic, Milena}, title = {Advances in Verification of ReLU Neural Networks}, journal = {Journal of Global Optimization}, publisher = {Springer}, doi = {10.1007/s10898-020-00949-1}, year = {2020}, abstract = {We consider the problem of verifying linear properties of neural networks. Despite their success in many classification and prediction tasks, neural networks may return unexpected results for certain inputs. This is highly problematic with respect to the application of neural networks for safety-critical tasks, e.g. in autonomous driving. We provide an overview of algorithmic approaches that aim to provide formal guarantees on the behavior of neural networks. Moreover, we present new theoretical results with respect to the approximation of ReLU neural networks. On the other hand, we implement a solver for verification of ReLU neural networks which combines mixed integer programming (MIP) with specialized branching and approximation techniques. To evaluate its performance, we conduct an extensive computational study. For that we use test instances based on the ACAS Xu System and the MNIST handwritten digit data set. Our solver is publicly available and able to solve the verification problem for instances which do not have independent bounds for each input neuron.}, language = {en} } @misc{GotzesHoppmann2019, author = {Gotzes, Uwe and Hoppmann, Kai}, title = {Bounds for the final ranks during a round robin tournament}, journal = {Operational Research - An International Journal (ORIJ)}, doi = {https://doi.org/10.1007/s12351-020-00546-w}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74638}, year = {2019}, abstract = {This article answers two kinds of questions regarding the Bundesliga which is Germany's primary football (soccer) competition having the highest average stadium attendance worldwide. First "At any point of the season, what final rank will a certain team definitely reach?" and second "At any point of the season, what final rank can a certain team at most reach?". Although we focus especially on the Bundesliga, the models that we use to answer the two questions can easily be adopted to league systems that are similar to that of the Bundesliga.}, language = {en} } @article{Gotzes2019, author = {Gotzes, Uwe}, title = {Ein neuer Ansatz zur Optimierung des Bilanzausgleichs in einem Gasmarktgebiet}, journal = {Zeitschrift f{\"u}r Energiewirtschaft}, doi = {10.1007/s12398-019-00257-6}, year = {2019}, abstract = {Im BDEW/VKU/GEODE-Leitfaden Krisenvorsorge Gas ist zu lesen, dass als oberster Grundsatz zur Vermeidung von Versorgungsengp{\"a}ssen in Gasversorgungssystemen gilt, m{\"o}glichst laufend einen Bilanzausgleich in allen Teilen des Netzes zu erreichen. Wir entwickeln Modelle zur Optimierung des laufenden Bilanzausgleichs. Als Gasversorgungssystem betrachten wir modellhaft die Fernleitungsnetze eines Marktgebiets. Als Teile des Gasversorgungssystems fassen wir vereinfachend die jeweiligen Netze der Fernleitungsnetzbetreiber auf. Die Optimierung erfolgt in zwei Schritten. Im ersten Schritt wird der optimale Einsatz netzbezogener Maßnahmen ermittelt. Beispiele f{\"u}r netzbezogene Maßnahmen sind die Nutzung von Netzpuffer und Mengenverlagerungen mit anderen Infrastrukturbetreibern. Falls sich die Bilanzen durch netzbezogene Maßnahmen nicht vollst{\"a}ndig ausgleichen lassen, werden Fehlmengen angesetzt, die so gleichm{\"a}ßig wie m{\"o}glich auf die Teile des Netzes verteilt werden. Im zweiten Schritt werden die verbliebenen Fehlmengen, welche in der Regel durch marktbezogene Maßnahmen bereinigt werden, regulierungskonform auf m{\"o}glichst große Teile des Gasversorgungssystems verteilt. Im Ergebnis erhalten wir ein transparentes, gerechtes, flexibel parametrier- und erweiterbares Verfahren, welches zyklisch im Dispatchingprozess eingesetzt werden kann, um die Integrit{\"a}t der Netze zu unterst{\"u}tzen. Dies wird an Beispielen verdeutlicht.}, language = {de} } @misc{Roessig2019, author = {R{\"o}ssig, Ansgar}, title = {Verification of Neural Networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74174}, year = {2019}, language = {en} } @misc{Hoppmann2019, author = {Hoppmann, Kai}, title = {On the Complexity of the Maximum Minimum Cost Flow Problem}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73359}, year = {2019}, abstract = {Consider a flow network, i.e., a directed graph where each arc has a nonnegative capacity and an associated length, together with nonempty supply-intervals for the sources and nonempty demand-intervals for the sinks. The goal of the Maximum Minimum Cost Flow Problem (MMCF) is to find fixed supply and demand values within these intervals, such that the optimal objective value of the induced Minimum Cost Flow Problem (MCF) is maximized. In this paper, we show that MMCF is APX-hard and remains NP-hard in the uncapacitated case.}, language = {en} } @misc{HoppmannHenningsLenzetal.2019, author = {Hoppmann, Kai and Hennings, Felix and Lenz, Ralf and Gotzes, Uwe and Heinecke, Nina and Spreckelsen, Klaus and Koch, Thorsten}, title = {Optimal Operation of Transient Gas Transport Networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73639}, year = {2019}, language = {en} } @misc{HenningsAndersonHoppmannetal.2019, author = {Hennings, Felix and Anderson, Lovis and Hoppmann, Kai and Turner, Mark and Koch, Thorsten}, title = {Controlling transient gas flow in real-world pipeline intersection areas}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73645}, year = {2019}, abstract = {Compressor stations are the heart of every high-pressure gas transport network. Located at intersection areas of the network they are contained in huge complex plants, where they are in combination with valves and regulators responsible for routing and pushing the gas through the network. Due to their complexity and lack of data compressor stations are usually dealt with in the scientific literature in a highly simplified and idealized manner. As part of an ongoing project with one of Germany's largest Transmission System Operators to develop a decision support system for their dispatching center, we investigated how to automatize control of compressor stations. Each station has to be in a particular configuration, leading in combination with the other nearby elements to a discrete set of up to 2000 possible feasible operation modes in the intersection area. Since the desired performance of the station changes over time, the configuration of the station has to adapt. Our goal is to minimize the necessary changes in the overall operation modes and related elements over time, while fulfilling a preset performance envelope or demand scenario. This article describes the chosen model and the implemented mixed integer programming based algorithms to tackle this challenge. By presenting extensive computational results on real world data we demonstrate the performance of our approach.}, language = {en} } @misc{PetkovicChenGamrathetal.2019, author = {Petkovic, Milena and Chen, Ying and Gamrath, Inken and Gotzes, Uwe and Hadjidimitriou, Natalia Selini and Zittel, Janina and Xu, Xiaofei and Koch, Thorsten}, title = {A Hybrid Approach for High Precision Prediction of Gas Flows}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73525}, year = {2019}, abstract = {About 20\% of the German energy demand is supplied by natural gas. Ad- ditionally, for about twice the amount Germany serves as a transit country. Thereby, the German network represents a central hub in the European natural gas transport network. The transport infrastructure is operated by so-called transmissions system operators or TSOs. The number one priority of the TSOs is to ensure security of supply. However, the TSOs have no knowledge of the intentions and planned actions of the shippers (traders). Open Grid Europe (OGE), one of Germany's largest TSO, operates a high- pressure transport network of about 12.000 km length. Since flexibility and security of supply is of utmost importance to the German Energy Transition ("Energiewende") especially with the introduction of peak-load gas power stations, being able to predict in- and out-flow of the network is of great importance. In this paper we introduce a new hybrid forecast method applied to gas flows at the boundary nodes of a transport network. The new method employs optimized feature minimization and selection. We use a combination of an FAR, LSTM DNN and mathematical programming to achieve robust high quality forecasts on real world data for different types of network nodes. Keywords: Gas Forecast, Time series, Hybrid Method, FAR, LSTM, Mathematical Optimisation}, language = {en} } @misc{GamrathPetkovic2019, author = {Gamrath, Inken and Petkovic, Milena}, title = {Prediction of Intermitted Flows in Large Gas Networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73717}, year = {2019}, language = {en} } @article{ChenChuaKoch2018, author = {Chen, Ying and Chua, Wee Song and Koch, Thorsten}, title = {Forecasting day-ahead high-resolution natural-gas demand and supply in Germany}, journal = {Applied Energy}, number = {Volume 228}, doi = {https://doi.org/10.1016/j.apenergy.2018.06.137}, pages = {1091 -- 1110}, year = {2018}, abstract = {Forecasting natural gas demand and supply is essential for an efficient operation of the German gas distribution system and a basis for the operational decisions of the transmission system operators. The German gas market is moving towards more short-term planning, in particular, day-ahead contracts. This increases the difficulty that the operators in the dispatching centre are facing, as well as the necessity of accurate forecasts. This paper presents a novel predictive model that provides day-ahead forecasts of the high resolution gas flow by developing a Functional AutoRegressive model with eXogenous variables (FARX). The predictive model allows the dynamic patterns of hourly gas flows to be described in a wide range of historical profiles, while also taking the relevant determinants data into account. By taking into account a richer set of information, FARX provides stronger performance in real data analysis, with both accuracy and high computational efficiency. Compared to several alternative models in out-of-sample forecasts, the proposed model can improve forecast accuracy by at least 12\% and up to 5-fold for one node, 3\% to 2-fold and 2-fold to 4-fold for the other two nodes. The results show that lagged 1-day gas flow and nominations are important predictors, and with their presence in the forecast model, temperature becomes insignificant for short-term predictions.}, language = {en} }