@misc{Hennings2021, author = {Hennings, Felix}, title = {Large-scale empirical study on the momentum equation's inertia term}, issn = {1438-0064}, doi = {10.1016/j.jngse.2021.104153}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-81881}, year = {2021}, abstract = {A common approach to reduce the Euler equations' complexity for the simulation and optimization of gas networks is to neglect small terms that contribute little to the overall equations. An example is the inertia term of the momentum equation since it is said to be of negligible size under real-world operating conditions. However, this justification has always only been based on experience or single sets of artificial data points. This study closes this gap by presenting a large-scale empirical evaluation of the absolute and relative size of the inertia term when operating a real-world gas network. Our data consists of three years of fine-granular state data of one of the largest gas networks in Europe, featuring over 6,000 pipes with a total length of over 10,000 km. We found that there are only 120 events in which a subnetwork consisting of multiple pipes has an inertia term of high significance for more than three minutes. On average, such an event occurs less often than once every ten days. Therefore, we conclude that the inertia term is indeed negligible for real-world transient gas network control problems.}, language = {en} } @article{Le2021, author = {Le, Thi Thai}, title = {Effect of water depth on Kelvin - Helmholtz instability in a shallow-water flow}, volume = {62}, journal = {Journal of Mathematical Physics}, number = {10}, publisher = {AIP Publishing}, doi = {10.1063/1.5145060}, pages = {103101}, year = {2021}, abstract = {It is well known that the interface between two regions of an incompressible ideal fluid flow moving in a relative motion is necessarily destabilized, regardless of the velocity difference's strength. This phenomenon is the so-called Kelvin-Helmholtz instability (KHI). However, a large number of works demonstrated a surprising result that the instability is suppressed for shallow water flows; the interface is stabilized if the Froude number, defined by the velocity difference's ratio to the gravity wave's speed, is sufficiently large. In a limited way, these authors have been used the shallow-water equations without the higher-order effect of the dispersive terms. Thus, this investigation aims to examine these higher-order dispersive effects to analyze the interface stability problem of tangential-velocity discontinuity in shallow-water flows. In particular, we use the Green-Naghdi equations to introduce the dispersive terms related to the depth and the depth-averaged horizontal velocities of the fluid. We show that the interface stability depends on the Froude number (i.e., the velocity difference's strength) and the water depth. A critical value of the Froude number to stabilize the interface is smaller than the case of no dispersive terms, and the flow in a deeper region is more stable than in a shallower one. We also consider the distribution of kinetic and potential energy to clarify a feature characteristic of a large class of instabilities in shallow water flow. The instability of flows is caused by the decrease in the kinetic energy during the perturbation of waves. This phenomenon is known as negative energy modes and plays a vital role in applying the model to industrial equipment. A conclusion is that the equipartition of energies occurs if and only if the velocity difference is zero and the water depth is shallow enough to ignore the dispersive terms.}, language = {en} } @article{TawfikGendronLimbourg2021, author = {Tawfik, Christine and Gendron, Bernard and Limbourg, Sabine}, title = {An iterative two-stage heuristic algorithm for a bilevel service network design and pricing model}, journal = {European Journal of Operational Research}, publisher = {Elsevier}, address = {European Journal of Operational Research}, doi = {https://doi.org/10.1016/j.ejor.2021.07.052}, year = {2021}, abstract = {Building upon earlier research, we revisit a bilevel formulation of service design and pricing for freight networks, with the aim of investigating its algorithmic aspects. The model adds substantial computational challenges to the existing literature, as it deals with general integer network design variables. An iterative heuristic algorithm is introduced, based on the concepts of inverse optimization and neighbourhood search. The procedure alternates between two versions of restricted formulations of the model while inducing promising changes into the service assignments. The approach has proven a high performance for all of the considered real-world instances. Its efficiency rests on its ability to deliver results within a close proximity to those obtained by the exact solver in terms of quality, yet within a significantly smaller amount of time, and to land feasible solutions for the large-sized instances that could not be previously solved. In line with the sustainable transport goals, a deeper observation of the transport management side highlights the strategy of the algorithm favouring freight consolidation and achieving high load factors.}, language = {en} } @inproceedings{PedersenSchachlerHeideretal.2021, author = {Pedersen, Jaap and Schachler, Birgit and Heider, Anya and Pleßmann, Guido}, title = {Distribution System Planning with Battery Storage using Multiperiod Optimal Power Flow}, volume = {6}, booktitle = {14th International Renewable Energy Storage Conference 2020 (IRES 2020)}, doi = {https://doi.org/10.2991/ahe.k.210202.007}, pages = {41 -- 48}, year = {2021}, abstract = {The ongoing energy transition introduces new challenges for distribution networks and brings about the need to expand existing power grid capacities. In order to contain network expansion and with it economic costs, utilization of various flexibility options to reduce expansion needs is discussed. This paper proposes a multiperiod optimal power flow (MPOPF) approach with a new continuous network expansion formulation to optimize the deployment of flexibility options under the objective of minimizing network expansion costs. In a comparison of the newly proposed continuous network expansion formulation with an existing mixed integer formulation and a continuous interpretation of the latter the here proposed formulation is shown to be useful in order to obtain a solvable problem and contain computational efforts. The presented MPOPF including the flexibility options storage units and curtailment is then assessed on synthetic medium voltage grids and applied to evaluate the benefit of a combined vs. a stepwise optimization of these flexibility options. It is demonstrated that using a local solver the proposed approach is applicable and yields a solution in reasonable time. Furthermore, it is shown that the combined optimization generally leads to a more efficient utilization of the considered flexibility options and therefore lower grid expansion costs than the stepwise consideration.}, 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} } @article{RehfeldtKoch2021, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {On the exact solution of prize-collecting Steiner tree problems}, journal = {INFORMS Journal on Computing}, doi = {10.1287/ijoc.2021.1087}, year = {2021}, 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} } @inproceedings{GleixnerKempkeKochetal.2020, author = {Gleixner, Ambros and Kempke, Nils-Christian and Koch, Thorsten and Rehfeldt, Daniel and Uslu, Svenja}, title = {First Experiments with Structure-Aware Presolving for a Parallel Interior-Point Method}, booktitle = {Operations Research Proceedings 2019}, edition = {1}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-030-48439-2_13}, pages = {105 -- 111}, year = {2020}, abstract = {In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware implementations of presolving as part of a parallel interior-point method to solve linear programs with block-diagonal structure, including both linking variables and linking constraints. While presolving reductions are often mathematically simple, their implementation in a high-performance computing environment is a complex endeavor. We report results on impact, performance, and scalability of the resulting presolving routines on real-world energy system models with up to 700 million nonzero entries in the constraint matrix.}, 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} } @inproceedings{RiedmuellerRivettaZittel2025, author = {Riedm{\"u}ller, Stephanie and Rivetta, Fabian and Zittel, Janina}, title = {Long-Term Multi-Objective Optimization for Integrated Unit Commitment and Investment Planning for District Heating Networks}, booktitle = {Operations Research Proceedings 2024}, publisher = {Springer Cham}, arxiv = {http://arxiv.org/abs/2410.06673}, doi = {10.1007/978-3-031-92575-7_33}, pages = {235 -- 241}, year = {2025}, abstract = {The need to decarbonize the energy system has intensified the focus on district heating networks in urban and suburban areas. Therefore, exploring transformation pathways with reasonable trade-offs between economic viability and environmental goals became necessary. We introduce a network-flow-based model class integrating unit commitment and long-term investment planning for multi-energy systems. While the integration of unit commitment and investment planning has been applied to multi-energy systems, a formal introduction and suitability for the application of long-term portfolio planning of an energy provider on an urban scale has yet to be met. Based on mixed integer linear programming, the model bridges the gap between overly detailed industrial modeling tools not designed for computational efficiency at scale and rather abstract academic models. The formulation is tested on Berlin's district heating network. Hence, the challenge lies in a large number of variables and constraints and the coupling of time steps, for example, through investment decisions. A case study explores different solutions on the Pareto front defined by optimal trade-offs between minimizing costs and CO2 emissions through a lexicographic optimization approach. The resulting solution catalog can provide decision-makers valuable insights into feasible transformation pathways, highlighting distinctions between robust and target-dependent investments.}, language = {en} } @inproceedings{PetkovicZittel2025, author = {Petkovic, Milena and Zittel, Janina}, title = {Resilient Forecasting of High-Dimensional Network Time Series in the Energy Domain: A Hybrid Approach}, booktitle = {Operations Research Proceedings 2023. OR 2023}, publisher = {Springer}, doi = {10.1007/978-3-031-58405-3_48}, pages = {375 -- 381}, year = {2025}, abstract = {Energy systems are complex networks consisting of various interconnected components. Accurate energy demand and supply forecasts are crucial for efficient system operation and decision-making. However, high-dimensional data, complex network structures, and dynamic changes and disruptions in energy networks pose significant challenges for forecasting models. To address this, we propose a hybrid approach for resilient forecasting of network time series (HRF-NTS) in the energy domain. Our approach combines mathematical optimization methods with state-of-the-art machine learning techniques to achieve accurate and robust forecasts for high-dimensional energy network time series. We incorporate an optimization framework to account for uncertainties and disruptive changes in the energy system. The effectiveness of the proposed approach is demonstrated through a case study of forecasting energy demand and supply in a complex, large-scale natural gas transmission network. The results show that the hybrid approach outperforms alternative prediction models in terms of accuracy and resilience to structural changes and disruptions, providing stable, multi-step ahead forecasts for different short to mid-term forecasting horizons.}, language = {en} } @inproceedings{YuekselErguenKochZittel2025, author = {Yueksel-Erguen, Inci and Koch, Thorsten and Zittel, Janina}, title = {Consistent flow scenario generation based on open data for operational analysis of European gas transport networks}, booktitle = {Operations Research Proceedings 2023. OR 2023}, publisher = {Springer}, doi = {10.1007/978-3-031-58405-3_63}, pages = {493 -- 499}, year = {2025}, abstract = {In recent years, European gas transport has been affected by major disruptive events like political issues such as, most recently, the Russian war on Ukraine. To incorporate the impacts of such events into decision-making during the energy transition, more complex models for gas network analysis are required. However, the limited availability of consistent data presents a significant obstacle in this endeavor. We use a mathematical-modeling-based scenario generator to deal with this obstacle. The scenario generator consists of capacitated network flow models representing the gas network at different aggregation levels. In this study, we present the coarse-to-fine approach utilized in this scenario generator.}, language = {en} } @inproceedings{KochRehfeldtShinano2025, author = {Koch, Thorsten and Rehfeldt, Daniel and Shinano, Yuji}, title = {On the state of QUBO solving}, booktitle = {Operations Research Proceedings 2023. OR 2023}, publisher = {Springer}, doi = {10.1007/978-3-031-58405-3_46}, pages = {357 -- 365}, year = {2025}, abstract = {It is regularly claimed that quantum computers will bring breakthrough progress in solving challenging combinatorial optimization problems relevant in practice. In particular, Quadratic Unconstrained Binary Optimization (QUBO) problems are said to be the model of choice for use in (adiabatic) quantum systems during the noisy intermediate- scale quantum (NISQ) era. Even the first commercial quantum-based systems are advertised to solve such problems. Theoretically, any Integer Program can be converted into a QUBO. In practice, however, there are some caveats, as even for problems that can be nicely modeled as a QUBO, this might not be the most effective way to solve them. We review the state of QUBO solving on digital and quantum computers and provide insights regarding current benchmark instances and modeling.}, language = {en} } @inproceedings{YuekselErguenLitzelPeng2025, author = {Yueksel Erguen, Inci and Litzel, Ida and Peng, Hanqiu}, title = {Integrating Large Citation Datasets}, booktitle = {Operations Research Proceedings 2024. OR 2024}, doi = {10.1007/978-3-031-92575-7_7}, pages = {46 -- 52}, year = {2025}, abstract = {This paper explores methods for building a comprehensive citation graph using big data techniques to evaluate scientific impact more accurately. Traditional citation metrics have limitations, and this work investigates merging large citation datasets to create a more accurate picture. Challenges of big data, like inconsistent data formats and lack of unique identifiers, are addressed through deduplication efforts, resulting in a streamlined and reliable merged dataset with over 119 million records and 1.4 billion citations. We demonstrate that merging large citation datasets builds a more accurate citation graph facilitating a more robust evaluation of scientific impact.}, language = {en} } @article{ZakiyevaPetkovic2025, author = {Zakiyeva, Nazgul and Petkovic, Milena}, title = {High-dimensional high-frequency time series prediction with a mixed integer optimisation method}, journal = {Operations Research Proceedings 2023. OR 2023}, issn = {1438-0064}, doi = {10.1007/978-3-031-58405-3_54}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-93068}, pages = {423 -- 429}, year = {2025}, abstract = {We study a functional autoregressive model for high-frequency time series. We approach the estimation of the proposed model using a Mixed Integer Optimisation method. The proposed model captures serial dependence in the functional time series by including high-dimensional curves. We illustrate our methodology on large-scale natural gas network data. Our model provides more accurate day-ahead hourly out-of-sample forecast of the gas in and out-flows compared to alternative prediction models.}, language = {en} } @phdthesis{Rehfeldt2021, author = {Rehfeldt, Daniel}, title = {Faster algorithms for Steiner tree and related problems: From theory to practice}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-85148}, year = {2021}, language = {en} } @misc{HenningsPetkovicStreubel2021, author = {Hennings, Felix and Petkovic, Milena and Streubel, Tom}, title = {On the Numerical Treatment of Interlaced Target Values - Modeling, Optimization and Simulation of Regulating Valves in Gas Networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-85359}, year = {2021}, abstract = {Due to the current and foreseeable shifts in energy production, the trading and transport operations of gas will become more dynamic, volatile, and hence also less predictable. Therefore, computer-aided support in terms of rapid simulation and control optimization will further broaden its importance for gas network dispatching. In this paper, we aim to contribute and openly publish two new mathematical models for regulators, also referred to as control valves, which together with compressors make up the most complex and involved types of active elements in gas network infrastructures. They provide full direct control over gas networks but are in turn controlled via target values, also known as set-point values, themselves. Our models incorporate up to six dynamical target values to define desired transient states for the elements' local vicinity within the network. That is, each pair of every two target values defines a bounding box for the inlet pressure, outlet pressure as well as the passing mass flow of gas. In the proposed models, those target values are prioritized differently and are constantly in competition with each other, which can only be resolved dynamically at run-time of either a simulation or optimization process. Besides careful derivation, we compare simulation and optimization results with predictions of the commercial simulation tool SIMONE.}, language = {en} } @article{AignerClarnerLiersetal.2021, author = {Aigner, Kevin-Martin and Clarner, Jan-Patrick and Liers, Frauke and Martin, Alexander}, title = {Robust Approximation of Chance Constrained DC Optimal Power Flow under Decision-Dependent Uncertainty}, journal = {European Journal of Operational Research}, year = {2021}, abstract = {We propose a mathematical optimization model and its solution for joint chance constrained DC Optimal Power Flow. In this application, it is particularly important that there is a high probability of transmission limits being satisfied, even in the case of uncertain or fluctuating feed-in from renewable energy sources. In critical network situations where the network risks overload, renewable energy feed-in has to be curtailed by the transmission system operator (TSO). The TSO can reduce the feed-in in discrete steps at each network node. The proposed optimization model minimizes curtailment while ensuring that there is a high probability of transmission limits being maintained. The latter is modeled via (joint) chance constraints that are computationally challenging. Thus, we propose a solution approach based on the robust safe approximation of these constraints. Hereby, probabilistic constraints are replaced by robust constraints with suitably defined uncertainty sets constructed from historical data. The ability to discretely control the power feed-in then leads to a robust optimization problem with decision-dependent uncertainties, i.e. the uncertainty sets depend on decision variables. We propose an equivalent mixed-integer linear reformulation for box uncertainties with the exact linearization of bilinear terms. Finally, we present numerical results for different test cases from the Nesta archive, as well as for a real network. We consider the discrete curtailment of solar feed-in, for which we use real-world weather and network data. The experimental tests demonstrate the effectiveness of this method and run times are very fast. Moreover, on average the calculated robust solutions only lead to a small increase in curtailment, when compared to nominal solutions.}, language = {en} } @inproceedings{TateiwaShinanoYamamuraetal.2021, author = {Tateiwa, Nariaki and Shinano, Yuji and Yamamura, Keiichiro and Yoshida, Akihiro and Kaji, Shizuo and Yasuda, Masaya and Fujisawa, Katsuki}, title = {CMAP-LAP: Configurable Massively Parallel Solver for Lattice Problems}, booktitle = {HiPC 2021 proceedings}, year = {2021}, abstract = {Lattice problems are a class of optimization problems that are notably hard. There are no classical or quantum algorithms known to solve these problems efficiently. Their hardness has made lattices a major cryptographic primitive for post-quantum cryptography. Several different approaches have been used for lattice problems with different computational profiles; some suffer from super-exponential time, and others require exponential space. This motivated us to develop a novel lattice problem solver, CMAP-LAP, based on the clever coordination of different algorithms that run massively in parallel. With our flexible framework, heterogeneous modules run asynchronously in parallel on a large-scale distributed system while exchanging information, which drastically boosts the overall performance. We also implement full checkpoint-and-restart functionality, which is vital to high-dimensional lattice problems. Through numerical experiments with up to 103,680 cores, we evaluated the performance and stability of our system and demonstrated its high capability for future massive-scale experiments.}, language = {en} } @article{XuChenZhangetal.2021, author = {Xu, Xiaofei and Chen, Ying and Zhang, Ge and Koch, Thorsten}, title = {Modeling functional time series and mixed-type predictors with partially functional autoregressions*}, journal = {Journal of Business and Economic Statistics}, doi = {10.1080/07350015.2021.2011299}, pages = {1 -- 43}, year = {2021}, abstract = {In many business and economics studies, researchers have sought to measure the dynamic dependence of curves with high-dimensional mixed-type predictors. We propose a partially functional autoregressive model (pFAR) where the serial dependence of curves is controlled by coefficient operators that are defined on a two-dimensional surface, and the individual and group effects of mixed-type predictors are estimated with a two-layer regularization. We develop an efficient estimation with the proven asymptotic properties of consistency and sparsity. We show how to choose the sieve and tuning parameters in regularization based on a forward-looking criterion. In addition to the asymptotic properties, numerical validation suggests that the dependence structure is accurately detected. The implementation of the pFAR within a real-world analysis of dependence in German daily natural gas flow curves, with seven lagged curves and 85 scalar predictors, produces superior forecast accuracy and an insightful understanding of the dynamics of natural gas supply and demand for the municipal, industry, and border nodes, respectively.}, language = {en} } @misc{MostLotharSchmittetal.2021, author = {Most, Dieter and Lothar, Wyrwoll and Schmitt, Carlo and Y{\"u}ksel-Erg{\"u}n, Inci}, title = {plan4res D2.2 - Case Study 1 Report - Multimodal energy concept for achieving Europe's carbon reduction goals}, doi = {10.5281/zenodo.5809338}, year = {2021}, language = {en} }