@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} } @misc{BeckerHiller2020, author = {Becker, Kai-Helge and Hiller, Benjamin}, title = {Efficient Enumeration of Acyclic Graph Orientations with Sources or Sinks Revisited}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-77684}, year = {2020}, abstract = {In a recent paper, Conte et al. [CGMR2017] presented an algorithm for enumerating all acyclic orientations of a graph G=(V,E) with a single source (and related orientations) with delay O(|V||E|). In this paper we revisit the problem by going back to an early paper by de Fraysseix et al. [FMR1995], who proposed an algorithm for enumerating all bipolar orientations of a graph based on a recursion formula. We first formalize de Fraysseix et al.'s algorithm for bipolar orientations and determine that its delay is also O(|V||E|). We then apply their recursion formula to the case of Conte et al.'s enumeration problem and show that this yields a more efficient enumeration algorithm with delay O(\sqrt(|V|)|E|). Finally, a way to further streamline the algorithm that leads to a particularly simple implementation is suggested.}, language = {en} } @misc{Weltsch2018, type = {Master Thesis}, author = {Weltsch, Andr{\´e}}, title = {Fast Approximation of Equations of transient Gasflow}, year = {2018}, language = {en} } @inproceedings{TurnerBertholdBesanconetal.2023, author = {Turner, Mark and Berthold, Timo and Besan{\c{c}}on, Mathieu and Koch, Thorsten}, title = {Cutting Plane Selection with Analytic Centers and Multiregression}, volume = {13884}, booktitle = {Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2023.}, publisher = {Springer}, doi = {10.1007/978-3-031-33271-5_4}, pages = {52 -- 68}, year = {2023}, abstract = {Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of a cut by quantifying the extent to which it separates relevant parts of the relaxed feasible set. For this purpose, we use the analytic centers of the relaxation polytope or of its optimal face, as well as alternative optimal solutions of the linear programming relaxation. We assess the impact of the choice of distance measure on root node performance and throughout the whole branch-and-bound tree, comparing our measures against those prevalent in the literature. Finally, by a multi-output regression, we predict the relative performance of each measure, using static features readily available before the separation process. Our results indicate that analytic center-based methods help to significantly reduce the number of branch-and-bound nodes needed to explore the search space and that our multiregression approach can further improve on any individual method.}, language = {en} } @phdthesis{HoppmannBaum2022, author = {Hoppmann-Baum, Kai}, title = {Mathematical programming for stable control and safe operation of gas transport networks}, publisher = {TU Berlin}, doi = {10.14279/depositonce-15837}, year = {2022}, abstract = {The fight against climate change makes extreme but inevitable changes in the energy sector necessary. These in turn lead to novel and complex challenges for the transmission system operators (TSOs) of gas transport networks. In this thesis, we consider four different planning problems emerging from real-world operations and present mathematical programming models and solution approaches for all of them. Due to regulatory requirements and side effects of renewable energy production, controlling today's gas networks with their involved topologies is becoming increasingly difficult. Based on the network station modeling concept for approximating the technical capabilities of complex subnetworks, e.g., compressor stations, we introduce a tri-level MIP model to determine important global control decisions. Its goal is to avoid changes in the network elements' settings while deviations from future inflow pressures as well as supplies and demands are minimized. A sequential linear programming inspired post-processing routine is run to derive physically accurate solutions w.r.t. the transient gas flow in pipelines. Computational experiments based on real-world data show that meaningful solutions are quickly and reliably determined. Therefore, the algorithmic approach is used within KOMPASS, a decision support system for the transient network control that we developed together with the Open Grid Europe GmbH (OGE), one of Europe's largest natural gas TSOs. Anticipating future use cases, we adapt the aforementioned algorithmic approach for hydrogen transport. We investigate whether the natural gas infrastructure can be repurposed and how the network control changes when energy-equivalent amounts of hydrogen are transported. Besides proving the need for purpose-built compressors, we observe that, due to the reduced linepack, the network control becomes more dynamic, compression energy increases by 440\% on average, and stricter regulatory rules regarding the balancing of supply and demand become necessary. Extreme load flows expose the technical limits of gas networks and are therefore of great importance to the TSOs. In this context, we introduce the Maximum Transportation Problem and the Maximum Potential Transport Moment Problem to determine severe transport scenarios. Both can be modeled as linear bilevel programs where the leader selects supplies and demands, maximizing the follower's transport effort. To solve them, we identify solution-equivalent instances with acyclic networks, provide variable bounds regarding their KKT reformulations, apply the big-M technique, and solve the resulting MIPs. A case study shows that the obtained scenarios exceed the maximum severity values of a provided test set by at least 23\%. OGE's transmission system is 11,540km long. Monitoring it is crucial for safe operations. To this end, we discuss the idea of using uncrewed aerial vehicles and introduce the Length-Constrained Cycle Partition Problem to optimize their routing. Its goal is to find a smallest cycle partition satisfying vertex-induced length requirements. Besides a greedy-style heuristic, we propose two MIP models. Combining them with symmetry-breaking constraints as well as valid inequalities and lower bounds from conflict hypergraphs yields a highly performant solution algorithm for this class of problems.}, language = {en} } @article{ChenXuKoch2020, author = {Chen, Ying and Xu, Xiuqin and Koch, Thorsten}, title = {Day-ahead high-resolution forecasting of natural gas demand and supply in Germany with a hybrid model}, volume = {262}, journal = {Applied Energy}, number = {114486}, doi = {https://doi.org/10.1016/j.apenergy.2019.114486}, year = {2020}, abstract = {As the natural gas market is moving towards short-term planning, accurate and robust short-term forecasts of the demand and supply of natural gas is of fundamental importance for a stable energy supply, a natural gas control schedule, and transport operation on a daily basis. We propose a hybrid forecast model, Functional AutoRegressive and Convolutional Neural Network model, based on state-of-the-art statistical modeling and artificial neural networks. We conduct short-term forecasting of the hourly natural gas flows of 92 distribution nodes in the German high-pressure gas pipeline network, showing that the proposed model provides nice and stable accuracy for different types of nodes. It outperforms all the alternative models, with an improved relative accuracy up to twofold for plant nodes and up to fourfold for municipal nodes. For the border nodes with rather flat gas flows, it has an accuracy that is comparable to the best performing alternative model.}, language = {en} } @phdthesis{Turner2024, author = {Turner, Mark}, title = {Cutting Plane Selection for Mixed-Integer Linear Programming}, year = {2024}, abstract = {Mixed-Integer Linear Programming (MILP) is a ubiquitous and practical modelling paradigm that is essential for optimising a broad range of real-world systems. The backbone of all modern MILP solvers is the branch-and-cut algorithm, which is a hybrid of the branch-and-bound and cutting planes algorithms. Cutting planes (cuts) are linear inequalities that tighten the relaxation of a MILP. While a lot of research has gone into deriving valid cuts for MILPs, less emphasis has been put on determining which cuts to select. Cuts in general are generated in rounds, and a subset of the generated cuts must be added to the relaxation. The decision on which subset of cuts to add is called cut selection. This is a crucial task since adding too many cuts makes the relaxation large and slow to optimise over. Conversely, adding too few cuts results in an insufficiently tightened relaxation, and more relaxations need to be enumerated. To further emphasise the difficulty, the effectiveness of an applied cut is both dependent on the other applied cuts, and the state of the MILP solver. In this thesis, we present theoretical results on the importance and difficulty of cut selection, as well as practical results that use cut selection to improve general MILP solver performance. Improving general MILP solver performance is of great importance for practitioners and has many runoff effects. Reducing the solve time of currently solved systems can directly improve efficiency within the application area. In addition, improved performance enables larger systems to be modelled and optimised, and MILP to be used in areas where it was previously impractical due to time restrictions. Each chapter of this thesis corresponds to a publication on cut selection, where the contributions of this thesis can naturally be divided into four components. The first two components are motivated by instance-dependent performance. In practice, for each subroutine, including cut selection, MILP solvers have adjustable parameters with hard-coded default values. It is ultimately unrealistic to expect these default values to perform well for every instance. Rather, it would be ideal if the parameters were dependent on the given instance. To show this motivation is well founded, we first introduce a family of parametric MILP instances and cuts to showcase worst-case performance of cut selection for any fixed parameter value. We then introduce a graph neural network architecture and reinforcement learning framework for learning instance-dependent cut scoring parameters. In the following component, we formalise language for determining if a cut has theoretical usefulness from a polyhedral point of view in relation to other cuts. In addition, to overcome issues of infeasible projections and dual degeneracy, we introduce analytic center based distance measures. We then construct a lightweight multi-output regression model that predicts relative solver performance of an instance for a set of distance measures. The final two components are motivated by general MILP solver improvement via cut selection. Such improvement was shown to be possible, albeit difficult to achieve, by the first half of this thesis. We relate branch-and-bound and cuts through their underlying disjunctions. Using a history of previously computed Gomory mixed-integer cuts, we reduce the solve time of SCIP over the 67\% of affected MIPLIB 2017 instances by 4\%. In the final component, we introduce new cut scoring measures and filtering methods based on information from other MILP solving processes. The new cut selection techniques reduce the solve time of SCIP over the 97\% of affected MIPLIB 2017 instances by 5\%.}, language = {en} } @phdthesis{Hennings2023, author = {Hennings, Felix}, title = {Modeling and solving real-world transient gas network transport problems using mathematical programming}, year = {2023}, abstract = {This thesis considers the transient gas network control optimization problem for on-shore pipeline-based transmission networks with numerous gas routing options. As input, the problem is given the network's topology, its initial state, and future demands at the boundaries of the network, which prescribe the gas flow exchange and potentially the pressure values. The task is to find a set of future control measures for all the active, i.e., controllable, elements in the network that minimizes a combination of different penalty functions. The problem is examined in the context of a decision support tool for gas network dispatchers. This results in detailed models featuring a diverse set of constraints, large and challenging real-world instances, and demanding time limit requirements. All these factors further complicate the problem, which is already difficult to solve in theory due to the inherent combination of non-linear and combinatorial aspects. Our contributions concern different steps of the process of solving the problem. Regarding the model formulation, we investigate the validity of two common approximations of the gas flow description in transport pipes: neglecting the inertia term and assuming a friction term that linearly depends on the gas flow and the pressure. For both, we examine if they can be applied under real-world conditions by evaluating a large amount of historical state data of the network of our project partner, the gas network operator Open Grid Europe. While we can confirm that it is reasonable to ignore the influence of the inertia term, the friction term linearization leads to significant errors and, as a consequence, cannot be used for describing the general gas flow behavior in transport pipes. As another topic of this thesis, we introduce the target value concept as a more realistic approach to express control actions of dispatchers regarding regulators and compressor stations. Here, we derive the mechanisms defined for target values based on the gas flow principles in pipes and develop a mixed-integer programming model capturing their behavior. The accuracy of this model is demonstrated in comparison to a target-value-based industry-standard simulator. Furthermore, we present two heuristics for the transient gas network control optimization problem featuring target values that are based on approximative models for the target-value-based control and determine the final decisions in a post-processing step. To compare the performance of the two heuristics with the approach of directly solving the corresponding model, we evaluate them on a set of artificially created test instances. Finally, we develop problem-specific algorithms for two variants of the described problem. One considers the control optimization for a single network station, which represents a local operation site featuring a large number of active elements. The used transient model is very detailed and includes a sophisticated representation of the compressor stations. Based on the shortness of the pipes in the station, the corresponding algorithm finds valid solutions by solving a series of stationary model variants as well as a transient rolling horizon approach. As the second variant, we consider the problem on the entire network but assume an approximative model representing the control capabilities of network stations. Aside from a new description of the compression capabilities, we introduce an algorithm that uses a combination of sequential mixed-integer programming, two heuristics based on reduced time horizons, and a specialized dynamic branch-and-bound node limit to determine promising values for the binary variables of the model. Complete solutions for the problem are obtained by fixing the binary values and solving the remaining non-linear program. Both algorithms are investigated in extensive empirical studies based on real-world instances of the corresponding model variants.}, language = {en} } @misc{PrauseHoppmannBaumDefournyetal.2020, author = {Prause, Felix and Hoppmann-Baum, Kai and Defourny, Boris and Koch, Thorsten}, title = {The Maximum Diversity Assortment Selection Problem}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-81039}, year = {2020}, abstract = {In this paper, we introduce the Maximum Diversity Assortment Selection Problem (MADASS), which is a generalization of the 2-dimensional Cutting Stock Problem (2CSP). Given a set of rectangles and a rectangular container, the goal of 2CSP is to determine a subset of rectangles that can be placed in the container without overlapping, i.e., a feasible assortment, such that a maximum area is covered. In MADASS, we need to determine a set of feasible assortments, each of them covering a certain minimum threshold of the container, such that the diversity among them is maximized. Thereby, diversity is defined as minimum or average normalized Hamming-Distance of all assortment pairs. The MADASS Problem was used in the 11th AIMMS-MOPTA Competition in 2019. The methods we describe in this article and the computational results won the contest. In the following, we give a definition of the problem, introduce a mathematical model and solution approaches, determine upper bounds on the diversity, and conclude with computational experiments conducted on test instances derived from the 2CSP literature.}, language = {en} }