@article{StreubelTischendorfGriewank2020, author = {Streubel, Tom and Tischendorf, Caren and Griewank, Andreas}, title = {Piecewise Polynomial Taylor Expansions - The Generalization of Fa{\`a} di Bruno's Formula}, journal = {Modeling, Simulation and Optimization of Complex Processes HPSC 2018}, number = {Modeling, Simulation and Optimization of Complex Processes HPSC 2018}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-030-55240-4_3}, pages = {63 -- 82}, year = {2020}, abstract = {We present an extension of Taylor's Theorem for the piecewise polynomial expansion of non-smooth evaluation procedures involving absolute value operations. Evaluation procedures are computer programs of mathematical functions in closed form expression and allow a different treatment of smooth operations or calls to the absolute value function. The well known classical Theorem of Taylor defines polynomial approximations of sufficiently smooth functions and is widely used for the derivation and analysis of numerical integrators for systems of ordinary differential- or differential-algebraic equations, for the construction of solvers for continuous non-linear optimization of finite dimensional objective functions and for root solving of non-linear systems of equations. The long term goal is the stabilization and acceleration of already known methods and the derivation of new methods by incorporating piecewise polynomial Taylor expansions. The herein provided proof of the higher order approximation quality of the new generalized expansions is constructive and allows efficiently designed algorithms for the execution and computation of the piecewise polynomial expansions. As a demonstration towards the ultimate goal we will derive a prototype of a {\\$}{\\$}k{\\$}{\\$}k-step method on the basis of polynomial interpolation and the proposed generalized expansions.}, language = {en} } @article{LeKoch2021, author = {Le, Thi Thai and Koch, Thorsten}, title = {Instability of a tangential discontinuity surface in a three-dimensional compressible medium}, volume = {33}, journal = {Physics of Fluids}, number = {1}, doi = {10.1063/5.0033753}, pages = {016106}, year = {2021}, abstract = {Compressible flows appear in many natural and technological processes, for instance, the flow of natural gases in a pipe system. Thus, a detailed study of the stability of tangential velocity discontinuity in compressible media is relevant and necessary. The first early investigation in two-dimensional (2D) media was given more than 70 years ago. In this article, we continue investigating the stability in three-dimensional (3D) media. The idealized statement of this problem in an infinite spatial space was studied by Syrovatskii in 1954. However, the omission of the absolute sign of cos θ with θ being the angle between vectors of velocity and wave number in a certain inequality produced the inaccurate conclusion that the flow is always unstable for entire values of the Mach number M. First, we revisit this case to arrive at the correct conclusion, namely that the discontinuity surface is stabilized for a large Mach number with a given value of the angle θ. Next, we introduce a real finite spatial system such that it is bounded by solid walls along the flow direction. We show that the discontinuity surface is stable if and only if the dispersion relation equation has only real roots, with a large value of the Mach number; otherwise, the surface is always unstable. In particular, we show that a smaller critical value of the Mach number is required to make the flow in a narrow channel stable.}, language = {en} } @article{HoppmannBaumHenningsZitteletal.2021, author = {Hoppmann-Baum, Kai and Hennings, Felix and Zittel, Janina and Gotzes, Uwe and Spreckelsen, Eva-Maria and Spreckelsen, Klaus and Koch, Thorsten}, title = {An Optimization Approach for the Transient Control of Hydrogen Transport Networks}, journal = {Mathematical Methods of Operations Research}, number = {Special Issue on Energy Networks}, year = {2021}, language = {en} } @misc{HoppmannBaumMexiBurdakovetal.2020, author = {Hoppmann-Baum, Kai and Mexi, Gioni and Burdakov, Oleg and Casselgren, Carl Johan and Koch, Thorsten}, title = {Length-Constrained Cycle Partition with an Application to UAV Routing}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-80489}, year = {2020}, abstract = {In this article, we discuss the Length-Constrained Cycle Partition Problem (LCCP). Besides edge weights, the undirected graph in LCCP features an individual critical weight value for each vertex. A cycle partition, i.e., a vertex disjoint cycle cover, is a feasible solution if the length of each cycle is not greater than the critical weight of each of the vertices in the cycle. The goal is to find a feasible partition with the minimum number of cycles. In this article, we discuss theoretical properties, preprocessing techniques, and two mixed-integer programming models (MIP) for LCCP both inspired by formulations for the closely related Travelling Salesperson Problem (TSP). Further, we introduce conflict hypergraphs, whose cliques yield valid constraints for the MIP models. We conclude with a report on computational experiments conducted on (A)TSPLIB-based instances. As an example, we use a routing problem in which a fleet of uncrewed aerial vehicles (UAVs) patrols a set of areas.}, language = {en} } @article{GotzesHoppmannBaum2020, author = {Gotzes, Uwe and Hoppmann-Baum, Kai}, title = {Bounding the final rank during a round robin tournament with integer programming}, volume = {1866-1505}, journal = {Operational Research}, doi = {https://doi.org/10.1007/s12351-020-00546-w}, year = {2020}, abstract = {This article is mainly motivated by the urge to answer two kinds of questions regarding the Bundesliga, which is Germany's primary football (soccer) division having the highest average stadium attendance worldwide: "At any point in the season, what is the lowest final rank a certain team can achieve?" and "At any point in the season, what is the highest final rank a certain team can achieve?". Although we focus on the Bundesliga in particular, the integer programming formulations we introduce to answer these questions can easily be adapted to a variety of other league systems and tournaments.}, language = {en} } @article{KochSchmidtHilleretal.2020, author = {Koch, Thorsten and Schmidt, Martin and Hiller, Benjamin and Pfetsch, Marc and Geißler, Bj{\"o}rn and Henrion, Ren{\´e} and Joormann, Imke and Martin, Alexander and Morsi, Antonio and R{\"o}misch, Werner and Schewe, Lars and Schultz, R{\"u}diger}, title = {Capacity Evaluation for Large-Scale Gas Networks}, volume = {35}, journal = {German Success Stories in Industrial Mathematics}, isbn = {978-3-030-81454-0}, doi = {10.1007/978-3-030-81455-7}, pages = {23 -- 28}, year = {2020}, language = {en} } @article{ChenZakiyevaZhuetal.2020, author = {Chen, Ying and Zakiyeva, Nazgul and Zhu, Bangzhu and Koch, Thorsten}, title = {Modeling and Forecasting the Dynamics of the Natural Gas Transmission Network in Germany with the Demand and Supply Balance Constraint}, journal = {Applied Energy}, number = {278}, doi = {10.1016/j.apenergy.2020.115597}, year = {2020}, language = {en} } @article{KochChenLimetal.2020, author = {Koch, Thorsten and Chen, Ying and Lim, Kian Guan and Xu, Xiaofei and Zakiyeva, Nazgul}, title = {A review study of functional autoregressive models with application to energy forecasting}, journal = {WIREs Computational Statistics}, doi = {10.1002/wics.1525}, year = {2020}, language = {en} } @misc{HoppmannBaumHenningsZitteletal.2020, author = {Hoppmann-Baum, Kai and Hennings, Felix and Zittel, Janina and Gotzes, Uwe and Spreckelsen, Eva-Maria and Spreckelsen, Klaus and Koch, Thorsten}, title = {From Natural Gas towards Hydrogen - A Feasibility Study on Current Transport Network Infrastructure and its Technical Control}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-79901}, year = {2020}, abstract = {This study examines the usability of a real-world, large-scale natural gas transport infrastructure for hydrogen transport. We investigate whether a converted network can transport the amounts of hydrogen necessary to satisfy current energy demands. After introducing an optimization model for the robust transient control of hydrogen networks, we conduct computational experiments based on real-world demand scenarios. Using a representative network, we demonstrate that replacing each turbo compressor unit by four parallel hydrogen compressors, each of them comprising multiple serial compression stages, and imposing stricter rules regarding the balancing of in- and outflow suffices to realize transport in a majority of scenarios. However, due to the reduced linepack there is an increased need for technical and non-technical measures leading to a more dynamic network control. Furthermore, the amount of energy needed for compression increases by 364\% on average.}, language = {en} } @article{HoppmannBaumHenningsLenzetal.2021, author = {Hoppmann-Baum, 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}, volume = {22}, journal = {Optimization and Engineering}, doi = {10.1007/s11081-020-09584-x}, pages = {735 -- 781}, year = {2021}, abstract = {In this paper, we describe an algorithmic framework for the optimal operation of transient gas transport networks consisting of a hierarchical MILP formulation together with a sequential linear programming inspired post-processing routine. Its implementation is part of the KOMPASS decision support system, which is currently used in an industrial setting. Real-world gas transport networks are controlled by operating complex pipeline intersection areas, which comprise multiple compressor units, regulators, and valves. In the following, we introduce the concept of network stations to model them. Thereby, we represent the technical capabilities of a station by hand-tailored artificial arcs and add them to network. Furthermore, we choose from a predefined set of flow directions for each network station and time step, which determines where the gas enters and leaves the station. Additionally, we have to select a supported simple state, which consists of two subsets of artificial arcs: Arcs that must and arcs that cannot be used. The goal is to determine a stable control of the network satisfying all supplies and demands. The pipeline intersections, that are represented by the network stations, were initially built centuries ago. Subsequently, due to updates, changes, and extensions, they evolved into highly complex and involved topologies. To extract their basic properties and to model them using computer-readable and optimizable descriptions took several years of effort. To support the dispatchers in controlling the network, we need to compute a continuously updated list of recommended measures. Our motivation for the model presented here is to make fast decisions on important transient global control parameters, i.e., how to route the flow and where to compress the gas. Detailed continuous and discrete technical control measures realizing them, which take all hardware details into account, are determined in a subsequent step. In this paper, we present computational results from the KOMPASS project using detailed real-world data.}, language = {en} } @article{GriewankStreubelTischendorf2020, author = {Griewank, Andreas and Streubel, Tom and Tischendorf, Caren}, title = {On the abs-polynomial expansion of piecewise smooth functions}, journal = {Optimization Methods and Software}, publisher = {Taylor \& Francis}, doi = {10.1080/10556788.2020.1817448}, year = {2020}, abstract = {Tom Streubel has observed that for functions in abs-normal form, generalized Taylor expansions of arbitrary order \$\bar d-1\$ can be generated by algorithmic piecewise differentiation. Abs-normal form means that the real or vector valued function is defined by an evaluation procedure that involves the absolute value function \$|...|\$ apart from arithmetic operations and \$\bar d\$ times continuously differentiable univariate intrinsic functions. The additive terms in Streubel's expansion are abs-polynomial, i.e. involve neither divisions nor intrinsics. When and where no absolute values occur, Moore's recurrences can be used to propagate univariate Taylor polynomials through the evaluation procedure with a computational effort of \$\mathcal O({\bar d}^2)\$, provided all univariate intrinsics are defined as solutions of linear ODEs. This regularity assumption holds for all standard intrinsics, but for irregular elementaries one has to resort to Faa di Bruno's formula, which has exponential complexity in \$\bar d\$. As already conjectured we show that the Moore recurrences can be adapted for regular intrinsics to the abs-normal case. Finally, we observe that where the intrinsics are real analytic the expansions can be extended to infinite series that converge absolutely on spherical domains.}, language = {en} } @incollection{HoppmannBaumMexiBurdakovetal.2020, author = {Hoppmann-Baum, Kai and Mexi, Gioni and Burdakov, Oleg and Casselgren, Carl Johan and Koch, Thorsten}, title = {Minimum Cycle Partition with Length Requirements}, volume = {12296}, booktitle = {Integration of Constraint Programming, Artificial Intelligence, and Operations Research}, editor = {Hebrard, Emmanuel and Musliu, Nysret}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-030-58941-7}, doi = {10.1007/978-3-030-58942-4_18}, pages = {273 -- 282}, year = {2020}, abstract = {In this article we introduce a Minimum Cycle Partition Problem with Length Requirements (CPLR). This generalization of the Travelling Salesman Problem (TSP) originates from routing Unmanned Aerial Vehicles (UAVs). Apart from nonnegative edge weights, CPLR has an individual critical weight value associated with each vertex. A cycle partition, i.e., a vertex disjoint cycle cover, is regarded as a feasible solution if the length of each cycle, which is the sum of the weights of its edges, is not greater than the critical weight of each of its vertices. The goal is to find a feasible partition, which minimizes the number of cycles. In this article, a heuristic algorithm is presented together with a Mixed Integer Programming (MIP) formulation of CPLR. We furthermore introduce a conflict graph, whose cliques yield valid constraints for the MIP model. Finally, we report on computational experiments conducted on TSPLIB-based test instances.}, language = {en} } @article{PrauseHoppmannBaumDefournyetal.2021, author = {Prause, Felix and Hoppmann-Baum, Kai and Defourny, Boris and Koch, Thorsten}, title = {The maximum diversity assortment selection problem}, volume = {93}, journal = {Mathematical Methods of Operations Research}, publisher = {Mathematical Methods of Operations Research}, doi = {https://doi.org/10.1007/s00186-021-00740-2}, pages = {521 -- 554}, year = {2021}, abstract = {In this article, we introduce the Maximum Diversity Assortment Selection Problem (MDASP), which is a generalization of the two-dimensional Knapsack Problem (2D-KP). Given a set of rectangles and a rectangular container, the goal of 2D-KP 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. MDASP is 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 the minimum or average normalized Hamming distance of all assortment pairs. MDASP was the topic of the 11th AIMMS-MOPTA Competition in 2019. The methods described in this article and the resulting 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 2D-KP literature.}, language = {en} } @misc{YuekselErguenZittelWangetal.2020, author = {Yueksel-Erguen, Inci and Zittel, Janina and Wang, Ying and Hennings, Felix and Koch, Thorsten}, title = {Lessons learned from gas network data preprocessing}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-78262}, year = {2020}, abstract = {The German high-pressure natural gas transport network consists of thousands of interconnected elements spread over more than 120,000 km of pipelines built during the last 100 years. During the last decade, we have spent many person-years to extract consistent data out of the available sources, both public and private. Based on two case studies, we present some of the challenges we encountered. Preparing consistent, high-quality data is surprisingly hard, and the effort necessary can hardly be overestimated. Thus, it is particularly important to decide which strategy regarding data curation to adopt. Which precision of the data is necessary? When is it more efficient to work with data that is just sufficiently correct on average? In the case studies we describe our experiences and the strategies we adopted to deal with the obstacles and to minimize future effort. Finally, we would like to emphasize that well-compiled data sets, publicly available for research purposes, provide the grounds for building innovative algorithmic solutions to the challenges of the future.}, language = {en} } @misc{PetkovicZakiyeva2022, author = {Petkovic, Milena and Zakiyeva, Nazgul}, title = {Mathematical Optimization for Analyzing and Forecasting Nonlinear Network Time Series}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-88037}, year = {2022}, abstract = {This work presents an innovative short to mid-term forecasting model that analyzes nonlinear complex spatial and temporal dynamics in energy networks under demand and supply balance constraints using Network Nonlinear Time Series (TS) and Mathematical Programming (MP) approach. We address three challenges simultaneously, namely, the adjacency matrix is unknown; the total amount in the network has to be balanced; dependence is unnecessarily linear. We use a nonparametric approach to handle the nonlinearity and estimate the adjacency matrix under the sparsity assumption. The estimation is conducted with the Mathematical Optimisation method. We illustrate the accuracy and effectiveness of the model on the example of the natural gas transmission network of one of the largest transmission system operators (TSOs) in Germany, Open Grid Europe. The obtained results show that, especially for shorter forecasting horizons, the proposed method outperforms all considered benchmark models, improving the average nMAPE for 5.1\% and average RMSE for 79.6\% compared to the second-best model. The model is capable of capturing the nonlinear dependencies in the complex spatial-temporal network dynamics and benefits from both sparsity assumption and the demand and supply balance constraint.}, language = {en} } @article{PetkovicZakiyeva2022, author = {Petkovic, Milena and Zakiyeva, Nazgul}, title = {Mathematical Optimization for Analyzing and Forecasting Nonlinear Network Time Series}, journal = {Operations Research Proceedings 2022}, year = {2022}, abstract = {This work presents an innovative short to mid-term forecasting model that analyzes nonlinear complex spatial and temporal dynamics in energy networks under demand and supply balance constraints using Network Nonlinear Time Series (TS) and Mathematical Programming (MP) approach. We address three challenges simultaneously, namely, the adjacency matrix is unknown; the total amount in the network has to be balanced; dependence is unnecessarily linear. We use a nonparametric approach to handle the nonlinearity and estimate the adjacency matrix under the sparsity assumption. The estimation is conducted with the Mathematical Optimisation method. We illustrate the accuracy and effectiveness of the model on the example of the natural gas transmission network of one of the largest transmission system operators (TSOs) in Germany, Open Grid Europe. The obtained results show that, especially for shorter forecasting horizons, proposed method outperforms all considered benchmark models, improving the avarage nMAPE for 5.1\% and average RMSE for 79.6\% compared to the second-best model. The model is capable to capture the nonlinear dependencies in the complex spatial-temporal network dynamics and benefits from both sparsity assumption and the demand and supply balance constraint.}, language = {en} } @misc{HenningsHoppmannBaumZittel2022, author = {Hennings, Felix and Hoppmann-Baum, Kai and Zittel, Janina}, title = {Optimizing transient gas network control for challenging real-world instances using MIP-based heuristics}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-86842}, year = {2022}, abstract = {Optimizing the transient control of gas networks is a highly challenging task. The corresponding model incorporates the combinatorial complexity of determining the settings for the many active elements as well as the non-linear and non-convex nature of the physical and technical principles of gas transport. In this paper, we present the latest improvements of our ongoing work to solve this problem for real-world, large-scale problem instances: By adjusting our mixed-integer non-linear programming model regarding the gas compression capabilities in the network, we reflect the technical limits of the underlying units more accurately while maintaining a similar overall model size. In addition, we introduce a new algorithmic approach that is based on splitting the complexity of the problem by first finding assignments for discrete variables and then determining the continuous variables as locally optimal solution of the corresponding non-linear program. For the first task, we design multiple different heuristics based on concepts for general time-expanded optimization problems that find solutions by solving a sequence of sub-problems defined on reduced time horizons. To demonstrate the competitiveness of our approach, we test our algorithm on particularly challenging historic demand scenarios. The results show that high-quality solutions are obtained reliably within short solving times, making the algorithm well-suited to be applied at the core of time-critical industrial applications.}, language = {en} } @misc{PedersenLeKochetal.2022, author = {Pedersen, Jaap and Le, Thi Thai and Koch, Thorsten and Zittel, Janina}, title = {Optimal discrete pipe sizing for tree-shaped CO2 networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-87574}, year = {2022}, abstract = {While energy-intensive industries like the steel industry plan to switch to renewable energy sources, other industries, such as the cement industry, have to rely on carbon capture storage and utilization technologies to reduce the inevitable carbon dioxide (CO2) emissions of their production processes. In this context, we investigate the problem of finding optimal pipeline diameters from a discrete set of diameters for a tree-shaped network transporting captured CO2 from multiple sources to a single sink. The general problem of optimizing arc capacities in potential-based fluid networks is a challenging mixed-integer nonlinear program. Additionally, the behaviour of CO2 is highly sensitive and nonlinear regarding temperature and pressure changes. We propose an iterative algorithm splitting the problem into two parts: a) the pipe-sizing problem under a fixed supply scenario and temperature distribution and b) the thermophysical modelling including mixing effects, the Joule-Thomson effect, and heat exchange with the surrounding environment. We show the effectiveness of our approach by applying our algorithm to a real-world network planning problem for a CO2 network in Western Germany.}, language = {en} } @article{LeKoch2022, author = {Le, Thi Thai and Koch, Thorsten}, title = {Viscosity and porosity effects on tangential-discontinuity surface stability in 3D Compressible Media}, volume = {34}, journal = {Physics of Fluids}, number = {7}, publisher = {AIP Publishing}, doi = {10.1063/5.0095970}, year = {2022}, abstract = {The stability of a flow in porous media relates to the velocity rate of injecting and withdrawing natural gases inside porous storage. We thus aim to analyze the stability of flows in porous media to accelerate the energy transition process. This research examines a flow model of a tangential--velocity discontinuity with porosity and viscosity changes in a three-dimensional (3D) compressible medium because of a co-existence of different gases in a storage. The fluids are assumed to move in a relative motion where the plane y=0 is a tangential-velocity discontinuity surface. We obtain that the critical value of the Mach number to stabilize a tangential discontinuity surface of flows via porous media is smaller than the one of flows in a plane. The critical value of the Mach number M to stabilize a discontinuity surface of the 3D flow is different by a factor |cosθ| compared to the two-dimensional (2D) flow. Here, θ is the angle between velocity and wavenumber vectors. Our results also show that the flow model with viscosity and porosity effects is stable faster than those without these terms. Our analysis is done for both infinite and finite flows. The effect of solid walls along the flow direction could suppress the instability, i.e., the tangential-discontinuity surface is stabilized faster}, language = {en} } @article{LenzSerrano2022, author = {Lenz, Ralf and Serrano, Felipe}, title = {Tight Convex Relaxations for the Expansion Planning Problem}, volume = {194}, journal = {Journal of Optimization Theory and Applications}, doi = {10.1007/s10957-022-02029-8}, pages = {325 -- 352}, year = {2022}, abstract = {Secure energy transport is considered as highly relevant for the basic infrastructure of nowadays society and economy. To satisfy increasing demands and to handle more diverse transport situations, operators of energy networks regularly expand the capacity of their network by building new network elements, known as the expansion planning problem. A key constraint function in expansion planning problems is a nonlinear and nonconvex potential loss function. In order to improve the algorithmic performance of state-of-the-art MINLP solvers, this paper presents an algebraic description for the convex envelope of this function. Through a thorough computational study, we show that this tighter relaxation tremendously improves the performance of the MINLP solver SCIP on a large test set of practically relevant instances for the expansion planning problem. In particular, the results show that our achievements lead to an improvement of the solver performance for a development version by up to 58\%.}, language = {en} } @misc{HosodaMaherShinano2024, author = {Hosoda, Junko and Maher, Stephen J. and Shinano, Yuji}, title = {Combining Benders' decomposition and parallelisation to solve large-scale adaptive network supply chain management problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-98744}, year = {2024}, abstract = {Integrated supply chain network design—combining warehouse clustering with inter- and intra-cluster vehicle routing—is a fundamental feature of supply chain management problems. In this paper, a Benders' decomposition-based parallel heuristic approach for the integrated long-haul and local vehicle routing problem is proposed. The proposed algorithm comprises lower- and upper-bound search algorithms running in parallel to find high-quality solutions for challenging supply chain management problems. A novel Benders' decomposition approach is proposed to aid the improvement in the lower bound for large-scale problems. The results demonstrate that the Benders' decomposition approach is effective in finding strong lower bounds and is beneficial for obtaining high-quality solutions.}, language = {en} } @article{ChenKochZakiyevaetal.2022, author = {Chen, Ying and Koch, Thorsten and Zakiyeva, Nazgul and Liu, Kailiang and Xu, Zhitong and Chen, Chun-houh and Nakano, Junji and Honda, Keisuke}, title = {Article's Scientific Prestige: Measuring the Impact of Individual Articles in the Web of Science}, volume = {17}, number = {1}, doi = {https://doi.org/10.1016/j.joi.2023.101379}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-86380}, pages = {101379}, year = {2022}, abstract = {We performed a citation analysis on the Web of Science publications consisting of more than 63 million articles and 1.45 billion citations on 254 subjects from 1981 to 2020. We proposed the Article's Scientific Prestige (ASP) metric and compared this metric to number of citations (\#Cit) and journal grade in measuring the scientific impact of individual articles in the large-scale hierarchical and multi-disciplined citation network. In contrast to \#Cit, ASP, that is computed based on the eigenvector centrality, considers both direct and indirect citations, and provides steady-state evaluation cross different disciplines. We found that ASP and \#Cit are not aligned for most articles, with a growing mismatch amongst the less cited articles. While both metrics are reliable for evaluating the prestige of articles such as Nobel Prize winning articles, ASP tends to provide more persuasive rankings than \#Cit when the articles are not highly cited. The journal grade, that is eventually determined by a few highly cited articles, is unable to properly reflect the scientific impact of individual articles. The number of references and coauthors are less relevant to scientific impact, but subjects do make a difference.}, language = {en} } @misc{TurnerKochSerranoetal.2022, author = {Turner, Mark and Koch, Thorsten and Serrano, Felipe and Winkler, Michael}, title = {Adaptive Cut Selection in Mixed-Integer Linear Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-86055}, year = {2022}, abstract = {Cut selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter combinations, and so are excellent candidates for parameter tuning. Cut selection scoring rules are usually weighted sums of different measurements, where the weights are parameters. We present a parametric family of mixed-integer linear programs together with infinitely many family-wide valid cuts. Some of these cuts can induce integer optimal solutions directly after being applied, while others fail to do so even if an infinite amount are applied. We show for a specific cut selection rule, that any finite grid search of the parameter space will always miss all parameter values, which select integer optimal inducing cuts in an infinite amount of our problems. We propose a variation on the design of existing graph convolutional neural networks, adapting them to learn cut selection rule parameters. We present a reinforcement learning framework for selecting cuts, and train our design using said framework over MIPLIB 2017. Our framework and design show that adaptive cut selection does substantially improve performance over a diverse set of instances, but that finding a single function describing such a rule is difficult. Code for reproducing all experiments is available at https://github.com/Opt-Mucca/Adaptive-Cutsel-MILP.}, language = {en} } @article{HoppmannBaumBurdakovMexietal.2022, author = {Hoppmann-Baum, Kai and Burdakov, Oleg and Mexi, Gioni and Casselgren, Carl Johan and Koch, Thorsten}, title = {Length-Constrained Cycle Partition with an Application to UAV Routing}, journal = {Optimization Methods and Software}, doi = {10.1080/10556788.2022.2053972}, year = {2022}, abstract = {This article discusses the Length-Constrained Cycle Partition Problem (LCCP), which constitutes a new generalization of the Travelling Salesperson Problem (TSP). Apart from nonnegative edge weights, the undirected graph in LCCP features a nonnegative critical length parameter for each vertex. A cycle partition, i.e., a vertex-disjoint cycle cover, is a feasible solution for LCCP if the length of each cycle is not greater than the critical length of each vertex contained in it. The goal is to find a feasible partition having a minimum number of cycles. Besides analyzing theoretical properties and developing preprocessing techniques, we propose an elaborate heuristic algorithm that produces solutions of good quality even for large-size instances. Moreover, we present two exact mixed-integer programming formulations (MIPs) for LCCP, which are inspired by well-known modeling approaches for TSP. Further, we introduce the concept of conflict hypergraphs, whose cliques yield valid constraints for the MIP models. We conclude with a discussion on computational experiments that we conducted using (A)TSPLIB-based problem instances. As a motivating example application, we describe a routing problem where a fleet of uncrewed aerial vehicles (UAVs) must patrol a given set of areas.}, language = {en} } @article{TurnerKochSerranoetal.2023, author = {Turner, Mark and Koch, Thorsten and Serrano, Felipe and Winkler, Michael}, title = {Adaptive Cut Selection in Mixed-Integer Linear Programming}, volume = {4}, journal = {Open Journal of Mathematical Optimization}, doi = {10.5802/ojmo.25}, pages = {5}, year = {2023}, abstract = {Cutting plane selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter combinations, and so are excellent candidates for parameter tuning. Cut selection scoring rules are usually weighted sums of different measurements, where the weights are parameters. We present a parametric family of mixed-integer linear programs together with infinitely many family-wide valid cuts. Some of these cuts can induce integer optimal solutions directly after being applied, while others fail to do so even if an infinite amount are applied. We show for a specific cut selection rule, that any finite grid search of the parameter space will always miss all parameter values, which select integer optimal inducing cuts in an infinite amount of our problems. We propose a variation on the design of existing graph convolutional neural networks, adapting them to learn cut selection rule parameters. We present a reinforcement learning framework for selecting cuts, and train our design using said framework over MIPLIB 2017 and a neural network verification data set. Our framework and design show that adaptive cut selection does substantially improve performance over a diverse set of instances, but that finding a single function describing such a rule is difficult. Code for reproducing all experiments is available at https://github.com/Opt-Mucca/Adaptive-Cutsel-MILP.}, language = {en} } @misc{Pedersen2020, type = {Master Thesis}, author = {Pedersen, Jaap}, title = {Multiperiod Optimal Power Flow Problem In Distribution System Planning}, pages = {61}, year = {2020}, abstract = {Growing demand, distributed generation, such as renewable energy sources (RES), and the increasing role of storage systems to mitigate the volatility of RES on a medium voltage level, push existing distribution grids to their limits. Therefore, necessary network expansion needs to be evaluated to guarantee a safe and reliable electricity supply in the future taking these challenges into account. This problem is formulated as an optimal power flow (OPF) problem which combines network expansion, volatile generation and storage systems, minimizing network expansion and generation costs. As storage systems introduce a temporal coupling into the system, a multiperiod OPF problem is needed and analysed in this thesis. To reduce complexity, the network expansion problem is represented in a continuous nonlinear programming formulation by using fundamental properties of electrical engeneering. This formulation is validated succesfully against a common mixed integer programming approach on a 30 and 57 bus network with respect to solution and computing time. As the OPF problem is, in general, a nonconvex, nonlinear problem and, thus, hard to solve, convex relaxations of the power flow equations have gained increasing interest. Sufficient conditions are represented which guarantee exactness of a second-order cone (SOC) relaxation of an operational OPF in radial networks. In this thesis, these conditions are enhanced for the network expansion planning problem. Additionally, nonconvexities introduced by the choice of network expansion variables are relaxed by using McCormick envelopes. These relaxations are then applied on the multiperiod OPF and compared to the original problem on a 30 and a 57 bus network. In particular, the computational time is decreased by an order up to 10^2 by the SOC relaxation while it provides either an exact solution or a sufficient lower bound on the original problem. Finally, a sensitivity study is performed on weights of network expansion costs showing strong dependency of both the solution of performed expansion and solution time on the chosen weights.}, language = {en} } @article{RiedmuellerLindner2025, author = {Riedm{\"u}ller, Stephanie and Lindner, Niels}, title = {Column Generation for Periodic Timetabling}, arxiv = {http://arxiv.org/abs/2510.12466}, year = {2025}, abstract = {Periodic timetabling for public transportation networks is typically modelled as a Periodic Event Scheduling Problem (PESP). Solving instances of the benchmark library PESPlib to optimality continues to pose a challenge. As a further approach towards this goal, we remodel the problem by a time discretization of the underlying graph and consider arc-based as well as path-based integer programming formulations. For the path-based case, we use cycles on the graph expansion of the operational lines as variables and, therefore, include more of the problem inherent structure into the model. A consequence is the validity of several known inequalities and a lower bound on the LP-relaxation, that is the best known to date. As an extension we integrate passenger routing into the new model. The proposed models have an advantage in the linear programming relaxation, on the one hand, but have an increased problem size, on the other hand. We define the corresponding pricing problems for the use of column generation to handle the size. Both models are practically tested on different problem instances.}, language = {en} } @misc{LindnerMehlBartoszuketal.2025, author = {Lindner, Niels and Mehl, Lukas and Bartoszuk, Karolina and Berendes, Sarah and Zittel, Janina}, title = {Demand Uncertainty in Energy Systems: Scenario Catalogs vs. Integrated Robust Optimization}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-102404}, year = {2025}, abstract = {Designing efficient energy systems is indispensable for shaping a more sustainable society. This involves making infrastructure investment decisions that must be valid for a long-term time horizon. While energy system optimization models constitute a powerful technique to support planning decisions, they need to cope with inherent uncertainty. For example, predicting future demand on a scale of decades is not only an intricate challenge in itself, but small fluctuations in such a forecast might also largely impact the layout of a complex energy system. In this paper, we compare two methodologies of capturing demand uncertainty for linear-programming based energy system optimization models. On one hand, we generate and analyze catalogs of varying demand scenarios, where each individual scenario is considered independently, so that the optimization produces scenario-specific investment pathways. On the other hand, we make use of robust linear programming to meet the demand of all scenarios at once. Since including a multitude of scenarios increases the size and complexity of the optimization model, we will show how to use warm-starting approaches to accelerate the computation process, by exploiting the similar structure of the linear program across different demand inputs. This allows to integrate a meaningful number of demand scenarios with fully-fledged energy system models. We demonstrate the practical use of our methods in a case study of the Berlin-Brandenburg area in Germany, a region that contains both a metropolitan area and its rural surroundings. As a backbone, we use the open-source framework oemof to create a sector-coupled optimization model for planning an energy system with up to 100\% reduction of greenhouse gas emissions. This model features a fine-grained temporal resolution of one hour for the full year 2050. We consider uncertainty in demand for electricity, hydrogen, natural gas, central, and decentral heat. Based on our computations, we analyze the trade-offs in terms of quality and computation time for scenario catalogs and the robust optimization approach. We further demonstrate that our procedure provides a valuable strategy for decision makers to gain insight on the robustness and sensitivity of solutions regarding demand variability.}, language = {en} } @inproceedings{LindnerMehlBartoszuketal.2025, author = {Lindner, Niels and Mehl, Lukas and Bartoszuk, Karolina and Berendes, Sarah and Zittel, Janina}, title = {Demand Uncertainty in Energy Systems: Scenario Catalogs vs. Integrated Robust Optimization}, booktitle = {Proceedings of the 38th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems}, year = {2025}, abstract = {Designing efficient energy systems is indispensable for shaping a more sustainable society. This involves making infrastructure investment decisions that must be valid for a long-term time horizon. While energy system optimization models constitute a powerful technique to support planning decisions, they need to cope with inherent uncertainty. For example, predicting future demand on a scale of decades is not only an intricate challenge in itself, but small fluctuations in such a forecast might also largely impact the layout of a complex energy system. In this paper, we compare two methodologies of capturing demand uncertainty for linear-programming based energy system optimization models. On one hand, we generate and analyze catalogs of varying demand scenarios, where each individual scenario is considered independently, so that the optimization produces scenario-specific investment pathways. On the other hand, we make use of robust linear programming to meet the demand of all scenarios at once. Since including a multitude of scenarios increases the size and complexity of the optimization model, we will show how to use warm-starting approaches to accelerate the computation process, by exploiting the similar structure of the linear program across different demand inputs. This allows to integrate a meaningful number of demand scenarios with fully-fledged energy system models. We demonstrate the practical use of our methods in a case study of the Berlin-Brandenburg area in Germany, a region that contains both a metropolitan area and its rural surroundings. As a backbone, we use the open-source framework oemof to create a sector-coupled optimization model for planning an energy system with up to 100\% reduction of greenhouse gas emissions. This model features a fine-grained temporal resolution of one hour for the full year 2050. We consider uncertainty in demand for electricity, hydrogen, natural gas, central, and decentral heat. Based on our computations, we analyze the trade-offs in terms of quality and computation time for scenario catalogs and the robust optimization approach. We further demonstrate that our procedure provides a valuable strategy for decision makers to gain insight on the robustness and sensitivity of solutions regarding demand variability.}, language = {en} } @misc{TurnerChmielaKochetal.2023, author = {Turner, Mark and Chmiela, Antonia and Koch, Thorsten and Winkler, Michael}, title = {PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-93095}, year = {2023}, abstract = {A standard tool for modelling real-world optimisation problems is mixed-integer programming (MIP). However, for many of these problems there is either incomplete information describing variable relations, or the relations between variables are highly complex. To overcome both these hurdles, machine learning (ML) models are often used and embedded in the MIP as surrogate models to represent these relations. Due to the large amount of available ML frameworks, formulating ML models into MIPs is highly non-trivial. In this paper we propose a tool for the automatic MIP formulation of trained ML models, allowing easy integration of ML constraints into MIPs. In addition, we introduce a library of MIP instances with embedded ML constraints. The project is available at https://github.com/Opt-Mucca/PySCIPOpt-ML.}, language = {en} } @inproceedings{TurnerChmielaKochetal.2025, author = {Turner, Mark and Chmiela, Antonia and Koch, Thorsten and Winkler, Michael}, title = {PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs}, volume = {15763}, booktitle = {Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2025}, doi = {10.1007/978-3-031-95976-9_14}, year = {2025}, abstract = {A standard tool for modelling real-world optimisation problems is mixed-integer programming (MIP). However, for many of these problems there is either incomplete information describing variable relations, or the relations between variables are highly complex. To overcome both these hurdles, machine learning (ML) models are often used and embedded in the MIP as surrogate models to represent these relations. Due to the large amount of available ML frameworks, formulating ML models into MIPs is highly non-trivial. In this paper we propose a tool for the automatic MIP formulation of trained ML models, allowing easy integration of ML constraints into MIPs. In addition, we introduce a library of MIP instances with embedded ML constraints. The project is available at https://github.com/Opt-Mucca/PySCIPOpt-ML.}, language = {en} } @article{KotilPelofskeRiedmuelleretal.2025, author = {Kotil, Ayse and Pelofske, Elijah and Riedm{\"u}ller, Stephanie and Egger, Daniel J. and Eidenbenz, Stephan and Koch, Thorsten and Woerner, Stefan}, title = {Quantum Approximate Multi-Objective Optimization}, journal = {Nature Computational Science}, arxiv = {http://arxiv.org/abs/2503.22797}, doi = {10.1038/s43588-025-00873-y}, pages = {1168 -- 1177}, year = {2025}, abstract = {The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, i.e., the set of all Pareto optimal solutions, where no objective can be improved without degrading another one. Multi-objective optimization can be challenging classically, even if the corresponding single-objective optimization problems are efficiently solvable. Thus, multi-objective optimization represents a compelling problem class to analyze with quantum computers. In this work, we use low-depth Quantum Approximate Optimization Algorithm to approximate the optimal Pareto front of certain multi-objective weighted maximum cut problems. We demonstrate its performance on an IBM Quantum computer, as well as with Matrix Product State numerical simulation, and show its potential to outperform classical approaches.}, language = {en} } @article{ZittelPetkovicEinck2025, author = {Zittel, Janina and Petkovic, Milena and Einck, Mathias}, title = {Forecasting Hourly Gas Flows}, volume = {79}, journal = {Foresight - The International Journal of Applied Forecasting}, pages = {40 -- 44}, year = {2025}, language = {en} } @article{ShimadaMakoYaegashietal.2025, author = {Shimada, Naoki and Mako, Sato and Yaegashi, Yuta and Koch, Thorsten and Le, Thi Thai}, title = {An Application of Modified S-CLSVOF Method to Kelvin-Helmholtz Instability and Comparison with Theoretical Result}, volume = {58}, journal = {Journal of Chemical Engineering of Japan}, number = {1}, publisher = {Taylor and Francis}, doi = {10.1080/00219592.2025.2451953}, year = {2025}, abstract = {This study focuses on validating a two-phase flow solver based on the modified Simple Coupled Level Set and Volume of Fluid method (Uchihashi et al. (2023)) through viscous Kelvin-Helmholtz instability simulations. Our numerical simulation results are compared with the ones given by Funada and Joseph (2001) to provide reliable predictions of interface behavior under the influence of viscosity. The primary goal is to accurately assess the solver's ability to replicate theoretical analysis of interface behaviors under various conditions. First, the wave between two fluids of identical density is calculated. In addition, the effect of surface tension is investigated. By comparing growth rates, numerical simulations obtain well-agreements with the analytical results on the effect of the fluid viscosity, the wave number, and the surface tension. Finally, fluid density is changed to an air-water system. When relative velocity U is smaller than the criteria of relative velocity U_c given by analytical solutions, the wave is not broken. However, waves are splashed into droplets in the condition of U>U_c. This result agrees with the analysis by Funada and Joseph (2001). These findings provide a robust framework for applying the solver to more complex two-phase flow problems, supporting advancements in numerical simulations of fluid interfaces.}, language = {en} } @article{RongChenKochetal.2026, author = {Rong, Guoyang and Chen, Ying and Koch, Thorsten and Honda, Keisuke}, title = {Assessing data quality in citation analysis: A case study of web of science and Crossref}, volume = {20}, journal = {Journal of Informetrics}, number = {1}, publisher = {Elsevier BV}, issn = {1751-1577}, doi = {10.1016/j.joi.2026.101775}, year = {2026}, language = {en} } @misc{KempkeKoch2025, author = {Kempke, Nils-Christian and Koch, Thorsten}, title = {Low-precision first-order method-based fix-and-propagate heuristics for large-scale mixed-integer linear optimization}, issn = {1438-0064}, arxiv = {http://arxiv.org/abs/2503.10344}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-99612}, year = {2025}, abstract = {We investigate the use of low-precision first-order methods (FOMs) within a fix-and-propagate (FP) framework for solving mixed-integer programming problems (MIPs). FOMs, using only matrix-vector products instead of matrix factorizations, are well suited for GPU acceleration and have recently gained more attention for their application to large-scale linear programming problems (LPs). We employ PDLP, a variant of the Primal-Dual Hybrid Gradient (PDHG) method specialized to LP problems, to solve the LP-relaxation of our MIPs to low accuracy. This solution is used to motivate fixings within our fix-and-propagate framework. We implemented four different FP variants using primal and dual LP solution information. We evaluate the performance of our heuristics on MIPLIB 2017, showcasing that the low-accuracy LP solution produced by the FOM does not lead to a loss in quality of the FP heuristic solutions when compared to a high-accuracy interior-point method LP solution. Further, we use our FP framework to produce high-accuracy solutions for large-scale (up to 243 million non-zeros and 8 million decision variables) unit-commitment energy-system optimization models created with the modeling framework REMix. For the largest problems, we can generate solutions with under 2\% primal-dual gap in less than 4 hours, whereas commercial solvers cannot generate feasible solutions within two days of runtime. This study represents the first successful application of FOMs in large-scale mixed-integer optimization, demonstrating their efficacy and establishing a foundation for future research in this domain.}, language = {en} } @inproceedings{GhannamGleixner2025, author = {Ghannam, Mohammed and Gleixner, Ambros}, title = {Hybrid Genetic Search for Dynamic Vehicle Routing with Time Windows}, booktitle = {Operations Research Proceedings 2023. OR 2023}, doi = {10.1007/978-3-031-58405-3_35}, year = {2025}, language = {en} } @inproceedings{PedersenLindnerRehfeldtetal.2026, author = {Pedersen, Jaap and Lindner, Niels and Rehfeldt, Daniel and Koch, Thorsten}, title = {Comparing Branching Rules for the Quota Steiner Tree Problem with Interference}, booktitle = {Operations Research Proceedings 2025}, year = {2026}, abstract = {Branching decisions play a crucial role in branch-and-bound algorithms for solving combinatorial optimization problems. In this paper, we investigate several branching rules applied to the Quota Steiner Tree Problem with Interference (QSTPI). The Quota Steiner Tree Problem (QSTP) generalizes the classical Steiner Tree Problem (STP) in graphs by seeking a minimum-cost tree that connects a subset of profit-associated vertices whose cumulative profit meets or exceeds a given quota. The QSTPI introduces interference among vertices: Selecting certain vertices simultaneously reduces their individual contributions to the overall profit. This problem arises, for example, in positioning and connecting wind turbines, where turbines possibly shadow other turbines, reducing their energy yield. Unlike classical STP variants, large QSTPI instances require significantly more branching to compute provably optimal solutions. In contrast to branching on variables, we utilize the combinatorial structure of the QSTPI by branching on the graph's vertices. We adapt classical and problem-specific branching rules and present a comprehensive computational study comparing the effectiveness of these branching strategies.}, language = {en} } @inproceedings{KochKempkeLindneretal.2026, author = {Koch, Thorsten and Kempke, Nils-Christian and Lindner, Niels and Mehl, Lukas and Wetzel, Manuel and Zittel, Janina}, title = {High-Performance Robust Energy System Planning with Storage: A Single-LP Approach}, booktitle = {Proceedings of URBSENSE 2026 - 1st International Workshop on URBan SENSEmaking and Intelligence for Safer Cities}, year = {2026}, language = {en} } @article{TurnerBertholdBesanconetal.2023, author = {Turner, Mark and Berthold, Timo and Besan{\c{c}}on, Mathieu and Koch, Thorsten}, title = {Branching via Cutting Plane Selection: Improving Hybrid Branching}, publisher = {Springer}, year = {2023}, abstract = {Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for some cutting planes. We relate branching decisions and cutting planes to each other through the underlying disjunctions that they are based on, with a focus on Gomory mixed-integer cuts and their corresponding split disjunctions. We show that selecting branching decisions based on quality measures of Gomory mixed-integer cuts leads to relatively small branch-and-bound trees, and that the result improves when using cuts that more accurately represent the branching decisions. Finally, we show how the history of previously computed Gomory mixed-integer cuts can be used to improve the performance of the state-of-the-art hybrid branching rule of SCIP. Our results show a \$4\\%\$ decrease in solve time, and an \$8\\%\$ decrease in number of nodes over affected instances of MIPLIB 2017.}, language = {en} } @article{HadjidimitriouKochLippietal.2026, author = {Hadjidimitriou, Natalia Selini and Koch, Thorsten and Lippi, Marco and Petkovic, Milena and Mamei, Marco}, title = {Spatial analysis of COVID-19 and the Russia-Ukraine war impacts on natural gas flows using statistical and machine learning models}, volume = {29}, journal = {World Wide Web}, number = {2}, publisher = {Springer Science and Business Media LLC}, issn = {1386-145X}, doi = {https://doi.org/10.1007/s11280-025-01402-7}, year = {2026}, language = {en} } @misc{KempkeMaherRehfeldtetal.2026, author = {Kempke, Nils-Christian and Maher, Stephen John and Rehfeldt, Daniel and Gleixner, Ambros and Koch, Thorsten and Uslu, Svenja}, title = {Distributed Parallel Structure-Aware Presolving for Arrowhead Linear Programs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-103034}, year = {2026}, abstract = {We present a structure-aware parallel presolve framework specialized to arrowhead linear programs (AHLPs) and designed for high-performance computing (HPC) environments, integrated into the parallel interior point solver PIPS-IPM++. Large-scale LPs arising from automated model generation frequently contain redundancies and numerical pathologies that necessitate effective presolve, yet existing presolve techniques are primarily serial or structure-agnostic and can become time-consuming in parallel solution workflows. Within PIPS-IPM++, AHLPs are stored in distributed memory, and our presolve builds on this to apply a highly parallel, distributed presolve across compute nodes while keeping communication overhead low and preserving the underlying arrowhead structure. We demonstrate the scalability and effectiveness of our approach on a diverse set of AHLPs and compare it against state-of-the-art presolve implementations, including PaPILO and the presolve implemented within Gurobi. Even on a single machine, our presolve significantly outperforms PaPILO by a factor of 18 and Gurobi's presolve by a factor of 6 in terms of shifted geometric mean runtime, while reducing the problems by a similar amount to PaPILO. Using a distributed compute environment, we outperform Gurobi's presolve by a factor of 13.}, language = {en} } @article{SatoKochLe2026, author = {Sato, Mako and Koch, Thorsten and Le, Thi Thai}, title = {Influence of frictional drag on Kelvin-Helmholtz instability in viscous fluids}, volume = {38}, journal = {Physics of Fluids}, number = {1}, publisher = {AIP Publishing}, address = {Physics of Fluids}, doi = {10.1063/5.0306177}, year = {2026}, abstract = {The Kelvin-Helmholtz instability arises at the interface between two fluid layers with a tangential velocity discontinuity, significantly impacting the safety of systems in industrial applications. Despite extensive studies, many theoretical analyses neglect viscosity and frictional drag due to the complexity of solving the dispersion equation. However, including these effects is crucial, as viscosity alters the growth rate of the instability, while frictional drag influences energy dissipation and momentum transfer. In this study, these effects are incorporated into both finite and infinite flows. The assumption of a potential flow combined with a dissipation method is employed to derive the dispersion equation, providing a more tractable approach than direct calculation methods. The results indicate that, in the case of infinite flows, the frictional drag suppresses the growth of the instability for long waves (small wavenumber k) but enhances it for short waves (large k). In contrast, the surface tension dominates, while the frictional drag only slightly affects the growth rate in the case of finite flows bounded by solid walls.}, language = {en} } @inproceedings{RiedmuellerZittelKoch2026, author = {Riedm{\"u}ller, Stephanie and Zittel, Janina and Koch, Thorsten}, title = {Warm-starting Strategies in Scalarization Methods for Multi-Objective Optimization}, booktitle = {Operations Research Proceedings 2025}, arxiv = {http://arxiv.org/abs/2507.21933}, year = {2026}, abstract = {We explore how warm-starting strategies can be integrated into scalarization-based approaches for multi-objective optimization in (mixed) integer linear programming. Scalarization methods remain widely used classical techniques to compute Pareto-optimal solutions in applied settings. They are favored due to their algorithmic simplicity and broad applicability across continuous and integer programs with an arbitrary number of objectives. While warm-starting has been applied in this context before, a systematic methodology and analysis remain lacking. We address this gap by providing a theoretical characterization of warm-starting within scalarization methods, focusing on the sequencing of subproblems. However, optimizing the order of subproblems to maximize warm-start efficiency may conflict with alternative criteria, such as early identification of infeasible regions. We quantify these trade-offs through an extensive computational study.}, language = {en} }