TY - GEN A1 - Kempke, Nils-Christian A1 - Maher, Stephen John A1 - Rehfeldt, Daniel A1 - Gleixner, Ambros A1 - Koch, Thorsten A1 - Uslu, Svenja T1 - Distributed Parallel Structure-Aware Presolving for Arrowhead Linear Programs N2 - 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. T3 - ZIB-Report - 26-01 KW - Linear Programming KW - Presolving KW - Large-Scale Optimization KW - Distributed Parallel Computing KW - Arrowhead Y1 - 2026 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-103034 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - Mehl, Lukas A1 - Bartoszuk, Karolina A1 - Berendes, Sarah A1 - Zittel, Janina T1 - Demand Uncertainty in Energy Systems: Scenario Catalogs vs. Integrated Robust Optimization N2 - 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. T3 - ZIB-Report - 25-19 Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-102404 SN - 1438-0064 ER - TY - GEN A1 - Ebert, Patricia A1 - Schlechte, Thomas A1 - Schwartz, Stephan T1 - Scheduling for German Road Inspectors N2 - For the yearly over 500,000 vehicle inspections of the German Federal Logistics and Mobility Office (BALM), crew rosters must be scheduled to efficiently achieve Germany's road inspection control targets. For that, we present a model to solve the respective duty scheduling and crew rostering problem in order to obtain duty rosters that comply with numerous legal regulations while maximizing the 'control success' to achieve the control targets. We formulate the Template Assignment Problem, which can be modelled as a large scale mixed-integer linear program. Here, feasible combinations of control topics are assigned to the duties using a hypergraph approach. The model is used in production by BALM, and we prove its effectiveness on a number of real-world instances. T3 - ZIB-Report - 25-13 KW - scheduling KW - rostering KW - mixed-integer linear program KW - crew scheduling KW - hypergraph Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-101999 SN - 1438-0064 ER - TY - GEN A1 - Zakiyeva, Nazgul A1 - Petkovic, Milena T1 - Large-scale functional network time series model solved with mathematical programming approach T2 - Econometrics and Statistics N2 - A functional network autoregressive model is proposed for studying large-scale network time series observed at high temporal resolution. The model incorporates high-dimensional curves to capture both serial and cross-sectional dependence in large-scale network functional time series. Estimation of the model is approached using a Mixed Integer Optimization method. Simulation studies confirm the consistency of parameter and adjacency matrix estimation. The method is applied to data from a real-life natural gas supply network. Compared to alternative prediction models, the proposed model delivers more accurate day-ahead hourly out-of-sample forecasts of the gas inflows and outflows at most gas nodes. T3 - ZIB-Report - 25-17 Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-101936 ER - TY - GEN A1 - Shinano, Yuji A1 - Vigerske, Stefan T1 - Smoothie: Mixing the strongest MIP solvers to solve hard MIP instances on supercomputers - Phase I development N2 - Mixed-Integer Linear Programming (MIP) is applicable to such a wide range of real-world decision problems that the competition for the best code to solve such problems has lead to tremendous progress over the last decades. While current solvers can solve some of the problems that seemed completely out-of-reach just 10 years ago, there are always relevant MIP problems that currently cannot be solved. With the Smoothie solver we intend to solve extremely hard MIP problems by building on the many years that went into the development of several state-of-the-art MIP solvers and by utilizing some of the largest computing resources available. The high-level task parallelization framework UG (Ubiquity Generator) is used and extended by Smoothie to build a solver that uses large-scale parallelization to distribute the solution of a single MIP on a shared- or distributed-memory computing infrastructure, thereby employing several established MIP solvers simultaneously. For the first development phase, which is the topic of this report, both FICO Xpress and Gurobi are used in concurrent mode on a single machine, while information on incumbent solutions and explored branch-and-bound subtrees is exchanged. A dynamic restarting mechanism ensures that solver configurations are selected that promise most suitable for the MIP to be solved. We report on initial findings using this early version of Smoothie on unsolved problems from MIPLIB 2017. T3 - ZIB-Report - 25-18 KW - MIPLIB, MIP, UG, Parallelization Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-101906 SN - 1438-0064 ER - TY - GEN A1 - Pedersen, Jaap A1 - Lindner, Niels A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Comparing Branching Rules for the Quota Steiner Tree Problem with Interference N2 - 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 to meet a given quota. The extended version, 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. While exact solvers for standard STP-related problems often rely heavily on reduction techniques and cutting-plane methods – rarely generating large branch-and-bound trees – experiments reveal that large instances of QSTPI 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. T3 - ZIB-Report - 25-16 Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-101250 SN - 1438-0064 ER - TY - GEN A1 - Mehl, Lukas A1 - Lindner, Niels A1 - Bartoszuk, Karolina A1 - Zittel, Janina T1 - Prototypical warm-starts for demand-robust LP-based energy system optimization N2 - The expressiveness of energy system optimization models (ESOMs) depends on a multitude of exogenous parameters. For example, sound estimates of the future energy demand are essential to enable qualified decisions on long-term investments. However, the enormous demand fluctuations even on a fine-grained scale diminish the computational performance of large-scale ESOMs. We therefore propose a clustering-and-decomposition method for linear programming based ESOMs that first identifies and solves prototypical demand scenarios with the dual simplex algorithm, and then composes dual optimal prototype bases to a warm-start basis for the full model. We evaluate the feasibility and computational efficiency our approach on a real-world case study, using a sector-coupled ESOM with hourly resolution for the Berlin-Brandenburg area in Germany, based on the oemof framework. T3 - ZIB-Report - 25-15 Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-101242 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - Liebchen, Christian T1 - A two-stage model for periodic timetabling with fixed line activities N2 - The timetable is a central pillar of any public transportation system. Constructing and optimizing periodic timetables in terms of passenger comfort and operational efficiency leads to NP-hard optimization problems that are also computationally challenging in applications. The Periodic Event Scheduling Problem (PESP) as standard mathematical tool benefits from its succinct formulation and rich combinatorial structure, but suffers from poor linear programming relaxations and weak dual bounds. These difficulties persist in a reduced version, where driving and dwelling activities of the lines are assumed to be fixed. In this case, fixing the initial departure time of each line fully determines the timetable, and for each pair of lines, the resulting (weighted) transfer durations can be expressed in terms of a piecewise linear non-convex function in terms of the difference of the initial times. When the number of activities between two lines is bounded, this function can be computed in polynomial time. By inserting precomputed piecewise linear functions into a mixed-integer program with the initial departure times as variables, we introduce an equivalent formulation for reduced PESP instances. The model bears analogies with quadratic semi-assignment approaches and offers alternative ways to compute primal and dual bounds. We evaluate the computational behavior of our approach on realistic benchmarking instances. T3 - ZIB-Report - 25-14 Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-101234 SN - 1438-0064 ER - TY - GEN A1 - Riedmüller, Stephanie A1 - Zittel, Janina A1 - Koch, Thorsten T1 - Warm-starting Strategies in Scalarization Methods for Multi-Objective Optimization N2 - 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. T3 - ZIB-Report - 25-12 Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-101073 SN - 1438-0064 ER - TY - CHAP A1 - Kunt, Tim A1 - Buchholz, Annika A1 - Khebouri, Imene A1 - Koch, Thorsten A1 - Litzel, Ida A1 - Vu, Thi Huong T1 - Mapping the Web of Science, a large-scale graph and text-based dataset with LLM embeddings T2 - Operations Research Proceedings 2025. OR 2025 N2 - Large text data sets, such as publications, websites, and other text-based media, inherit two distinct types of features: (1) the text itself, its information conveyed through semantics, and (2) its relationship to other texts through links, references, or shared attributes. While the latter can be described as a graph structure and can be handled by a range of established algorithms for classification and prediction, the former has recently gained new potential through the use of LLM embedding models. Demonstrating these possibilities and their practicability, we investigate the Web of Science dataset, containing ~56 million scientific publications through the lens of our proposed embedding method, revealing a self-structured landscape of texts. T3 - ZIB-Report - 25-11 Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-100646 SN - 1438-0064 ER - TY - GEN A1 - Kempke, Nils-Christian A1 - Koch, Thorsten T1 - A GPU accelerated variant of Schroeppel-Shamir's algorithm for solving the market split problem N2 - The market split problem (MSP), introduced by Cornuéjols and Dawande (1998), is a challenging binary optimization problem that performs poorly on state-of-the-art linear programming-based branch-and-cut solvers. We present a novel algorithm for solving the feasibility version of this problem, derived from Schroeppel–Shamir's algorithm for the one-dimensional subset sum problem. Our approach is based on exhaustively enumerating one-dimensional solutions of MSP and utilizing GPUs to evaluate candidate solutions across the entire problem. The resulting hybrid CPU-GPU implementation efficiently solves instances with up to 10 constraints and 90 variables. We demonstrate the algorithm's performance on benchmark problems, solving instances of size (9, 80) in less than fifteen minutes and (10, 90) in up to one day. T3 - ZIB-Report - 25-10 Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-100554 SN - 1438-0064 ER - TY - GEN A1 - Vu, Thi Huong A1 - Litzel, Ida A1 - Koch, Thorsten T1 - Similarity-based fuzzy clustering scientific articles: potentials and challenges from mathematical and computational perspectives N2 - Fuzzy clustering, which allows an article to belong to multiple clusters with soft membership degrees, plays a vital role in analyzing publication data. This problem can be formulated as a constrained optimization model, where the goal is to minimize the discrepancy between the similarity observed from data and the similarity derived from a predicted distribution. While this approach benefits from leveraging state-of-the-art optimization algorithms, tailoring them to work with real, massive databases like OpenAlex or Web of Science -- containing about 70 million articles and a billion citations -- poses significant challenges. We analyze potentials and challenges of the approach from both mathematical and computational perspectives. Among other things, second-order optimality conditions are established, providing new theoretical insights, and practical solution methods are proposed by exploiting the problem’s structure. Specifically, we accelerate the gradient projection method using GPU-based parallel computing to efficiently handle large-scale data. T3 - ZIB-Report - 25-09 KW - bibliometrics KW - fuzzy clustering KW - large-scale publication data KW - non-convex optimization KW - second-order optimality KW - gradient projection methods KW - Nesterov acceleration KW - GPU-based parallel computing Y1 - 2025 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/10036 ER - TY - GEN A1 - Vu, Thi Huong A1 - Koch, Thorsten T1 - Clustering scientific publications: lessons learned through experiments with a real citation network N2 - Clustering scientific publications helps uncover research structures within bibliographic databases. Graph-based methods such as spectral, Louvain, and Leiden clustering are commonly used due to their ability to model citation networks. However, their effectiveness can diminish when applied to real-world data. This study evaluates these clustering algorithms on a citation graph of about 700,000 articles and 4.6 million citations from the Web of Science. The results show that while scalable methods like Louvain and Leiden perform efficiently, their default settings often yield poor partitioning. Meaningful outcomes require careful parameter tuning, especially for large networks with uneven structures, including a dense core and loosely connected papers. These findings highlight practical lessons about the challenges of large-scale data, method selection and tuning based on specific structures of bibliometric clustering tasks. T3 - ZIB-Report - 25-05 KW - graph clustering KW - citation networks KW - Web of Science KW - bibliometric analysis KW - unsupervised learning Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-100418 ER - TY - GEN A1 - Riedmüller, Stephanie A1 - Buchholz, Annika A1 - Zittel, Janina T1 - Enhancing Multi-Energy Modeling: The Role of Mixed-Integer Optimization Decisions N2 - The goal to decarbonize the energy sector has led to increased research in modeling and optimizing multi-energy systems. One of the most promising and popular techniques for modeling and solving (multi-)energy optimization problems is (multi-objective) mixed-integer programming, valued for its ability to represent the complexities of integrated energy systems. While the literature often focuses on deriving mathematical formulations and parameter settings, less attention is given to critical post-formulation decisions. Modeling multi-energy systems as mixed-integer linear optimization programs demands decisions across multiple degrees of freedom. Key steps include reducing a real-world multi energy network into an abstract topology, defining variables, formulating the relevant (in-)equalities to represent technical requirements, setting (multiple) objectives, and integrating these elements into a mixed-integer program (MIP). However, with these elements fixed, the specific transformation of the abstract topology into a graph structure and the construction of the MIP remain non-uniquely. These choices can significantly impact user-friendliness, problem size, and computational efficiency, thus affecting the feasibility and efficiency of modeling efforts. In this work, we identify and analyze the additional degrees of freedom and describe two distinct approaches to address them. The approaches are compared regarding mathematical equivalence, suitability for solution algorithms, and clarity of the underlying topology. A case study on a realistic subarea of Berlin’s district heating network involving tri-objective optimization for a unit commitment problem demonstrates the practical significance of these decisions. By highlighting these critical yet often overlooked aspects, our work equips energy system modelers with insights to improve computational efficiency, scalability, and interpretability in their optimization efforts, ultimately enhancing the practicality and effectiveness of multi-energy system models. T3 - ZIB-Report - 25-08 Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-100329 SN - 1438-0064 ER - TY - GEN A1 - Kempke, Nils-Christian A1 - Koch, Thorsten T1 - Low-precision first-order method-based fix-and-propagate heuristics for large-scale mixed-integer linear optimization N2 - 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. T3 - ZIB-Report - 25-04 KW - Integer programming KW - Large scale optimization KW - Linear Programming KW - Primal heuristics KW - OR in energy Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-99612 SN - 1438-0064 ER - TY - GEN A1 - Kempke, Nils-Christian A1 - Kunt, Tim A1 - Katamish, Bassel A1 - Vanaret, Charlie A1 - Sasanpour, Shima A1 - Clarner, Jan-Patrick A1 - Koch, Thorsten T1 - Developing heuristic solution techniques for large-scale unit commitment models N2 - Shifting towards renewable energy sources and reducing carbon emissions necessitate sophisticated energy system planning, optimization, and extension. Energy systems optimization models (ESOMs) often form the basis for political and operational decision-making. ESOMs are frequently formulated as linear (LPs) and mixed-integer linear (MIP) problems. MIPs allow continuous and discrete decision variables. Consequently, they are substantially more expressive than LPs but also more challenging to solve. The ever-growing size and complexity of ESOMs take a toll on the computational time of state-of-the-art commercial solvers. Indeed, for large-scale ESOMs, solving the LP relaxation -- the basis of modern MIP solution algorithms -- can be very costly. These time requirements can render ESOM MIPs impractical for real-world applications. This article considers a set of large-scale decarbonization-focused unit commitment models with expansion decisions based on the REMix framework (up to 83 million variables and 900,000 discrete decision variables). For these particular instances, the solution to the LP relaxation and the MIP optimum lie close. Based on this observation, we investigate the application of relaxation-enforced neighborhood search (RENS), machine learning guided rounding, and a fix-and-propagate (FP) heuristic as a standalone solution method. Our approach generated feasible solutions 20 to 100 times faster than GUROBI, achieving comparable solution quality with primal-dual gaps as low as 1% and up to 35%. This enabled us to solve numerous scenarios without lowering the quality of our models. For some instances that Gurobi could not solve within two days, our FP method provided feasible solutions in under one hour. T3 - ZIB-Report - 25-03 KW - Energy system optimization models KW - Unit commitment KW - Mixed-integer programming KW - Large-scale optimization KW - Primal heuristics Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-99555 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels T1 - A Multi-Commodity Flow Heuristic for Integrated Periodic Timetabling for Railway Construction Sites N2 - Rescheduling a railway system comprises many aspects, such as line planning, timetabling, track allocation, and vehicle scheduling. For periodic timetables, these features can be integrated into a single mixed-integer program extending the Periodic Event Scheduling Problem (PESP) with a routing component. We develop a multi-commodity-flow-based heuristic that allows to compute better solutions faster than a black-box MIP approach on real construction site scenarios on the S-Bahn Berlin network. T3 - ZIB-Report - 25-02 KW - Railway Timetabling KW - Periodic Timetabling KW - Rescheduling KW - Railway Track Allocation Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-99449 SN - 1438-0064 ER - TY - GEN A1 - Pedersen, Jaap A1 - Lindner, Niels A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Integrated Wind Farm Design: Optimizing Turbine Placement and Cable Routing with Wake Effects N2 - An accelerated deployment of renewable energy sources is crucial for a successful transformation of the current energy system, with wind energy playing a key role in this transition. This study addresses the integrated wind farm layout and cable routing problem, a challenging nonlinear optimization problem. We model this problem as an extended version of the Quota Steiner Tree Problem (QSTP), optimizing turbine placement and network connectivity simultaneously to meet specified expansion targets. Our proposed approach accounts for the wake effect - a region of reduced wind speed induced by each installed turbine - and enforces minimum spacing between turbines. We introduce an exact solution framework in terms of the novel Quota Steiner Tree Problem with interference (QSTPI). By leveraging an interference-based splitting strategy, we develop an advanced solver capable of tackling large-scale problem instances. The presented approach outperforms generic state-of-the-art mixed integer programming solvers on our dataset by up to two orders of magnitude. Moreover, we demonstrate that our integrated method significantly reduces the costs in contrast to a sequential approach. Thus, we provide a planning tool that enhances existing planning methodologies for supporting a faster and cost-efficient expansion of wind energy. T3 - ZIB-Report - 25-01 Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-99218 SN - 1438-0064 ER - TY - GEN A1 - Kempke, Nils-Christian A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - A Massively Parallel Interior-Point-Method for Arrowhead Linear Programs N2 - In practice, non-specialized interior point algorithms often cannot utilize the massively parallel compute resources offered by modern many- and multi-core compute platforms. However, efficient distributed solution techniques are required, especially for large-scale linear programs. This article describes a new decomposition technique for systems of linear equations implemented in the parallel interior-point solver PIPS-IPM++. The algorithm exploits a matrix structure commonly found in optimization problems: a doubly-bordered block-diagonal or arrowhead structure. This structure is preserved in the linear KKT systems solved during each iteration of the interior-point method. We present a hierarchical Schur complement decomposition that distributes and solves the linear optimization problem; it is designed for high-performance architectures and scales well with the availability of additional computing resources. The decomposition approach uses the border constraints’ locality to decouple the factorization process. Our approach is motivated by large-scale unit-commitment problems. We demonstrate the performance of our method on a set of mid-to large-scale instances, some of which have more than 10^9 nonzeros in their constraint matrix. T3 - ZIB-Report - 24-13 KW - direct methods for linear systems KW - mathematical programming KW - parallel computation KW - linear programming KW - large-scale problems KW - interior-point methods Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-98829 SN - 1438-0064 ER - TY - GEN A1 - Hosoda, Junko A1 - Maher, Stephen J. A1 - Shinano, Yuji T1 - Combining Benders’ decomposition and parallelisation to solve large-scale adaptive network supply chain management problems N2 - 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. T3 - ZIB-Report - 24-12 Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-98744 SN - 1438-0064 ER - TY - GEN A1 - Yueksel-Erguen, Inci A1 - Litzel, Ida A1 - Peng, Hanqiu T1 - Integrating Large Citation Datasets N2 - This paper explores methods for building a comprehensive citation graph using big data techniques to evaluate scientific impact more accurately. Traditional citation metrics have limitations, and this work investigates merging large citation datasets to create a more accurate picture. Challenges of big data, like inconsistent data formats and lack of unique identifiers, are addressed through deduplication efforts, resulting in a streamlined and reliable merged dataset with over 119 million records and 1.4 billion citations. We demonstrate that merging large citation datasets builds a more accurate citation graph facilitating a more robust evaluation of scientific impact. T3 - ZIB-Report - 24-10 KW - big data preprocessing KW - data analytics KW - citation graphs Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-98033 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - Bartoszuk, Karolina A1 - Debgupta, Srinwanti A1 - Gering, Marie-Claire A1 - Muschner, Christoph A1 - Zittel, Janina T1 - Warm-starting modeling to generate alternatives for energy transition paths in the Berlin-Brandenburg area N2 - Energy system optimization models are key to investigate energy transition paths towards a decarbonized future. Since this approach comes with intrinsic uncertainties, it is insufficient to compute a single optimal solution assuming perfect foresight to provide a profound basis for decision makers. The paradigm of modeling to generate alternatives enables to explore the near-optimal solution space to a certain extent. However, large-scale energy models require a non-negligible computation time to be solved. We propose to use warm start methods to accelerate the process of finding close-to-optimal alternatives. In an extensive case study for the energy transition of the Berlin-Brandenburg area, we make use of the sector-coupled linear programming oemof-B3 model to analyze a scenario for the year 2050 with a resolution of one hour and 100% reduction of greenhouse gas emissions. We demonstrate that we can actually achieve a significant computational speedup. T3 - ZIB-Report - 24-08 KW - Energy System Optimization KW - Energy Transition KW - Modeling to Generate Alternatives Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-97835 SN - 1438-0064 ER - TY - GEN A1 - Ebert, Patricia A1 - Masing, Berenike A1 - Lindner, Niels A1 - Gleixner, Ambros T1 - Sorting Criteria for Line-based Periodic Timetabling Heuristics N2 - It is well-known that optimal solutions are notoriously hard to find for the Periodic Event Scheduling Problem (PESP), which is the standard mathematical formulation to optimize periodic timetables in public transport. We consider a class of incremental heuristics that have been demonstrated to be effective by Lindner and Liebchen (2023), however, for only one fixed sorting strategy of lines along which a solution is constructed. Thus, in this paper, we examine a variety of sortings based on the number, weight, weighted span, and lower bound of arcs, and test for each setting various combinations of the driving, dwelling, and transfer arcs of lines. Additionally, we assess the impact on the incremental extension of the event-activity network by minimizing resp. maximizing a connectivity measure between subsets of lines. We compare our 27 sortings on the railway instances of the benchmarking library PESPlib within the ConcurrentPESP solver framework. We are able to find five new incumbent solutions, resulting in improvements of up to 2%. T3 - ZIB-Report - 24-07 KW - Public Transport KW - Timetabling KW - Periodic Event Scheduling Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-97826 SN - 1438-0064 ER - TY - GEN A1 - Riedmüller, Stephanie A1 - Rivetta, Fabian A1 - Zittel, Janina T1 - Long-Term Multi-Objective Optimization for Integrated Unit Commitment and Investment Planning for District Heating Networks N2 - The need to decarbonize the energy system has intensified the focus on district heating networks in urban and suburban areas. Therefore, exploring transformation pathways with reasonable trade-offs between economic viability and environmental goals became necessary. We introduce a network-flow-based model class integrating unit commitment and long-term investment planning for multi-energy systems. While the integration of unit commitment and investment planning has been applied to multi-energy systems, a formal introduction and suitability for the application of long-term portfolio planning of an energy provider on an urban scale has yet to be met. Based on mixed integer linear programming, the model bridges the gap between overly detailed industrial modeling tools not designed for computational efficiency at scale and rather abstract academic models. The formulation is tested on Berlin's district heating network. Hence, the challenge lies in a large number of variables and constraints and the coupling of time steps, for example, through investment decisions. A case study explores different solutions on the Pareto front defined by optimal trade-offs between minimizing costs and emissions through a lexicographic optimization approach. The resulting solution catalog can provide decision-makers valuable insights into feasible transformation pathways, highlighting distinctions between robust and target-dependent investments. T3 - ZIB-Report - 24-09 KW - multi-objective optimization KW - multi-energy systems KW - investment planning KW - unit commitment Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-97804 SN - 1438-0064 ER - TY - THES A1 - Kunt, Tim T1 - The n-Queens Problem in Higher Dimensions N2 - How many mutually non-attacking queens can be placed on a d-dimensional chessboard of size n? The n-queens problem in higher dimensions is a generalization of the well-known n-queens problem. We provide a comprehensive overview of theoretical results, bounds, solution methods, and the interconnectivity of the problem within topics of discrete optimization and combinatorics. We present an integer programming formulation of the n-queens problem in higher dimensions and several strengthenings through additional valid inequalities. Compared to recent benchmarks, we achieve a speedup in computational time between 15-70x over all instances of the integer programs. Our computational results prove optimality of certificates for several large instances. Breaking additional, previously unsolved instances with the proposed methods is likely possible. On the primal side, we further discuss heuristic approaches to constructing solutions that turn out to be optimal when compared to the IP. We conclude with preliminary results on the number and density of the solutions. T3 - ZIB-Report - 24-05 KW - Integer Programming KW - Maximum Independent Set KW - n-Queens Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-96468 ER - TY - GEN A1 - Le, Thi Thai T1 - Effect of viscous forces on the interface stability of a tangential-velocity discontinuity in compressible fluids T2 - Journal N2 - Compressible flows are prevalent in natural and technological processes, particularly in the energy transition to renewable energy systems. Consequently, extensive research has focused on understanding the stability of tangential--velocity discontinuity in compressible media. Despite recent advancements that address industrial challenges more realistically, many studies have ignored viscous stress tensors' impact, leading to inaccuracies in predicting interface stability. This omission becomes critical, especially in high Reynolds or low Mach number flows, where viscous forces dissipate kinetic energy across interfaces, affect total energy dissipation, and dampen flow instabilities. Our work is thus motivated to analyze the viscosity force effect by including the viscous stress tensor terms in the motion equations. Our results show that by considering the effect of viscous forces, the tangential-velocity discontinuity interface is constantly destabilized for the entire range of the Mach number. T3 - ZIB-Report - 24-04 Y1 - 2024 ER - TY - GEN A1 - Yueksel-Erguen, Inci A1 - Koch, Thorsten A1 - Zittel, Janina T1 - Mathematical optimization based flow scenario generation for operational analysis of European gas transport networks based on open data N2 - The decarbonization of the European energy system demands a rapid and comprehensive transformation while securing energy supplies at all times. Still, natural gas plays a crucial role in this process. Recent unexpected events forced drastic changes in gas routes throughout Europe. Therefore, operational-level analysis of the gas transport networks and technical capacities to cope with these transitions using unconventional scenarios has become essential. Unfortunately, data limitations often hinder such analyses. To overcome this challenge, we propose a mathematical model-based scenario generator that enables operational analysis of the European gas network using open data. Our approach focuses on the consistent analysis of specific partitions of the gas transport network, whose network topology data is readily available. We generate reproducible and consistent node-based gas in/out-flow scenarios for these defined network partitions to enable feasibility analysis and data quality assessment. Our proposed method is demonstrated through several applications that address the feasibility analysis and data quality assessment of the German gas transport network. By using open data and a mathematical modeling approach, our method allows for a more comprehensive understanding of the gas transport network's behavior and assists in decision-making during the transition to decarbonization. T3 - ZIB-Report - 24-03 Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-95789 SN - 1438-0064 ER - TY - GEN A1 - Bolusani, Suresh A1 - Besançon, Mathieu A1 - Bestuzheva, Ksenia A1 - Chmiela, Antonia A1 - Dionísio, João A1 - Donkiewicz, Tim A1 - van Doornmalen, Jasper A1 - Eifler, Leon A1 - Ghannam, Mohammed A1 - Gleixner, Ambros A1 - Graczyk, Christoph A1 - Halbig, Katrin A1 - Hedtke, Ivo A1 - Hoen, Alexander A1 - Hojny, Christopher A1 - van der Hulst, Rolf A1 - Kamp, Dominik A1 - Koch, Thorsten A1 - Kofler, Kevin A1 - Lentz, Jurgen A1 - Manns, Julian A1 - Mexi, Gioni A1 - Mühmer, Erik A1 - E. Pfetsch, Marc A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Turner, Mark A1 - Vigerske, Stefan A1 - Weninger, Dieter A1 - Xu, Liding T1 - The SCIP Optimization Suite 9.0 N2 - The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming framework SCIP. This report discusses the enhancements and extensions included in the SCIP Optimization Suite 9.0. The updates in SCIP 9.0 include improved symmetry handling, additions and improvements of nonlinear handlers and primal heuristics, a new cut generator and two new cut selection schemes, a new branching rule, a new LP interface, and several bug fixes. The SCIP Optimization Suite 9.0 also features new Rust and C++ interfaces for SCIP, new Python interface for SoPlex, along with enhancements to existing interfaces. The SCIP Optimization Suite 9.0 also includes new and improved features in the LP solver SoPlex, the presolving library PaPILO, the parallel framework UG, the decomposition framework GCG, and the SCIP extension SCIP-SDP. These additions and enhancements have resulted in an overall performance improvement of SCIP in terms of solving time, number of nodes in the branch-and-bound tree, as well as the reliability of the solver. T3 - ZIB-Report - 24-02-29 KW - Constraint integer programming KW - Linear programming KW - Mixed-integer linear programming KW - Mixed-integer nonlinear programming KW - Optimization solver KW - Branch-and-cut KW - Branch-and-price KW - Column generation KW - Parallelization KW - Mixed-integer semidefinite programming Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-95528 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - Masing, Berenike T1 - SAT-Generated Initial Solutions for Integrated Line Planning and Turn-Sensitive Periodic Timetabling with Track Choice N2 - Periodic timetabling is a challenging planning task in public transport. As safety requirements are crucial, track allocation is indispensable for validating the practical feasibility of a railway timetable. For busy stations with limited capacities, this requires a detailed planning of turnarounds. It is therefore desirable to integrate timetabling not only with track allocation, but also with vehicle scheduling and line planning. This is captured by the Integrated Line Planning and Turn-Sensitive Periodic Timetabling Problem with Track Choice, whose MIP formulation has been demonstrated to be effective for construction site railway rescheduling, as long as a good quality initial solution is available. In this paper, we discuss how to generate such a solution by extending the SAT formulation of the Periodic Event Scheduling Problem with track choice, track occupation, and minimum service frequency components. The SAT approach is superior to pure MIP on real-world instances of the S-Bahn Berlin network. T3 - ZIB-Report - 24-01 KW - Periodic Timetabling KW - Railway Timetabling KW - Railway Track Allocation KW - Boolean Satisfiability Problem KW - Rescheduling KW - Line Planning Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-94644 SN - 1438-0064 ER - TY - GEN A1 - Prause, Felix T1 - A Multi-Swap Heuristic for Rolling Stock Rotation Planning with Predictive Maintenance N2 - We present a heuristic solution approach for the rolling stock rotation problem with predictive maintenance (RSRP-PdM). The task of this problem is to assign a sequence of trips to each of the vehicles and to schedule their maintenance such that all trips can be operated. Here, the health states of the vehicles are considered to be random variables distributed by a family of probability distribution functions, and the maintenance services should be scheduled based on the failure probability of the vehicles. The proposed algorithm first generates a solution by solving an integer linear program and then heuristically improves this solution by applying a local search procedure. For this purpose, the trips assigned to the vehicles are split up and recombined, whereby additional deadhead trips can be inserted between the partial assignments. Subse- quently, the maintenance is scheduled by solving a shortest path problem in a state-expanded version of a space-time graph restricted to the trips of the individual vehicles. The solution approach is tested and evaluated on a set of test instances based on real-world timetables. T3 - ZIB-Report - 23-29 KW - Rolling stock rotation planning KW - Predictive maintenance KW - Heuristic KW - State-expanded graph model KW - Integer linear program Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-93133 SN - 1438-0064 ER - TY - GEN A1 - Zakiyeva, Nazgul A1 - Petkovic, Milena T1 - High-dimensional high-frequency time series prediction with a mixed integer optimisation method T2 - Operations Research Proceedings T3 - ZIB-Report - 23-30 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-93114 SN - 1438-0064 ER - TY - GEN A1 - Turner, Mark A1 - Chmiela, Antonia A1 - Koch, Thorsten A1 - Winkler, Michael T1 - PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs N2 - 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. T3 - ZIB-Report - 23-28 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-93095 SN - 1438-0064 ER - TY - GEN A1 - Fujii, Koichi A1 - Kim, Sunyoung A1 - Kojima, Masakazu A1 - Mittelmann, Hans D. A1 - Shinano, Yuji T1 - An Exceptionally Difficult Binary Quadratic Optimization Problem with Symmetry: a Challenge for The Largest Unsolved QAP Instance Tai256c N2 - Tai256c is the largest unsolved quadratic assignment problem (QAP) instance in QAPLIB. It is known that QAP tai256c can be converted into a 256 dimensional binary quadratic optimization problem (BQOP) with a single cardinality constraint which requires the sum of the binary variables to be 92. As the BQOP is much simpler than the original QAP, the conversion increases the possibility to solve the QAP. Solving exactly the BQOP, however, is still very difficult. Indeed, a 1.48% gap remains between the best known upper bound (UB) and lower bound (LB) of the unknown optimal value. This paper shows that the BQOP admits a nontrivial symmetry, a property that makes the BQOP very hard to solve. The symmetry induces equivalent subproblems in branch and bound (BB) methods. To effectively improve the LB, we propose an efficient BB method that incorporates a doubly nonnegative relaxation, the standard orbit branching and a technique to prune equivalent subproblems. With this BB method, a new LB with 1.25% gap is successfully obtained, and computing an LB with 1.0% gap is shown to be still quite difficult. T3 - ZIB-Report - 23-27 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-93072 SN - 1438-0064 ER - TY - GEN A1 - Eifler, Leon A1 - Nicolas-Thouvenin, Jules A1 - Gleixner, Ambros T1 - Combining Precision Boosting with LP Iterative Refinement for Exact Linear Optimization N2 - This article studies a combination of the two state-of-the-art algorithms for the exact solution of linear programs (LPs) over the rational numbers, i.e., without any roundoff errors or numerical tolerances. By integrating the method of precision boosting inside an LP iterative refinement loop, the combined algorithm is able to leverage the strengths of both methods: the speed of LP iterative refinement, in particular in the majority of cases when a double-precision floating-point solver is able to compute approximate solutions with small errors, and the robustness of precision boosting whenever extended levels of precision become necessary. We compare the practical performance of the resulting algorithm with both puremethods on a large set of LPs and mixed-integer programs (MIPs). The results show that the combined algorithm solves more instances than a pure LP iterative refinement approach, while being faster than pure precision boosting. When embedded in an exact branch-and-cut framework for MIPs, the combined algorithm is able to reduce the number of failed calls to the exact LP solver to zero, while maintaining the speed of the pure LP iterative refinement approach. T3 - ZIB-Report - 23-26 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-92573 SN - 1438-0064 ER - TY - GEN A1 - Löbel, Fabian A1 - Borndörfer, Ralf A1 - Weider, Steffen T1 - Non-Linear Battery Behavior in Electric Vehicle Scheduling Problems N2 - The currently most popular approach to handle non-linear battery behavior for electric vehicle scheduling is to use a linear spline interpolation of the charge curve. We show that this can lead to approximate models that underestimate the charge duration and overestimate the state of charge, which is not desirable. While the error is of second order with respect to the interpolation step size, the associated mixed-integer linear programs do not scale well with the number of spline segments. It is therefore recommendable to use coarse interpolation grids adapted to the curvature of the charge curve, and to include sufficient safety margins to ensure solutions of approximate models remain feasible subjected to the exact charge curve. T3 - ZIB-Report - 23-24 KW - Electric Vehicle Scheduling KW - Non-Linear Charging Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-92441 SN - 1438-0064 ER - TY - GEN A1 - Bortoletto, Enrico A1 - Lindner, Niels T1 - Scaling and Rounding Periodic Event Scheduling Instances to Different Period Times N2 - The Periodic Event Scheduling Problem (PESP) is a notoriously hard combinatorial optimization problem, essential for the design of periodic timetables in public transportation. The coefficients of the integer variables in the standard mixed integer linear programming formulations of PESP are the period time, e.g., 60 for a horizon of one hour with a resolution of one minute. In many application scenarios, lines with different frequencies have to be scheduled, leading to period times with many divisors. It then seems natural to consider derived instances, where the period time is a divisor of the original one, thereby smaller, and bounds are scaled and rounded accordingly. To this end, we identify two rounding schemes: wide and tight. We then discuss the approximation performance of both strategies, in theory and practice. T3 - ZIB-Report - 23-23 KW - Timetabling KW - Mixed-Integer Programming KW - Public Transport Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-92315 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - Liebchen, Christian T1 - Incremental Heuristics for Periodic Timetabling N2 - We present incremental heuristics for the Periodic Event Scheduling Problem (PESP), the standard mathematical tool to optimize periodic timetables in public transport. The core of our method is to solve successively larger subinstances making use of previously found solutions. Introducing the technical notion of free stratifications, we formulate a general scheme for incremental heuristics for PESP. More practically, we use line and station information to create heuristics that add lines or stations one by one, and we evaluate these heuristics on instances of the benchmarking library PESPlib. This approach is indeed viable, and leads to new incumbent solutions for six PESPlib instances. T3 - ZIB-Report - 23-22 KW - Timetabling KW - Mixed-Integer Programming KW - Public Transport Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-92309 SN - 1438-0064 ER - TY - GEN A1 - Prause, Felix A1 - Borndörfer, Ralf T1 - Construction of a Test Library for the Rolling Stock Rotation Problem with Predictive Maintenance N2 - We describe the development of a test library for the rolling stock rotation problem with predictive maintenance (RSRP-PdM). Our approach involves the utilization of genuine timetables from a private German railroad company. The generated instances incorporate probability distribution functions for modeling the health states of the vehicles and the considered trips possess varying degradation functions. RSRP-PdM involves assigning trips to a fleet of vehicles and scheduling their maintenance based on their individual health states. The goal is to minimize the total costs consisting of operational costs and the expected costs associated with vehicle failures. The failure probability is dependent on the health states of the vehicles, which are assumed to be random variables distributed by a family of probability distributions. Each distribution is represented by the parameters characterizing it and during the operation of the trips, these parameters get altered. Our approach incorporates non-linear degradation functions to describe the inference of the parameters but also linear ones could be applied. The resulting instances consist of the timetables of the individual lines that use the same vehicle type. Overall, we employ these assumptions and utilize open-source data to create a library of instances with varying difficulty. Our approach is vital for evaluating and comparing algorithms designed to solve the RSRP-PdM. T3 - ZIB-Report - 23-20 KW - Rolling Stock Rotation Planning KW - Predictive Maintenance KW - Test Library Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91734 SN - 1438-0064 ER - TY - GEN A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu T1 - A Context-Aware Cutting Plane Selection Algorithm for Mixed-Integer Programming N2 - The current cut selection algorithm used in mixed-integer programming solvers has remained largely unchanged since its creation. In this paper, we propose a set of new cut scoring measures, cut filtering techniques, and stopping criteria, extending the current state-of-the-art algorithm and obtaining a 5\% performance improvement for SCIP over the MIPLIB 2017 benchmark set. T3 - ZIB-Report - 23-21 KW - cutting plane selection KW - mixed-integer programming Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91691 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization N2 - The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition. T3 - ZIB-Report - 23-19 KW - shortest path KW - flight planning KW - free flight KW - optimal control KW - global optimization KW - Newton's method Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91309 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - Masing, Berenike T1 - On the Split Closure of the Periodic Timetabling Polytope N2 - The Periodic Event Scheduling Problem (PESP) is the central mathematical tool for periodic timetable optimization in public transport. PESP can be formulated in several ways as a mixed-integer linear program with typically general integer variables. We investigate the split closure of these formulations and show that split inequalities are identical with the recently introduced flip inequalities. While split inequalities are a general mixed-integer programming technique, flip inequalities are defined in purely combinatorial terms, namely cycles and arc sets of the digraph underlying the PESP instance. It is known that flip inequalities can be separated in pseudo-polynomial time. We prove that this is best possible unless P $=$ NP, but also observe that the complexity becomes linear-time if the cycle defining the flip inequality is fixed. Moreover, introducing mixed-integer-compatible maps, we compare the split closures of different formulations, and show that reformulation or binarization by subdivision do not lead to stronger split closures. Finally, we estimate computationally how much of the optimality gap of the instances of the benchmark library PESPlib can be closed exclusively by split cuts, and provide better dual bounds for five instances. T3 - ZIB-Report - 23-16 KW - Periodic Event Scheduling Problem KW - Periodic Timetabling KW - Split Closure KW - Mixed-Integer Programming Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91156 SN - 1438-0064 ER - TY - GEN A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu A1 - Koch, Thorsten T1 - Branching via Cutting Plane Selection: Improving Hybrid Branching N2 - 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. T3 - ZIB-Report - 23-17 KW - cutting plane selection KW - variable selection KW - mixed-integer programming Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91120 SN - 1438-0064 ER - TY - GEN A1 - Tjusila, Gennesaret A1 - Besancon, Mathieu A1 - Turner, Mark A1 - Koch, Thorsten T1 - How Many Clues To Give? A Bilevel Formulation For The Minimum Sudoku Clue Problem N2 - It has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in any puzzle whose unique solution is the given grid? We call this problem the Minimum Sudoku Clue Problem (MSCP). We formulate MSCP as a binary bilevel linear program, present a class of globally valid inequalities, and provide a computational study on 50 MSCP instances of 9 by 9 Sudoku grids. Using a general bilevel solver, we solve 95\% of instances to optimality, and show that the solution process benefits from the addition of a moderate amount of inequalities. Finally, we extend the proposed model to other combinatorial problems in which uniqueness of the solution is of interest. T3 - ZIB-Report - 23-15 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-90902 ER - TY - GEN A1 - Pedersen, Jaap A1 - Weinand, Jann Michael A1 - Syranidou, Chloi A1 - Rehfeldt, Daniel T1 - An efficient solver for multi-objective onshore wind farm siting and network integration N2 - Existing planning approaches for onshore wind farm siting and network integration often do not meet minimum cost solutions or social and environmental considerations. In this paper, we develop an approach for the multi-objective optimization of turbine locations and their network connection using a Quota Steiner tree problem. Applying a novel transformation on a known directed cut formulation, reduction techniques, and heuristics, we design an exact solver that makes large problem instances solvable and outperforms generic MIP solvers. Although our case studies in selected regions of Germany show large trade-offs between the objective criteria of cost and landscape impact, small burdens on one criterion can significantly improve the other criteria. In addition, we demonstrate that contrary to many approaches for exclusive turbine siting, network integration must be simultaneously optimized in order to avoid excessive costs or landscape impacts in the course of a wind farm project. Our novel problem formulation and the developed solver can assist planners in decision making and help optimize wind farms in large regions in the future. T3 - ZIB-Report - 23-10 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-90590 SN - 1438-0064 ER - TY - GEN A1 - Eifler, Leon A1 - Gleixner, Ambros T1 - Safe and Verified Gomory Mixed Integer Cuts in a Rational MIP Framework N2 - This paper is concerned with the exact solution of mixed-integer programs (MIPs) over the rational numbers, i.e., without any roundoff errors and error tolerances. Here, one computational bottleneck that should be avoided whenever possible is to employ large-scale symbolic computations. Instead it is often possible to use safe directed rounding methods, e.g., to generate provably correct dual bounds. In this work, we continue to leverage this paradigm and extend an exact branch-and-bound framework by separation routines for safe cutting planes, based on the approach first introduced by Cook, Dash, Fukasawa, and Goycoolea in 2009. Constraints are aggregated safely using approximate dual multipliers from an LP solve, followed by mixed-integer rounding to generate provably valid, although slightly weaker inequalities. We generalize this approach to problem data that is not representable in floating-point arithmetic, add routines for controlling the encoding length of the resulting cutting planes, and show how these cutting planes can be verified according to the VIPR certificate standard. Furthermore, we analyze the performance impact of these cutting planes in the context of an exact MIP framework, showing that we can solve 21.5% more instances and reduce solving times by 26.8% on the MIPLIB 2017 benchmark test set. T3 - ZIB-Report - 23-09 KW - Mixed integer programming, Exact computation, Rational arithmetic, Cutting Planes, Symbolic Computations, Certificate of correctness Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-90159 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Newton's Method for Global Free Flight Trajectory Optimization N2 - Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case. T3 - ZIB-Report - 23-08 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89876 ER - TY - GEN A1 - Vohra, Sumit Kumar A1 - Harth, Philipp A1 - Isoe, Yasuko A1 - Bahl, Armin A1 - Fotowat, Haleh A1 - Engert, Florian A1 - Hege, Hans-Christian A1 - Baum, Daniel T1 - A Visual Interface for Exploring Hypotheses about Neural Circuits N2 - One of the fundamental problems in neurobiological research is to understand how neural circuits generate behaviors in response to sensory stimuli. Elucidating such neural circuits requires anatomical and functional information about the neurons that are active during the processing of the sensory information and generation of the respective response, as well as an identification of the connections between these neurons. With modern imaging techniques, both morphological properties of individual neurons as well as functional information related to sensory processing, information integration and behavior can be obtained. Given the resulting information, neurobiologists are faced with the task of identifying the anatomical structures down to individual neurons that are linked to the studied behavior and the processing of the respective sensory stimuli. Here, we present a novel interactive tool that assists neurobiologists in the aforementioned task by allowing them to extract hypothetical neural circuits constrained by anatomical and functional data. Our approach is based on two types of structural data: brain regions that are anatomically or functionally defined, and morphologies of individual neurons. Both types of structural data are interlinked and augmented with additional information. The presented tool allows the expert user to identify neurons using Boolean queries. The interactive formulation of these queries is supported by linked views, using, among other things, two novel 2D abstractions of neural circuits. The approach was validated in two case studies investigating the neural basis of vision-based behavioral responses in zebrafish larvae. Despite this particular application, we believe that the presented tool will be of general interest for exploring hypotheses about neural circuits in other species, genera and taxa. T3 - ZIB-Report - 23-07 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89932 SN - 1438-0064 ER - TY - GEN A1 - Schiewe, Philine A1 - Goerigk, Marc A1 - Lindner, Niels T1 - Introducing TimPassLib - A library for integrated periodic timetabling and passenger routing N2 - Classic models to derive a timetable for public transport often face a chicken-and-egg situation: A good timetable should offer passengers routes with small travel times, but the route choice of passengers depends on the timetable. While models that fix passenger routes were frequently considered in the literature, integrated models that simultaneously optimize timetables and passenger routes have seen increasing attention lately. This creates a growing need for a set of instances that allows to test and compare new algorithmic developments for the integrated problem. Our paper addresses this requirement by presenting TimPassLib, a new benchmark library of instances for integrated periodic timetabling and passenger routing. T3 - ZIB-Report - 23-06 KW - periodic timetabling KW - optimization in public transport KW - data sets KW - benchmarking Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89741 SN - 1438-0064 ER - TY - GEN A1 - Masing, Berenike A1 - Lindner, Niels A1 - Ebert, Patricia T1 - Forward and Line-Based Cycle Bases for Periodic Timetabling N2 - The optimization of periodic timetables is an indispensable planning task in public transport. Although the periodic event scheduling problem (PESP) provides an elegant mathematical formulation of the periodic timetabling problem that led to many insights for primal heuristics, it is notoriously hard to solve to optimality. One reason is that for the standard mixed-integer linear programming formulations, linear programming relaxations are weak and the integer variables are of pure technical nature and in general do not correlate with the objective value. While the first problem has been addressed by developing several families of cutting planes, we focus on the second aspect. We discuss integral forward cycle bases as a concept to compute improved dual bounds for PESP instances. To this end, we develop the theory of forward cycle bases on general digraphs. Specifically for the application of timetabling, we devise a generic procedure to construct line-based event-activity networks, and give a simple recipe for an integral forward cycle basis on such networks. Finally, we analyze the 16 railway instances of the benchmark library PESPlib, match them to the line-based structure and use forward cycle bases to compute better dual bounds for 14 out of the 16 instances. T3 - ZIB-Report - 23-05 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89731 SN - 1438-0064 ER - TY - GEN A1 - Hosoda, Junko A1 - Maher, Stephen J. A1 - Shinano, Yuji A1 - Villumsen, Jonas Christoffer T1 - A parallel branch-and-bound heuristic for the integrated long-haul and local vehicle routing problem on an adaptive transportation network N2 - Consolidation of commodities and coordination of vehicle routes are fundamental features of supply chain management problems. While locations for consolidation and coordination are typically known a priori, in adaptive transportation networks this is not the case. The identification of such consolidation locations forms part of the decision making process. Supply chain management problems integrating the designation of consolidation locations with the coordination of long haul and local vehicle routing is not only challenging to solve, but also very difficult to formulate mathematically. In this paper, the first mathematical model integrating location clustering with long haul and local vehicle routing is proposed. This mathematical formulation is used to develop algorithms to find high quality solutions. A novel parallel framework is developed that combines exact and heuristic methods to improve the search for high quality solutions and provide valid bounds. The results demonstrate that using exact methods to guide heuristic search is an effective approach to find high quality solutions for difficult supply chain management problems. T3 - ZIB-Report - 23-02 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89700 SN - 1438-0064 ER - TY - GEN A1 - Prause, Felix A1 - Borndörfer, Ralf A1 - Grimm, Boris A1 - Tesch, Alexander T1 - Approximating the RSRP with Predictive Maintenance N2 - We study the solution of the rolling stock rotation problem with predictive maintenance (RSRP-PM) by an iterative refinement approach that is based on a state-expanded event-graph. In this graph, the states are parameters of a failure distribution, and paths correspond to vehicle rotations with associated health state approximations. An optimal set of paths including maintenance can be computed by solving an integer linear program. Afterwards, the graph is refined and the procedure repeated. An associated linear program gives rise to a lower bound that can be used to determine the solution quality. Computational results for two instances derived from real world timetables of a German railway company are presented. The results show the effectiveness of the approach and the quality of the solutions. T3 - ZIB-Report - 23-04 KW - Rolling Stock Rotation Planning KW - Predictive Maintenance KW - Integer Linear Programming KW - Heuristic KW - Lower Bound Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89531 SN - 1438-0064 ER - TY - GEN A1 - Bestuzheva, Ksenia A1 - Chmiela, Antonia A1 - Müller, Benjamin A1 - Serrano, Felipe A1 - Vigerske, Stefan A1 - Wegscheider, Fabian T1 - Global Optimization of Mixed-Integer Nonlinear Programs with SCIP 8.0 N2 - For over ten years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs (MINLPs). With the recently published version~8.0, these capabilities have been largely reworked and extended. This paper discusses the motivations for recent changes and provides an overview of features that are particular to MINLP solving in SCIP. Further, difficulties in benchmarking global MINLP solvers are discussed and a comparison with several state-of-the-art global MINLP solvers is provided. T3 - ZIB-Report - 23-01 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89348 SN - 1438-0064 ER - TY - GEN A1 - Turner, Mark A1 - Berthold, Timo A1 - Besançon, Mathieu A1 - Koch, Thorsten T1 - Cutting Plane Selection with Analytic Centers and Multiregression N2 - 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. T3 - ZIB-Report - 22-28 KW - cut selection KW - anlalytic center KW - mixed-integer programming Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89065 SN - 1438-0064 ER - TY - GEN A1 - Schütte, Christof A1 - Klus, Stefan A1 - Hartmann, Carsten T1 - Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning N2 - One of the main challenges in molecular dynamics is overcoming the “timescale barrier”, a phrase used to describe that in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, not even on the largest or specifically dedicated supercomputers. This article discusses how to circumvent the timescale barrier by a collection of transfer operator-based techniques that have emerged from dynamical systems theory, numerical mathematics, and machine learning over the last two decades. We will focus on how transfer operators can be used to approximate the dynamical behavior on long timescales, review the introduction of this approach into molecular dynamics, and outline the respective theory as well as the algorithmic development from the early numerics-based methods, via variational reformulations, to modern data-based techniques utilizing and improving concepts from machine learning. Furthermore, its relation to rare event simulation techniques will be explained, revealing a broad equivalence of variational principles for long-time quantities in MD. The article will mainly take a mathematical perspective and will leave the application to real-world molecular systems to the more than 1000 research articles already written on this subject. T3 - ZIB-Report - 22-25 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-88637 SN - 1438-0064 ER - TY - GEN A1 - Masing, Berenike A1 - Lindner, Niels A1 - Liebchen, Christian T1 - Periodic Timetabling with Integrated Track Choice for Railway Construction Sites N2 - We propose a mixed-integer linear programming model to generate and optimize periodic timetables with integrated track choice in the context of railway construction sites. When a section of a railway network becomes unavailable, the nearby areas are typically operated close to their capacity limits, and hence carefully modeling headways and allowing flexible routings becomes vital. We therefore discuss first how to integrate headway constraints into the Periodic Event Scheduling Problem (PESP) that do not only prevent overtaking, but also guarantee conflict-free timetables in general and particularly inside stations. Secondly, we introduce a turn-sensitive event-activity network, which is able to integrate routing alternatives for turnarounds at stations, e.g., turning at a platform vs. at a pocket track for metro-like systems. We propose several model formulations to include track choice, and finally evaluate them on six real construction site scenarios on the S-Bahn Berlin network. T3 - ZIB-Report - 22-26 KW - Railway Timetabling KW - Periodic Timetabling KW - Periodic Event Scheduling KW - Train Routing KW - Turnarounds Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-88626 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Mexi, Gioni A1 - Salvagnin, Domenico T1 - Using Multiple Reference Vectors and Objective Scaling in the Feasibility Pump N2 - The Feasibility Pump (FP) is one of the best-known primal heuristics for mixed-integer programming (MIP): more than 15 papers suggested various modifications of all of its steps. So far, no variant considered information across multiple iterations, but all instead maintained the principle to optimize towards a single reference integer point. In this paper, we evaluate the usage of multiple reference vectors in all stages of the FP algorithm. In particular, we use LP-feasible vectors obtained during the main loop to tighten the variable domains before entering the computationally expensive enumeration stage. Moreover, we consider multiple integer reference vectors to explore further optimizing directions and introduce alternative objective scaling terms to balance the contributions of the distance functions and the original MIP objective. Our computational experiments demonstrate that the new method can improve performance on general MIP test sets. In detail, our modifications provide a 29.3% solution quality improvement and 4.0% running time improvement in an embedded setting, needing 16.0% fewer iterations over a large test set of MIP instances. In addition, the method’s success rate increases considerably within the first few iterations. In a standalone setting, we also observe a moderate performance improvement, which makes our version of FP suitable for the two main use-cases of the algorithm. T3 - ZIB-Report - 22-14 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-88513 SN - 1438-0064 ER - TY - GEN A1 - Bestuzheva, Ksenia A1 - Gleixner, Ambros A1 - Völker, Helena T1 - Strengthening SONC Relaxations with Constraints Derived from Variable Bounds N2 - Certificates of polynomial nonnegativity can be used to obtain tight dual bounds for polynomial optimization problems. We consider Sums of Nonnegative Circuit (SONC) polynomials certificates, which are well suited for sparse problems since the computational cost depends only on the number of terms in the polynomials and does not depend on the degrees of the polynomials. This work is a first step to integrating SONC-based relaxations of polynomial problems into a branch-and-bound algorithm. To this end, the SONC relaxation for constrained optimization problems is extended in order to better utilize variable bounds, since this property is key for the success of a relaxation in the context of branch-and-bound. Computational experiments show that the proposed extension is crucial for making the SONC relaxations applicable to most constrained polynomial optimization problems and for integrating the two approaches. T3 - ZIB-Report - 22-23 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-88306 SN - 1438-0064 ER - TY - GEN A1 - Rehfeldt, Daniel A1 - Fujisawa, Katsuki A1 - Koch, Thorsten A1 - Nakao, Masahiro A1 - Shinano, Yuji T1 - Computing single-source shortest paths on graphs with over 8 trillion edges N2 - This paper introduces an implementation for solving the single-source shortest path problem on distributed-memory machines. It is tailored to power-law graphs and scales to trillions of edges. The new implementation reached 2nd and 10th place in the latest Graph500 benchmark in June 2022 and handled the largest and second-largest graphs among all participants. T3 - ZIB-Report - 22-22 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-88180 SN - 1438-0064 ER - TY - GEN A1 - Straube, Arthur A1 - Winkelmann, Stefanie A1 - Höfling, Felix T1 - Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles N2 - Our theoretical study concerns an urea-urease-based pH oscillator confined to giant lipid vesicles. Under suitable conditions, differential transport of urea and hydrogen ion across the unilamellar vesicle membrane periodically resets the pH clock that switches the system from acid to basic, resulting in self-sustained oscillations. We analyse the structure of the limit cycle, which controls the dynamics for giant vesicles and dominates the strongly stochastic oscillations in small vesicles of submicrometer size. To this end, we derive reduced models, amenable to analytic treatments, and show that the accuracy of predictions, including the period of oscillations, is highly sensitive to the choice of the reduction scheme. In particular, we suggest an accurate two-variable model and show its equivalence to a three-variable model that admits an interpretation in terms of a chemical reaction network. The accurate description of a single pH oscillator appears crucial for rationalizing experiments and understanding communication of vesicles and synchronization of rhythms. T3 - ZIB-Report - 22-21 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-88179 SN - 1438-0064 ER - TY - GEN A1 - Fujii, Koichi A1 - Kim, Sunyoung A1 - Kojima, Masakazu A1 - Mittelmann, Hans D. A1 - Shinano, Yuji T1 - The Largest Unsolved QAP Instance Tai256c Can Be Converted into A 256-dimensional Simple BQOP with A Single Cardinality Constraint N2 - Tai256c is the largest unsolved quadratic assignment problem (QAP) instance in QAPLIB; a 1.48% gap remains between the best known feasible objective value and lower bound of the unknown optimal value. This paper shows that the instance can be converted into a 256 dimensional binary quadratic optimization problem (BQOP) with a single cardinality constraint which requires the sum of the binary variables to be 92.The converted BQOP is much simpler than the original QAP tai256c and it also inherits some of the symmetry properties. However, it is still very difficult to solve. We present an efficient branch and bound method for improving the lower bound effectively. A new lower bound with 1.36% gap is also provided. T3 - ZIB-Report - 22-18 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-88086 SN - 1438-0064 ER - TY - GEN A1 - Petkovic, Milena A1 - Zakiyeva, Nazgul T1 - Mathematical Optimization for Analyzing and Forecasting Nonlinear Network Time Series N2 - 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. T3 - ZIB-Report - 22-19 KW - nonlinear time series KW - mathematical optimization KW - energy networks Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-88037 SN - 1438-0064 ER - TY - GEN A1 - Yueksel-Erguen, Inci A1 - Most, Dieter A1 - Wyrwoll, Lothar A1 - Schmitt, Carlo A1 - Zittel, Janina T1 - Modeling the transition of the multimodal pan-European energy system including an integrated analysis of electricity and gas transport N2 - The European energy system has been through a fundamental transformation since the Paris Agreement to reduce greenhouse gas emissions. The transition involves several energy-generating and consuming sectors emphasizing sector coupling. The increase in the share of renewable energy sources has revealed the need for flexibility in the electri city grid. Thus, holistic planning of pathways towards decarbonized energy systems also involves assessing the gas infrastructure to provide such a flexibility and support for the security of supply. In this paper, we propose a workflow to investigate such optimal energy transition pathways considering sector coupling. This workflow involves an integrated operational analysis of the electricity market, its transmission grid, and the gas grid in high spatio-temporal resolution. In a case study on a pan-European scale between 2020-2050, we show that carbon neutrality can be reached within feasible additional costs and in time. However, the manifestation of the potential pathways strongly depends on political and technological constraints. Sector coupling acts as an enabler of cross-border cooperation to achieve both, decarbonization and security of supply. T3 - ZIB-Report - 22-17 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-87774 SN - 1438-0064 ER - TY - GEN A1 - Clarner, Jan-Patrick A1 - Tawfik, Christine A1 - Koch, Thorsten A1 - Zittel, Janina T1 - Network-induced Unit Commitment - A model class for investment and production portfolio planning for multi-energy systems N2 - In light of the energy transition production planning of future decarbonized energy systems lead to very large and complex optimization problems. A widely used modeling paradigm for modeling and solving such problems is mathematical programming. While there are various scientific energy system models and modeling tools, most of them do not provide the necessary level of detail or the modeling flexibility to be applicable for industrial usage. Industrial modeling tools, on the other hand, provide a high level of detail and modeling flexibility. However, those models often exhibit a size and complexity that restricts their scope to a time horizon of several months, severely complicating long-term planning. As a remedy, we propose a model class that is detailed enough for real-world usage but still compact enough for long-term planning. The model class is based on a generalized unit commitment problem on a network with investment decisions. The focus lies on the topological dependency of different energy production and transportation units. T3 - ZIB-Report - 22-16 KW - Multi-energy systems KW - Unit commitment KW - Investment planning Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-87607 SN - 1438-0064 ER - TY - GEN A1 - Pedersen, Jaap A1 - Le, Thi Thai A1 - Koch, Thorsten A1 - Zittel, Janina T1 - Optimal discrete pipe sizing for tree-shaped CO2 networks N2 - 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. T3 - ZIB-Report - 22-15 KW - CO2 Transport KW - Network Design KW - Pipeline Sizing Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-87574 SN - 1438-0064 ER - TY - GEN A1 - Bortoletto, Enrico A1 - Lindner, Niels A1 - Masing, Berenike T1 - Tropical Neighbourhood Search: A New Heuristic for Periodic Timetabling N2 - Periodic timetabling is a central aspect of both the long-term organization and the day-to-day operations of a public transportation system. The Periodic Event Scheduling Problem (PESP), the combinatorial optimization problem that forms the mathematical basis of periodic timetabling, is an extremely hard problem, for which optimal solutions are hardly ever found in practice. The most prominent solving strategies today are based on mixed-integer programming, and there is a concurrent PESP solver employing a wide range of heuristics [3]. We present tropical neighborhood search (tns), a novel PESP heuristic. The method is based on the relations between periodic timetabling and tropical geometry [4]. We implement tns into the concurrent solver, and test it on instances of the benchmarking library PESPlib. The inclusion of tns turns out to be quite beneficial to the solver: tns is able to escape local optima for the modulo network simplex algorithm, and the overall share of improvement coming from tns is substantial compared to the other methods available in the solver. Finally, we provide better primal bounds for five PESPlib instances. T3 - ZIB-Report - 22-13 KW - Periodic Timetabling KW - Tropical Geometry KW - Neighbourhood Search KW - Mixed-Integer Programming Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-87385 SN - 1438-0064 ER - TY - GEN A1 - Nava-Yazdani, Esfandiar A1 - Hanik, Martin A1 - Ambellan, Felix A1 - von Tycowicz, Christoph T1 - On Gradient Formulas in an Algorithm for the Logarithm of the Sasaki Metric N2 - The Sasaki metric is the canonical metric on the tangent bundle TM of a Riemannian manifold M. It is highly useful for data analysis in TM (e.g., when one is interested in the statistics of a set of geodesics in M). To this end, computing the Riemannian logarithm is often necessary, and an iterative algorithm was proposed by Muralidharan and Fletcher. In this note, we derive approximation formulas of the energy gradients in their algorithm that we use with success. T3 - ZIB-Report - 22-12 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-87174 SN - 1438-0064 ER - TY - GEN A1 - Hennings, Felix A1 - Hoppmann-Baum, Kai A1 - Zittel, Janina T1 - Optimizing transient gas network control for challenging real-world instances using MIP-based heuristics N2 - 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. T3 - ZIB-Report - 22-08 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-86842 SN - 1438-0064 ER - TY - GEN A1 - Kostré, Margarita A1 - Sunkara, Vikram A1 - Schütte, Christof A1 - Djurdjevac Conrad, Nataša T1 - Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia N2 - Spreading processes are important drivers of change in social systems. To understand the mechanisms of spreading it is fundamental to have information about the underlying contact network and the dynamical parameters of the process. However, in many real-wold examples, this information is not known and needs to be inferred from data. State-of-the-art spreading inference methods have mostly been applied to modern social systems, as they rely on availability of very detailed data. In this paper we study the inference challenges for historical spreading processes, for which only very fragmented information is available. To cope with this problem, we extend existing network models by formulating a model on a mesoscale with temporal spreading rate. Furthermore, we formulate the respective parameter inference problem for the extended model. We apply our approach to the romanization process of Northern Tunisia, a scarce dataset, and study properties of the inferred time-evolving interregional networks. As a result, we show that (1) optimal solutions consist of very different network structures and spreading rate functions; and that (2) these diverse solutions produce very similar spreading patterns. Finally, we discuss how inferred dominant interregional connections are related to available archaeological traces. Historical networks resulting from our approach can help understanding complex processes of cultural change in ancient times. T3 - ZIB-Report - 22-10 KW - mesoscale spreading process, network inference, time-evolving network, romanization spreading, scarce data Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-86764 SN - 1438-0064 ER - TY - GEN A1 - Bortoletto, Enrico A1 - Lindner, Niels A1 - Masing, Berenike T1 - The Tropical and Zonotopal Geometry of Periodic Timetables N2 - The Periodic Event Scheduling Problem (PESP) is the standard mathematical tool for optimizing periodic timetabling problems in public transport. A solution to PESP consists of three parts: a periodic timetable, a periodic tension, and integer periodic offset values. While the space of periodic tension has received much attention in the past, we explore geometric properties of the other two components, establishing novel connections between periodic timetabling and discrete geometry. Firstly, we study the space of feasible periodic timetables, and decompose it into polytropes, i.e., polytopes that are convex both classically and in the sense of tropical geometry. We then study this decomposition and use it to outline a new heuristic for PESP, based on the tropical neighbourhood of the polytropes. Secondly, we recognize that the space of fractional cycle offsets is in fact a zonotope. We relate its zonotopal tilings back to the hyperrectangle of fractional periodic tensions and to the tropical neighbourhood of the periodic timetable space. To conclude we also use this new understanding to give tight lower bounds on the minimum width of an integral cycle basis. T3 - ZIB-Report - 22-09 KW - periodic event scheduling KW - tropical geometry KW - zonotopal tilings Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-86708 SN - 1438-0064 ER - TY - JOUR A1 - Chen, Ying A1 - Koch, Thorsten A1 - Zakiyeva, Nazgul A1 - Liu, Kailiang A1 - Xu, Zhitong A1 - Chen, Chun-houh A1 - Nakano, Junji A1 - Honda, Keisuke T1 - Article's Scientific Prestige: Measuring the Impact of Individual Articles in the Web of Science N2 - 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. T3 - ZIB-Report - 22-07 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-86380 VL - 17 IS - 1 SP - 101379 ER - TY - GEN A1 - Turner, Mark A1 - Koch, Thorsten A1 - Serrano, Felipe A1 - Winkler, Michael T1 - Adaptive Cut Selection in Mixed-Integer Linear Programming N2 - 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. T3 - ZIB-Report - 22-04 KW - cut selection KW - mixed-integer linear programming KW - reinforcement learning Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-86055 SN - 1438-0064 ER - TY - GEN A1 - Rehfeldt, Daniel A1 - Koch, Thorsten A1 - Shinano, Yuji T1 - Faster exact solution of sparse MaxCut and QUBO problems T3 - ZIB-Report - 22-02 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-85715 SN - 1438-0064 ER - TY - GEN A1 - Masing, Berenike A1 - Lindner, Niels A1 - Borndörfer, Ralf T1 - The Price of Symmetric Line Plans in the Parametric City N2 - We consider the line planning problem in public transport in the Parametric City, an idealized model that captures typical scenarios by a (small) number of parameters. The Parametric City is rotation symmetric, but optimal line plans are not always symmetric. This raises the question to quantify the symmetry gap between the best symmetric and the overall best solution. For our analysis, we formulate the line planning problem as a mixed integer linear program, that can be solved in polynomial time if the solutions are forced to be symmetric. The symmetry gap is provably small when a specific Parametric City parameter is fixed, and we give an approximation algorithm for line planning in the Parametric City in this case. While the symmetry gap can be arbitrarily large in general, we show that symmetric line plans are a good choice in most practical situations. T3 - ZIB-Report - 22-01 KW - line planning KW - mixed integer programming KW - parametric city modeling Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-85648 SN - 1438-0064 ER - TY - GEN A1 - Hennings, Felix A1 - Petkovic, Milena A1 - Streubel, Tom T1 - On the Numerical Treatment of Interlaced Target Values - Modeling, Optimization and Simulation of Regulating Valves in Gas Networks N2 - Due to the current and foreseeable shifts in energy production, the trading and transport operations of gas will become more dynamic, volatile, and hence also less predictable. Therefore, computer-aided support in terms of rapid simulation and control optimization will further broaden its importance for gas network dispatching. In this paper, we aim to contribute and openly publish two new mathematical models for regulators, also referred to as control valves, which together with compressors make up the most complex and involved types of active elements in gas network infrastructures. They provide full direct control over gas networks but are in turn controlled via target values, also known as set-point values, themselves. Our models incorporate up to six dynamical target values to define desired transient states for the elements' local vicinity within the network. That is, each pair of every two target values defines a bounding box for the inlet pressure, outlet pressure as well as the passing mass flow of gas. In the proposed models, those target values are prioritized differently and are constantly in competition with each other, which can only be resolved dynamically at run-time of either a simulation or optimization process. Besides careful derivation, we compare simulation and optimization results with predictions of the commercial simulation tool SIMONE. T3 - ZIB-Report - 21-32 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-85359 SN - 1438-0064 ER - TY - GEN A1 - Bestuzheva, Ksenia A1 - Besançon, Mathieu A1 - Chen, Wei-Kun A1 - Chmiela, Antonia A1 - Donkiewicz, Tim A1 - van Doornmalen, Jasper A1 - Eifler, Leon A1 - Gaul, Oliver A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Gottwald, Leona A1 - Graczyk, Christoph A1 - Halbig, Katrin A1 - Hoen, Alexander A1 - Hojny, Christopher A1 - van der Hulst, Rolf A1 - Koch, Thorsten A1 - Lübbecke, Marco A1 - Maher, Stephen J. A1 - Matter, Frederic A1 - Mühmer, Erik A1 - Müller, Benjamin A1 - Pfetsch, Marc E. A1 - Rehfeldt, Daniel A1 - Schlein, Steffan A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Sofranac, Boro A1 - Turner, Mark A1 - Vigerske, Stefan A1 - Wegscheider, Fabian A1 - Wellner, Philipp A1 - Weninger, Dieter A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 8.0 N2 - The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type for cut selection, and a complete rework of the way nonlinear constraints are handled. Additionally, SCIP 8.0 now supports interfaces for Julia as well as Matlab. Further, UG now includes a unified framework to parallelize all solvers, a utility to analyze computational experiments has been added to GCG, dual solutions can be postsolved by PaPILO, new heuristics and presolving methods were added to SCIP-SDP, and additional problem classes and major performance improvements are available in SCIP-Jack. T3 - ZIB-Report - 21-41 KW - Constraint integer programming KW - Linear programming KW - Mixed-integer linear programming KW - Mixed-integer nonlinear programming KW - Optimization solver KW - Branch-and-cut KW - Branch-and-price KW - Column generation KW - Parallelization KW - Mixed-integer semidefinite programming Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-85309 SN - 1438-0064 ER - TY - GEN A1 - Ribera Borrell, Enric A1 - Quer, Jannes A1 - Richter, Lorenz A1 - Schütte, Christof T1 - Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics N2 - Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal importance sampling controls as a stochastic optimization problem, this then brings additional numerical challenges and the convergence of corresponding algorithms might as well suffer from metastabilty. In this article we address this issue by combining systematic control approaches with the heuristic adaptive metadynamics method. Crucially, we approximate the importance sampling control by a neural network, which makes the algorithm in principle feasible for high dimensional applications. We can numerically demonstrate in relevant metastable problems that our algorithm is more effective than previous attempts and that only the combination of the two approaches leads to a satisfying convergence and therefore to an efficient sampling in certain metastable settings. T3 - ZIB-Report - 21-40 KW - importance sampling KW - stochastic optimal control KW - rare event simulation KW - metastability KW - neural networks KW - metadynamics Y1 - 2021 SN - 1438-0064 ER - TY - GEN A1 - Tateiwa, Nariaki A1 - Shinano, Yuji A1 - Yasuda, Masaya A1 - Kaji, Shizuo A1 - Yamamura, Keiichiro A1 - Fujisawa, Katsuki T1 - Massively parallel sharing lattice basis reduction N2 - For cryptanalysis in lattice-based schemes, the performance evaluation of lattice basis reduction using high-performance computers is becoming increasingly important for the determination of the security level. We propose a distributed and asynchronous parallel reduction algorithm based on randomization and DeepBKZ, which is an improved variant of the block Korkine-Zolotarev (BKZ) reduction algorithm. Randomized copies of a lattice basis are distributed to up to 103,680 cores and independently reduced in parallel, while some basis vectors are shared asynchronously among all processes via MPI. There is a trade-off between randomization and information sharing; if a substantial amount of information is shared, all processes will work on the same problem, thereby diminishing the benefit of parallelization. To monitor this balance between randomness and sharing, we propose a metric to quantify the variety of lattice bases. We empirically find an optimal parameter of sharing for high-dimensional lattices. We demonstrate the efficacy of our proposed parallel algorithm and implementation with respect to both performance and scalability through our experiments. T3 - ZIB-Report - 21-38 KW - Discrete optimization KW - Lattice problem KW - Lattice-based cryptography KW - Shortest vector problem KW - Parallel algorithms KW - Ubiquity Generator Framework Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-85209 SN - 1438-0064 N1 - under review ER - TY - GEN A1 - Nava-Yazdani, Esfandiar A1 - Hege, Hans-Christian A1 - von Tycowicz, Christoph T1 - A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds N2 - In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall's shape space. In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics and employ the approach for longitudinal analysis of 2D rat skulls shapes as well as 3D shapes derived from an imaging study on osteoarthritis. Particularly, we perform hypothesis test and estimate the mean trends. T3 - ZIB-Report - 21-39 KW - Longitudinal KW - Hierarchical Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-85187 SN - 1438-0064 N1 - sumbitted to: Journal of Mathematical Imaging and Vision ER - TY - GEN A1 - Mokhtari, Zahra A1 - Patterson, Robert I. A. A1 - Höfling, Felix T1 - Spontaneous trail formation in populations of auto-chemotactic walkers N2 - We study the formation of trails in populations of self-propelled agents that make oriented deposits of pheromones and also sense such deposits to which they then respond with gradual changes of their direction of motion. Based on extensive off-lattice computer simulations aiming at the scale of insects, e.g., ants, we identify a number of emerging stationary patterns and obtain qualitatively the non-equilibrium \add{state} diagram of the model, spanned by the strength of the agent--pheromone interaction and the number density of the population. In particular, we demonstrate the spontaneous formation of persistent, macroscopic trails, and highlight some behaviour that is consistent with a dynamic phase transition. This includes a characterisation of the mass of system-spanning trails as a potential order parameter. We also propose a dynamic model for a few macroscopic observables, including the sub-population size of trail-following agents, which captures the early phase of trail formation. T3 - ZIB-Report - 21-36 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-84466 SN - 1438-0064 ER - TY - GEN A1 - Eifler, Leon A1 - Gleixner, Ambros A1 - Pulaj, Jonad T1 - A Safe Computational Framework for Integer Programming applied to Chvátal's Conjecture N2 - We describe a general and safe computational framework that provides integer programming results with the degree of certainty that is required for machine-assisted proofs of mathematical theorems. At its core, the framework relies on a rational branch-and-bound certificate produced by an exact integer programming solver, SCIP, in order to circumvent floating-point roundoff errors present in most state-of-the-art solvers for mixed-integer programs. The resulting certificates are self-contained and checker software exists that can verify their correctness independently of the integer programming solver used to produce the certificate. This acts as a safeguard against programming errors that may be present in complex solver software. The viability of this approach is tested by applying it to finite cases of Chvátal's conjecture, a long-standing open question in extremal combinatorics. We take particular care to verify also the correctness of the input for this specific problem, using the Coq formal proof assistant. As a result we are able to provide a first machine-assisted proof that Chvátal's conjecture holds for all downsets whose union of sets contains seven elements or less. T3 - ZIB-Report - 21-35 KW - exact rational mixed integer programming KW - extremal combinatorics Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-84444 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Schwartz, Stephan A1 - Surau, William T1 - Rooted Maximum Weight Connected Subgraphs with Balancing and Capacity Constraints T3 - ZIB-Report - 21-34 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-84427 SN - 1438-0064 ER - TY - GEN A1 - Tack, Alexander A1 - Shestakov, Alexey A1 - Lüdke, David A1 - Zachow, Stefan T1 - A deep multi-task learning method for detection of meniscal tears in MRI data from the Osteoarthritis Initiative database N2 - We present a novel and computationally efficient method for the detection of meniscal tears in Magnetic Resonance Imaging (MRI) data. Our method is based on a Convolutional Neural Network (CNN) that operates on a complete 3D MRI scan. Our approach detects the presence of meniscal tears in three anatomical sub-regions (anterior horn, meniscal body, posterior horn) for both the Medial Meniscus (MM) and the Lateral Meniscus (LM) individually. For optimal performance of our method, we investigate how to preprocess the MRI data or how to train the CNN such that only relevant information within a Region of Interest (RoI) of the data volume is taken into account for meniscal tear detection. We propose meniscal tear detection combined with a bounding box regressor in a multi-task deep learning framework to let the CNN implicitly consider the corresponding RoIs of the menisci. We evaluate the accuracy of our CNN-based meniscal tear detection approach on 2,399 Double Echo Steady-State (DESS) MRI scans from the Osteoarthritis Initiative database. In addition, to show that our method is capable of generalizing to other MRI sequences, we also adapt our model to Intermediate-Weighted Turbo Spin-Echo (IW TSE) MRI scans. To judge the quality of our approaches, Receiver Operating Characteristic (ROC) curves and Area Under the Curve (AUC) values are evaluated for both MRI sequences. For the detection of tears in DESS MRI, our method reaches AUC values of 0.94, 0.93, 0.93 (anterior horn, body, posterior horn) in MM and 0.96, 0.94, 0.91 in LM. For the detection of tears in IW TSE MRI data, our method yields AUC values of 0.84, 0.88, 0.86 in MM and 0.95, 0.91, 0.90 in LM. In conclusion, the presented method achieves high accuracy for detecting meniscal tears in both DESS and IW TSE MRI data. Furthermore, our method can be easily trained and applied to other MRI sequences. T3 - ZIB-Report - 21-33 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-84415 SN - 1438-0064 ER - TY - GEN A1 - Masing, Berenike A1 - Lindner, Niels A1 - Borndörfer, Ralf T1 - Optimal Line Plans in the Parametric City and the Impact of In-Motion Costs N2 - Line planning in public transport involves determining vehicle routes and assigning frequencies of service such that travel demands are satisfied. We evaluate how line plans, which are optimal with respect to in-motion costs (IMC), the objective function depending purely on arc-lengths for both user and operator costs, performs with respect to the value of resources consumed (VRC). The latter is an elaborate, socio-economic cost function which includes discomfort caused by delay, boarding and alighting times, and transfers. Even though discomfort is a large contributing factor to VRC and is entirely disregarded in IMC, we observe that the two cost functions are qualitatively comparable. T3 - ZIB-Report - 21-27 KW - line planning KW - public transport KW - mixed-integer prgramming Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-84195 SN - 1438-0064 ER - TY - GEN A1 - Euler, Ricardo A1 - Borndörfer, Ralf A1 - Strunk, Timo A1 - Takkula, Tuomo T1 - ULD Build-Up Scheduling with Dynamic Batching in an Air Freight Hub N2 - Air freight is usually shipped in standardized unit load devices (ULDs). The planning process for the consolidation of transit cargo from inbound flights or locally emerging shipments into ULDs for outbound flights is called build-up scheduling. More specifically, outbound ULDs must be assigned a time and a workstation subject to both workstation capacity constraints and the availability of shipments which in turn depends on break-down decisions for incoming ULDs. ULDs scheduled for the same outbound flight should be built up in temporal and spatial proximity. This serves both to minimize overhead in transportation times and to allow workers to move freight between ULDs. We propose to address this requirement by processing ULDs for the same outbound flight in batches. For the above build-up scheduling problem, we introduce a multi-commodity network design model. Outbound flights are modeled as commodities; transit cargo is represented by cargo flow volume and unpack and batch decisions are represented as design variables. The model is solved with standard MIP solvers on a set of benchmark data. For instances with a limited number of resource conflicts, near-optimal solutions are found in under two hours for a whole week of operations. T3 - ZIB-Report - 21-31 KW - Logistics KW - Airline Applications Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-83482 SN - 1438-0064 ER - TY - GEN A1 - Hosoda, Junko A1 - Maher, Stephen J. A1 - Shinano, Yuji A1 - Villumsen, Jonas Christoffer T1 - Location, transshipment and routing: An adaptive transportation network integrating long-haul and local vehicle routing N2 - The routing of commodities is a tactical problem in supply chain management that aims to synchronise transportation services connecting a network of warehouses and consolidation locations. This paper considers the routing of commodities in a transportation network that is flexible in response to demand through changes to regional warehouse clustering and the designation of consolidation locations. Traditionally, warehouse clustering and consolidation locations are determined as part of strategic planning that is performed months to years in advance of operations---limiting the flexibility in transportation networks to respond to changes in demand. A mathematical programming-based algorithmic framework is proposed to integrate the strategic decisions of location planning with tactical decisions of vehicle routing and synchronisation. A multi-armed bandit problem is developed to explore warehouse clustering decisions and exploit those that lead to small transportation costs. An extensive computational study will show that the proposed algorithmic framework effectively integrates strategic and tactical planning decisions to reduce the overall transportation costs. T3 - ZIB-Report - 21-12 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-83438 ER - TY - GEN A1 - Lindner, Niels A1 - van Lieshout, Rolf T1 - Benders Decomposition for the Periodic Event Scheduling Problem N2 - The Periodic Event Scheduling Problem (PESP) is the central mathematical model behind the optimization of periodic timetables in public transport. We apply Benders decomposition to the incidence-based MIP formulation of PESP. The resulting formulation exhibits particularly nice features: The subproblem is a minimum cost network flow problem, and feasibility cuts are equivalent to the well-known cycle inequalities by Odijk. We integrate the Benders approach into a branch-and-cut framework, and assess the performance of this method on instances derived from the benchmarking library PESPlib. T3 - ZIB-Report - 21-29 KW - Periodic Timetabling KW - Periodic Event Scheduling Problem KW - Benders Decomposition KW - Mixed-Integer Programming Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-83338 SN - 1438-0064 ER - TY - GEN A1 - Masing, Berenike T1 - Optimal Line Planning in the Parametric City N2 - We formulate the line planning problem in public transport as a mixed integer linear program (MILP), which selects both passenger and vehicle routes, such that travel demands are met with respect to minimized travel times for both operators and users. We apply MILP to the Parametric City, a generic city model developed by Fielbaum et al. While the infrastructure graph and demand are entirely rotation symmetric, asymmetric optimal line plans can occur. Using group theory, we analyze the properties of symmetric solutions and introduce a symmetry gap to measure their deviation of the optimum. We also develop a 1+(1+\sqrt{2})/g-approximation algorithm, depending only on the cost related parameter g. Supported by computational experiments, we conclude that in practice symmetric line plans provide good solutions for the line planning problem in the Parametric City. T3 - ZIB-Report - 21-26 KW - line planning KW - city modelling KW - symmetry KW - mixed integer programming KW - approximation algorithm Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-83238 SN - 1438-0064 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Schwartz, Stephan A1 - Surau, William T1 - Finding Minimum Balanced Separators - an Exact Approach T2 - Operations Research Proceedings 2021 N2 - Balanced separators are node sets that split the graph into size bounded components. They find applications in different theoretical and practical problems. In this paper we discuss how to find a minimum set of balanced separators in node weighted graphs. Our contribution is a new and exact algorithm that solves Minimum Balanced Separators by a sequence of Hitting Set problems. The only other exact method appears to be a mixed-integer program (MIP) for the edge weighted case. We adapt this model to node weighted graphs and compare it to our approach on a set of instances, resembling transit networks. It shows that our algorithm is far superior on almost all test instances. T3 - ZIB-Report - 21-25 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-83138 SN - 1438-0064 SP - 154 EP - 159 ER - TY - JOUR A1 - Zakiyeva, Nazgul A1 - Xu, X. T1 - Nonlinear network autoregressive model with application to natural gas network forecasting JF - Mathematics Japonica T3 - ZIB-Report - 21-24 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81025 ER - TY - GEN A1 - Zakiyeva, Nazgul A1 - Petkovic, Milena T1 - Modeling and forecasting gas network flows with multivariate time series and mathematical programming approach N2 - With annual consumption of approx. 95 billion cubic me-ters and similar amounts of gas just transshipped through Germany toother EU states, Germany’s gas transport system plays a vital role inEuropean energy supply. The complex, more than 40,000 km long high-pressure transmission network is controlled by several transmission sys-tem operators (TSOs) whose main task is to provide security of supplyin a cost-efficient way. Given the slow speed of gas flows through the gastransmission network pipelines, it has been an essential task for the gasnetwork operators to enhance the forecast tools to build an accurate andeffective gas flow prediction model for the whole network. By incorpo-rating the recent progress in mathematical programming and time seriesmodeling, we aim to model natural gas network and predict gas in- andout-flows at multiple supply and demand nodes for different forecastinghorizons. Our model is able to describe the dynamics in the network bydetecting the key nodes, which may help to build an optimal manage-ment strategy for transmission system operators. T3 - ZIB-Report - 21-23 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82966 SN - 1438-0064 ER - TY - GEN A1 - Petkovic, Milena A1 - Zakiyeva, Nazgul A1 - Zittel, Janina T1 - Statistical analysis and modeling for detecting regime changes in gas nomination time series N2 - As a result of the legislation for gas markets introduced by the European Union in 2005, separate independent companies have to conduct the transport and trading of natural gas. The current gas market of Germany, which has a market value of more than 54 billion USD, consists of Transmission System Operators (TSO), network users, and traders. Traders can nominate a certain amount of gas anytime and anywhere in the network. Such unrestricted access for the traders, on the other hand, increase the uncertainty in the gas supply management. Some customers’ behaviors may cause abrupt structural changes in gas flow time series. In particular, it is a challenging task for the TSO operators to predict gas nominations 6 to 10 hours ahead. In our study, we aim to investigate the regime changes in the time series of nominations to predict the 6 to 10 hours ahead of gas nominations. T3 - ZIB-Report - 21-22 KW - Time series Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82988 SN - 1438-0064 ER - TY - GEN A1 - Koch, Thorsten A1 - Berthold, Timo A1 - Pedersen, Jaap A1 - Vanaret, Charlie T1 - Progress in Mathematical Programming Solvers from 2001 to 2020 N2 - This study investigates the progress made in LP and MILP solver performance during the last two decades by comparing the solver software from the beginning of the millennium with the codes available today. On average, we found out that for solving LP/MILP, computer hardware got about 20 times faster, and the algorithms improved by a factor of about nine for LP and around 50 for MILP, which gives a total speed-up of about 180 and 1,000 times, respectively. However, these numbers have a very high variance and they considerably underestimate the progress made on the algorithmic side: many problem instances can nowadays be solved within seconds, which the old codes are not able to solve within any reasonable time. T3 - ZIB-Report - 21-20 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82779 SN - 1438-0064 ER - TY - GEN A1 - Pedersen, Jaap A1 - Hoppmann-Baum, Kai A1 - Zittel, Janina A1 - Koch, Thorsten T1 - Blending hydrogen into natural gas: An assessment of the capacity of the German gas grid; Technical Report N2 - In the transition towards a pure hydrogen infrastructure, utilizing the existing natural gas infrastructure is a necessity. In this study, the maximal technically feasible injection of hydrogen into the existing German natural gas transmission network is analysed with respect to regulatory limits regarding the gas quality. We propose a transient tracking model based on the general pooling problem including linepack. The analysis is conducted using real-world hourly gas flow data on a network of about 10,000 km length. T3 - ZIB-Report - 21-21 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82838 SN - 1438-0064 ER - TY - GEN A1 - Tateiwa, Nariaki A1 - Shinano, Yuji A1 - Yamamura, Keiichiro A1 - Yoshida, Akihiro A1 - Kaji, Shizuo A1 - Yasuda, Masaya A1 - Fujisawa, Katsuki T1 - CMAP-LAP: Configurable Massively Parallel Solver for Lattice Problems N2 - Lattice problems are a class of optimization problems that are notably hard. There are no classical or quantum algorithms known to solve these problems efficiently. Their hardness has made lattices a major cryptographic primitive for post-quantum cryptography. Several different approaches have been used for lattice problems with different computational profiles; some suffer from super-exponential time, and others require exponential space. This motivated us to develop a novel lattice problem solver, CMAP-LAP, based on the clever coordination of different algorithms that run massively in parallel. With our flexible framework, heterogeneous modules run asynchronously in parallel on a large-scale distributed system while exchanging information, which drastically boosts the overall performance. We also implement full checkpoint-and-restart functionality, which is vital to high-dimensional lattice problems. Through numerical experiments with up to 103,680 cores, we evaluated the performance and stability of our system and demonstrated its high capability for future massive-scale experiments. T3 - ZIB-Report - 21-16 KW - Discrete optimization KW - Lattice problem KW - Lattice-based cryptography KW - Shortest vector problem KW - Parallel algorithms KW - Ubiquity Generator Framework Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82802 SN - 1438-0064 N1 - Revised version is accepted to HiPC 2021 ER - TY - GEN A1 - Ray, Sourav A1 - Thies, Arne A1 - Sunkara, Vikram A1 - Wulkow, Hanna A1 - Celik, Özgür A1 - Yergöz, Fatih A1 - Schütte, Christof A1 - Stein, Christoph A1 - Weber, Marcus A1 - Winkelmann, Stefanie T1 - Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design N2 - Initiated by mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands in normal versus diseased (inflamed) environments, we previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. Uniquely, this design recognised that GPCRs function differently under pathological versus healthy conditions. We now present a novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels associated with parameters of inflamed tissue (pH, radicals). By means of molecular dynamics simulations, we also assessed qualitative changes of the reaction rates due to additional disulfide bridges inside the GPCR binding pocket and used these rates for stochastic simulations of the corresponding reaction jump process. The modelling results were validated with in vitro experiments measuring calcium currents and G-protein activation. We found markedly reduced G-protein dissociation and calcium channel inhibition induced by NFEPP at normal pH, and enhanced constitutive G-protein activation but lower probability of ligand binding with increasing radical concentrations. These results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account. T3 - ZIB-Report - 21-19 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82797 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - Liebchen, Christian A1 - Masing, Berenike T1 - Forward Cycle Bases and Periodic Timetabling N2 - Periodic timetable optimization problems in public transport can be modeled as mixed-integer linear programs by means of the Periodic Event Scheduling Problem (PESP). In order to keep the branch-and-bound tree small, minimum integral cycle bases have been proven successful. We examine forward cycle bases, where no cycle is allowed to contain a backward arc. After reviewing the theory of these bases, we describe the construction of an integral forward cycle basis on a line-based event-activity network. Adding turnarounds to the instance \texttt{R1L1} of the benchmark library PESPlib, we computationally evaluate three types of forward cycle bases in the Pareto sense, and come up with significant improvements concerning dual bounds. T3 - ZIB-Report - 21-18 KW - Periodic Timetabling KW - Cycle Bases KW - Mixed Integer Programming Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82756 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - Maristany de las Casas, Pedro A1 - Schiewe, Philine T1 - Optimal Forks: Preprocessing Single-Source Shortest Path Instances with Interval Data N2 - We investigate preprocessing for single-source shortest path queries in digraphs, where arc costs are only known to lie in an interval. More precisely, we want to decide for each arc whether it is part of some shortest path tree for some realization of costs. We show that this problem is solvable in polynomial time by giving a combinatorial algorithm, using optimal structures that we call forks. Our algorithm turns out to be very efficient in practice, and is sometimes even superior in quality to a heuristic developed for the one-to-one shortest path problem in the context of passenger routing in public transport. T3 - ZIB-Report - 21-17 KW - Preprocessing Shortest Path Problems KW - Interval Data KW - Graph Algorithms Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82716 SN - 1438-0064 ER - TY - GEN A1 - Ernst, Ariane A1 - Schütte, Christof A1 - Sigrist, Stephan A1 - Winkelmann, Stefanie T1 - Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics N2 - Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance to the calcium channels determines the release probability and thereby the postsynaptic signal. Suitable models of the process need to capture both the mean and the variance observed in electrophysiological measurements of the postsynaptic current. In this work, we propose a method to directly compute the exact first- and second-order moments for signals generated by a linear reaction network under convolution with an impulse response function, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. We show that the autocorrelation of the process is central for the calculation of the filtered signal’s second-order moments, and derive a system of PDEs for the cross-correlation functions (including the autocorrelations) of linear reaction networks with time-dependent rates. Finally, we employ our method to efficiently compare different spatial coarse graining approaches for a specific model of synaptic vesicle fusion. Beyond the application to neurotransmission processes, the developed theory can be applied to any linear reaction system that produces a filtered stochastic signal. T3 - ZIB-Report - 21-15 KW - linear reaction networks KW - cross-correlation KW - neurotransmission Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82674 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Schwartz, Stephan A1 - Surau, William T1 - Vertex Covering with Capacitated Trees N2 - The covering of a graph with (possibly disjoint) connected subgraphs is a fundamental problem in graph theory. In this paper, we study a version to cover a graph's vertices by connected subgraphs subject to lower and upper weight bounds, and propose a column generation approach to dynamically generate feasible and promising subgraphs. Our focus is on the solution of the pricing problem which turns out to be a variant of the NP-hard Maximum Weight Connected Subgraph Problem. We compare different formulations to handle connectivity, and find that a single-commodity flow formulation performs best. This is notable since the respective literature seems to have dismissed this formulation. We improve it to a new coarse-to-fine flow formulation that is theoretically and computationally superior, especially for large instances with many vertices of degree 2 like highway networks, where it provides a speed-up factor of 10 over the non-flow-based formulations. We also propose a preprocessing method that exploits a median property of weight constrained subgraphs, a primal heuristic, and a local search heuristic. In an extensive computational study we evaluate the presented connectivity formulations on different classes of instances, and demonstrate the effectiveness of the proposed enhancements. Their speed-ups essentially multiply to an overall factor of 20. Overall, our approach allows the reliabe solution of instances with several hundreds of nodes in a few minutes. These findings are further corroborated in a comparison to existing districting models on a set of test instances from the literature. T3 - ZIB-Report - 21-14 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82616 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Denißen, Jonas A1 - Heller, Simon A1 - Klug, Torsten A1 - Küpper, Michael A1 - Lindner, Niels A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Söhlke, Andreas A1 - Steadman, William T1 - Microscopic Timetable Optimization for a Moving Block System N2 - We present an optimization model which is capable of routing and ordering trains on a microscopic level under a moving block regime. Based on a general timetabling definition (GTTP) that allows the plug in of arbitrarily detailed methods to compute running and headway times, we describe a layered graph approach using velocity expansion, and develop a mixed integer linear programming formulation. Finally, we present promising results for a German corridor scenario with mixed traffic, indicating that applying branch-and-cut to our model is able to solve reasonably sized instances with up to hundred trains to optimality. T3 - ZIB-Report - 21-13 KW - Moving Block KW - Railway Track Allocation KW - Railway Timetabling KW - Train Routing Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82547 SN - 1438-0064 ER -