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 - 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 - JOUR A1 - Koch, Thorsten A1 - Bernal Neira, David E. A1 - Chen, Ying A1 - Cortiana, Giorgio A1 - Egger, Daniel J. A1 - Heese, Raoul A1 - Hegade, Narendra N. A1 - Gomez Cadavid, Alejandro A1 - Huang, Rhea A1 - Itoko, Toshinari A1 - Kleinert, Thomas A1 - Maciel Xavier, Pedro A1 - Mohseni, Naeimeh A1 - Montanez-Barrera, Jhon A. A1 - Nakano, Koji A1 - Nannicini, Giacomo A1 - O'Meara, Corey A1 - Pauckert, Justin A1 - Proissl, Manuel A1 - Ramesh, Anurag A1 - Schicker, Maximilian A1 - Shimada, Noriaki A1 - Takeori, Mitsuharu A1 - Valls, Victor A1 - Van Bulck, David A1 - Woerner, Stefan A1 - Zoufal, Christa T1 - Quantum Optimization Benchmark Library -- The Intractable Decathlon N2 - Through recent progress in hardware development, quantum computers have advanced to the point where benchmarking of (heuristic) quantum algorithms at scale is within reach. Particularly in combinatorial optimization -- where most algorithms are heuristics -- it is key to empirically analyze their performance on hardware and track progress towards quantum advantage. To this extent, we present ten optimization problem classes that are difficult for existing classical algorithms and can (mostly) be linked to practically-relevant applications, with the goal to enable systematic, fair, and comparable benchmarks for quantum optimization methods. Further, we introduce the Quantum Optimization Benchmark Library (QOBLIB) where the problem instances and solution track records can be found. The individual properties of the problem classes vary in terms of objective and variable type, coefficient ranges, and density. Crucially, they all become challenging for established classical methods already at system sizes ranging from less than 100 to, at most, an order of 100,000 decision variables, allowing to approach them with today's quantum computers. We reference the results from state-of-the-art solvers for instances from all problem classes and demonstrate exemplary baseline results obtained with quantum solvers for selected problems. The baseline results illustrate a standardized form to present benchmarking solutions, which has been designed to ensure comparability of the used methods, reproducibility of the respective results, and trackability of algorithmic and hardware improvements over time. We encourage the optimization community to explore the performance of available classical or quantum algorithms and hardware platforms with the benchmarking problem instances presented in this work toward demonstrating quantum advantage in optimization. Y1 - 2025 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 - Gotzes, Uwe A1 - Buchholz, Annika A1 - Kallrath, Josef A1 - Lindner, Niels A1 - Koch, Thorsten T1 - Flexible Pooling Pattern Design with Integer Programming T2 - Theory, Algorithms and Experiments in Applied Optimization. In Honor of the 70th Birthday of Panos Pardalos N2 - Sample pooling has the potential to significantly enhance large-scale screening procedures, especially in scenarios like the COVID-19 pandemic, where rapid and widespread PCR testing has been crucial. Efficient strategies are essential to increase the testing capacity, i.e., the number of tests that can be processed within a given timeframe. Non-adaptive pooling strategies can further streamline the testing process by reducing the required testing rounds. In contrast to adaptive strategies, where subsequent tests depend on prior results, non-adaptive pooling processes all samples in a single round, eliminating the need for sequential retesting and reducing delays. This paper presents a highly flexible method based on integer programming to design optimized pooling patterns suitable for various applications, including medical diagnostics and quality control in industrial production. Using coronavirus testing as a case study, we formulate and solve optimization and satisfiability models that compute efficient pool designs. Our optimized pooling does not only increase testing capacity, but also accelerates the testing process and reduces overall costs. The proposed method is adaptable and can be seamlessly integrated into automated testing systems. Y1 - 2025 VL - 226 PB - Springer ER - TY - JOUR A1 - Zhou, Lei A1 - Chen, Ying A1 - Peng, Hanqiu A1 - Koch, Thorsten T1 - Is innovation slowing down? Insights from the AIMS framework of patent values JF - Expert Systems with Applications N2 - Amidst the unprecedented expansion of scientific and technological knowledge over the past century, concerns persist regarding a slowdown in innovation. To address this, we introduce the AIMS framework, which categorizes patents into four types—Aurora, Invisible, Mirage, and Success—based on their respective inherent scientific values and market-recognized economic values. Utilizing USPTO patent and citation data from 1976 to 2022, our analysis reveals an increasing volume of patent issuances but a concerning dilution in scientific quality starting in the 2000s. This trend is primarily attributed to the rise of low scientific value patents—categorized as Mirage and Invisible—and a modest decline in high-impact scientific patents—categorized as Success and Aurora. Meanwhile, the economic value of patents has risen, especially noted with the growth in Mirage patents since the 2010s, indicating a shift towards strategies that prioritize market-driven patenting. This study highlights the evolving nature of patents from mere indicators of scientific innovation to strategic tools for market dominance, providing an alternative understanding of patent value and its implications for firms’ strategic decisions over patent issuance across different sectors. Y1 - 2025 U6 - https://doi.org/10.1016/j.eswa.2025.127355 VL - 280 SP - 127355 ER - TY - JOUR A1 - Riedmüller, Stephanie A1 - Koch, Thorsten T1 - Exact Objective Space Contraction for the Preprocessing of Multi-objective Integer Programs N2 - Solving integer optimization problems with large or widely ranged objective coefficients can lead to numerical instability and increased runtimes. When the problem also involves multiple objectives, the impact of the objective coefficients on runtimes and numerical issues multiplies. We address this issue by transforming the coefficients of linear objective functions into smaller integer coefficients. To the best of our knowledge, this problem has not been defined before. Next to a straightforward scaling heuristic, we introduce a novel exact transformation approach for the preprocessing of multi-objective binary problems. In this exact approach, the large or widely ranged integer objective coefficients are transformed into the minimal integer objective coefficients that preserve the dominance relation of the points in the objective space. The transformation problem is solved with an integer programming formulation with an exponential number of constraints. We present a cutting-plane algorithm that can efficiently handle the problem size. In a first computational study, we analyze how often and in which settings the transformation actually leads to smaller coefficients. In a second study, we evaluate how the exact transformation and a typical scaling heuristic, when used as preprocessing, affect the runtime and numerical stability of the Defining Point Algorithm. Y1 - 2025 ER - TY - JOUR A1 - Chen, Ying A1 - Koch, Thorsten A1 - Peng, Hanqui A1 - Zhang, Hongrui T1 - Benchmarking of Quantum and Classical Computing in Large-Scale Dynamic Portfolio Optimization Under Market Frictions N2 - Quantum computing is poised to transform the financial industry, yet its advantages over traditional methods have not been evidenced. As this technology rapidly evolves, benchmarking is essential to fairly evaluate and compare different computational strategies. This study presents a challenging yet solvable problem of large-scale dynamic portfolio optimization under realistic market conditions with frictions. We frame this issue as a Quadratic Unconstrained Binary Optimization (QUBO) problem, compatible with digital computing and ready for quantum computing, to establish a reliable benchmark. By applying the latest solvers to real data, we release benchmarks that help verify true advancements in dynamic trading strategies, either quantum or digital computing, ensuring that reported improvements in portfolio optimization are based on robust, transparent, and comparable metrics. Y1 - 2025 ER - TY - CHAP A1 - Yueksel-Erguen, Inci A1 - Koch, Thorsten A1 - Zittel, Janina T1 - Consistent flow scenario generation based on open data for operational analysis of European gas transport networks T2 - Operations Research Proceedings 2023. OR 2023 N2 - In recent years, European gas transport has been affected by major disruptive events like political issues such as, most recently, the Russian war on Ukraine. To incorporate the impacts of such events into decision-making during the energy transition, more complex models for gas network analysis are required. However, the limited availability of consistent data presents a significant obstacle in this endeavor. We use a mathematical-modeling-based scenario generator to deal with this obstacle. The scenario generator consists of capacitated network flow models representing the gas network at different aggregation levels. In this study, we present the coarse-to-fine approach utilized in this scenario generator. Y1 - 2025 U6 - https://doi.org/10.1007/978-3-031-58405-3_63 SP - 493 EP - 499 PB - Springer ER - TY - CHAP A1 - Koch, Thorsten A1 - Rehfeldt, Daniel A1 - Shinano, Yuji T1 - On the state of QUBO solving T2 - Operations Research Proceedings 2023. OR 2023 N2 - It is regularly claimed that quantum computers will bring breakthrough progress in solving challenging combinatorial optimization problems relevant in practice. In particular, Quadratic Unconstrained Binary Optimization (QUBO) problems are said to be the model of choice for use in (adiabatic) quantum systems during the noisy intermediate- scale quantum (NISQ) era. Even the first commercial quantum-based systems are advertised to solve such problems. Theoretically, any Integer Program can be converted into a QUBO. In practice, however, there are some caveats, as even for problems that can be nicely modeled as a QUBO, this might not be the most effective way to solve them. We review the state of QUBO solving on digital and quantum computers and provide insights regarding current benchmark instances and modeling. Y1 - 2025 U6 - https://doi.org/10.1007/978-3-031-58405-3_46 SP - 357 EP - 365 PB - Springer 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 - JOUR A1 - Kempke, Nils-Christian A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - A Massively Parallel Interior-Point-Method for Arrowhead Linear Programs JF - SIAM Journal on Scientific Computing Y1 - 2025 ER - TY - JOUR A1 - Rong, Guoyang A1 - Chen, Ying A1 - Ma, Feicheng A1 - Koch, Thorsten T1 - Exploring Interdisciplinary Research Trends through Critical Years for Interdisciplinary Citation JF - Journal of Informetrics Y1 - 2025 U6 - https://doi.org/10.1016/j.joi.2025.101726 VL - 19 IS - 4 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 - 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 - CHAP A1 - Stompor, Tomasz A1 - Zittel, Janina A1 - Koch, Thorsten A1 - Rusch, Beate T1 - Fully Algorithmic Librarian: Large-Scale Citation Experiments T2 - 20th International Society of Scientometrics and Informetrics Conference 2025, June 23-27, 2025 | Yerevan, Armenia N2 - The Fully Algorithmic Librarian (FAN) project explores application scenarios for algorithmic-intelligence(AI)-supported methods in academic libraries as central institutions for research support. To this end, the study builds on two algorithmic approaches for analyzing large-scale citation networks. A comparison of Web of Science (WoS) and OpenAlex structures using the PageRank algorithm reveals key differences. Additionally, a multi-label clustering technique designed for large-scale citation networks accounts for disciplinary variations in publication practices. Y1 - 2025 U6 - https://doi.org/10.51408/issi2025_204 ER - TY - JOUR A1 - Chen, Ying A1 - Koch, Thorsten A1 - Peng, Hanqui A1 - Zhang, Hongrui T1 - Benchmarking of Quantum and Classical Computing in Large-Scale Dynamic Portfolio Optimization Under Market Frictions Y1 - 2025 ER - TY - CHAP A1 - Turner, Mark A1 - Chmiela, Antonia A1 - Koch, Thorsten A1 - Winkler, Michael T1 - PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs T2 - Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2025 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. Y1 - 2025 U6 - https://doi.org/10.1007/978-3-031-95976-9_14 VL - 15763 ER - TY - JOUR A1 - Kotil, Ayse A1 - Pelofske, Elijah A1 - Riedmüller, Stephanie A1 - Egger, Daniel J. A1 - Eidenbenz, Stephan A1 - Koch, Thorsten A1 - Woerner, Stefan T1 - Quantum Approximate Multi-Objective Optimization JF - Nature Computational Science N2 - The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, i.e., the set of all Pareto optimal solutions, where no objective can be improved without degrading another one. Multi-objective optimization can be challenging classically, even if the corresponding single-objective optimization problems are efficiently solvable. Thus, multi-objective optimization represents a compelling problem class to analyze with quantum computers. In this work, we use low-depth Quantum Approximate Optimization Algorithm to approximate the optimal Pareto front of certain multi-objective weighted maximum cut problems. We demonstrate its performance on an IBM Quantum computer, as well as with Matrix Product State numerical simulation, and show its potential to outperform classical approaches. Y1 - 2025 U6 - https://doi.org/10.1038/s43588-025-00873-y SP - 1168 EP - 1177 ER - TY - JOUR A1 - Shimada, Naoki A1 - Mako, Sato A1 - Yaegashi, Yuta A1 - Koch, Thorsten A1 - Le, Thi Thai T1 - An Application of Modified S-CLSVOF Method to Kelvin-Helmholtz Instability and Comparison with Theoretical Result JF - Journal of Chemical Engineering of Japan N2 - This study focuses on validating a two-phase flow solver based on the modified Simple Coupled Level Set and Volume of Fluid method (Uchihashi et al. (2023)) through viscous Kelvin-Helmholtz instability simulations. Our numerical simulation results are compared with the ones given by Funada and Joseph (2001) to provide reliable predictions of interface behavior under the influence of viscosity. The primary goal is to accurately assess the solver's ability to replicate theoretical analysis of interface behaviors under various conditions. First, the wave between two fluids of identical density is calculated. In addition, the effect of surface tension is investigated. By comparing growth rates, numerical simulations obtain well-agreements with the analytical results on the effect of the fluid viscosity, the wave number, and the surface tension. Finally, fluid density is changed to an air-water system. When relative velocity U is smaller than the criteria of relative velocity U_c given by analytical solutions, the wave is not broken. However, waves are splashed into droplets in the condition of U>U_c. This result agrees with the analysis by Funada and Joseph (2001). These findings provide a robust framework for applying the solver to more complex two-phase flow problems, supporting advancements in numerical simulations of fluid interfaces. Y1 - 2025 U6 - https://doi.org/10.1080/00219592.2025.2451953 VL - 58 IS - 1 PB - Taylor and Francis 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 - 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 -