@inproceedings{EbertMasingLindneretal.2025, author = {Ebert, Patricia and Masing, Berenike and Lindner, Niels and Gleixner, Ambros}, title = {Sorting Criteria for Line-based Periodic Timetabling Heuristics}, booktitle = {Operations Research Proceedings 2024. OR 2024}, pages = {348 -- 354}, year = {2025}, abstract = {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\%.}, language = {en} } @misc{KempkeKoch2025, author = {Kempke, Nils-Christian and Koch, Thorsten}, title = {Low-precision first-order method-based fix-and-propagate heuristics for large-scale mixed-integer linear optimization}, issn = {1438-0064}, arxiv = {http://arxiv.org/abs/2503.10344}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-99612}, year = {2025}, abstract = {We investigate the use of low-precision first-order methods (FOMs) within a fix-and-propagate (FP) framework for solving mixed-integer programming problems (MIPs). FOMs, using only matrix-vector products instead of matrix factorizations, are well suited for GPU acceleration and have recently gained more attention for their application to large-scale linear programming problems (LPs). We employ PDLP, a variant of the Primal-Dual Hybrid Gradient (PDHG) method specialized to LP problems, to solve the LP-relaxation of our MIPs to low accuracy. This solution is used to motivate fixings within our fix-and-propagate framework. We implemented four different FP variants using primal and dual LP solution information. We evaluate the performance of our heuristics on MIPLIB 2017, showcasing that the low-accuracy LP solution produced by the FOM does not lead to a loss in quality of the FP heuristic solutions when compared to a high-accuracy interior-point method LP solution. Further, we use our FP framework to produce high-accuracy solutions for large-scale (up to 243 million non-zeros and 8 million decision variables) unit-commitment energy-system optimization models created with the modeling framework REMix. For the largest problems, we can generate solutions with under 2\% primal-dual gap in less than 4 hours, whereas commercial solvers cannot generate feasible solutions within two days of runtime. This study represents the first successful application of FOMs in large-scale mixed-integer optimization, demonstrating their efficacy and establishing a foundation for future research in this domain.}, language = {en} } @article{AndresArconesWeiserKoutsourelakisetal.2026, author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Phaedon-Stelios and Unger, J{\"o}rg F.}, title = {Embedded Model Form Uncertainty Quantification with Measurement Noise for Bayesian Model Calibration}, volume = {7}, journal = {Data-Centric Engineering}, arxiv = {http://arxiv.org/abs/2410.12037}, doi = {10.1017/dce.2025.10035}, year = {2026}, abstract = {A key factor in ensuring the accuracy of computer simulations that model physical systems is the proper calibration of their parameters based on real-world observations or experimental data. Inevitably, uncertainties arise, and Bayesian methods provide a robust framework for quantifying and propagating these uncertainties to model predictions. Nevertheless, Bayesian methods paired with inexact models usually produce predictions unable to represent the observed datapoints. Additionally, the quantified uncertainties of these overconfident models cannot be propagated to other Quantities of Interest (QoIs) reliably. A promising solution involves embedding a model inadequacy term in the inference parameters, allowing the quantified model form uncertainty to influence non-observed QoIs. This paper introduces a more interpretable framework for embedding the model inadequacy compared to existing methods. To overcome the limitations of current approaches, we adapt the existing likelihood models to properly account for noise in the measurements and propose two new formulations designed to address their shortcomings. Moreover, we evaluate the performance of this inadequacy-embedding approach in the presence of discrepancies between measurements and model predictions, including noise and outliers. Particular attention is given to how the uncertainty associated with the model inadequacy term propagates to the QoIs, enabling a more comprehensive statistical analysis of prediction's reliability. Finally, the proposed approach is applied to estimate the uncertainty in the predicted heat flux from a transient thermal simulation using temperature bservations.}, language = {en} } @misc{VanaretLeyffer2026, author = {Vanaret, Charlie and Leyffer, Sven}, title = {Implementing a unified solver for nonlinearly constrained optimization}, arxiv = {http://arxiv.org/abs/2406.13454}, year = {2026}, abstract = {SQP and interior-point methods (also referred to as Lagrange-Newton methods) typically share key algorithmic components, such as strategies for computing descent directions and mechanisms that promote global convergence. Building on this insight, we introduce a unifying framework with eight building blocks that abstracts the workflows of Lagrange-Newton methods. We then present Uno, a modular C++ solver that implements our unifying framework and allows the automatic combination of a wide range of strategies with no programming effort from the user. Uno is meant to (1) organize mathematical optimization strategies into a coherent hierarchy; (2) offer a wide range of efficient and robust methods that can be compared for a given instance; (3) enable researchers to experiment with novel optimization strategies; and (4) reduce the cost of development and maintenance of multiple optimization solvers. Uno's software design allows user to compose new customized solvers for emerging optimization areas such as robust optimization or optimization problems with complementarity constraints, while building on reliable nonlinear optimization techniques. We demonstrate that Uno is highly competitive against state-of-the-art solvers filterSQP, IPOPT, SNOPT, MINOS, LANCELOT, LOQO, and CONOPT on a subset of 429 small problems from the CUTE collection. Uno is available as open-source software under the MIT license at this https URL and via its C, Julia, Python, Fortran, and AMPL interfaces.}, language = {en} } @article{HalbigHoenGleixneretal.2025, author = {Halbig, Katrin and Hoen, Alexander and Gleixner, Ambros and Witzig, Jakob and Weninger, Dieter}, title = {A diving heuristic for mixed-integer problems with unbounded semi-continuous variables}, volume = {13}, journal = {EURO Journal on Computational Optimization}, doi = {10.1016/j.ejco.2025.100107}, year = {2025}, language = {en} } @article{BestuzhevaGleixnerAchterberg2025, author = {Bestuzheva, Ksenia and Gleixner, Ambros and Achterberg, Tobias}, title = {Efficient separation of RLT cuts for implicit and explicit bilinear terms}, volume = {210}, journal = {Mathematical Programming}, doi = {10.1007/s10107-024-02104-0}, pages = {47 -- 74}, year = {2025}, language = {en} } @inproceedings{GhannamGleixner2025, author = {Ghannam, Mohammed and Gleixner, Ambros}, title = {Hybrid Genetic Search for Dynamic Vehicle Routing with Time Windows}, booktitle = {Operations Research Proceedings 2023. OR 2023}, doi = {10.1007/978-3-031-58405-3_35}, year = {2025}, language = {en} } @article{HoenKampGleixner2025, author = {Hoen, Alexander and Kamp, Dominik and Gleixner, Ambros}, title = {MIP-DD: Delta Debugging for Mixed-Integer Programming Solvers}, journal = {INFORMS Journal on Computing}, doi = {10.1287/ijoc.2024.0844}, year = {2025}, language = {en} } @article{MehrmannJohnyEbbinghausetal.2026, author = {Mehrmann, Carolin and Johny, Jacob and Ebbinghaus, Petra and Hammerschmidt, Martin and Das, Ankita and Wei, Xin and Tesch, Marc F. and Rabe, Martin}, title = {Nano IR spectroscopy on Silicon-Supported Organic-Inorganic Hybrid Materials}, journal = {Phys. Chem. Chem. Phys.}, publisher = {Royal Society of Chemistry (RSC)}, doi = {10.1039/D5CP03815D}, year = {2026}, language = {en} } @inproceedings{PedersenLindnerRehfeldtetal.2026, author = {Pedersen, Jaap and Lindner, Niels and Rehfeldt, Daniel and Koch, Thorsten}, title = {Comparing Branching Rules for the Quota Steiner Tree Problem with Interference}, booktitle = {Operations Research Proceedings 2025}, year = {2026}, abstract = {Branching decisions play a crucial role in branch-and-bound algorithms for solving combinatorial optimization problems. In this paper, we investigate several branching rules applied to the Quota Steiner Tree Problem with Interference (QSTPI). The Quota Steiner Tree Problem (QSTP) generalizes the classical Steiner Tree Problem (STP) in graphs by seeking a minimum-cost tree that connects a subset of profit-associated vertices whose cumulative profit meets or exceeds a given quota. The QSTPI introduces interference among vertices: Selecting certain vertices simultaneously reduces their individual contributions to the overall profit. This problem arises, for example, in positioning and connecting wind turbines, where turbines possibly shadow other turbines, reducing their energy yield. Unlike classical STP variants, large QSTPI instances require significantly more branching to compute provably optimal solutions. In contrast to branching on variables, we utilize the combinatorial structure of the QSTPI by branching on the graph's vertices. We adapt classical and problem-specific branching rules and present a comprehensive computational study comparing the effectiveness of these branching strategies.}, language = {en} }