TY - CHAP A1 - Ebert, Patricia A1 - Masing, Berenike A1 - Lindner, Niels A1 - Gleixner, Ambros T1 - Sorting Criteria for Line-based Periodic Timetabling Heuristics T2 - Operations Research Proceedings 2024. OR 2024 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%. Y1 - 2025 SP - 348 EP - 354 ER - TY - GEN A1 - Vanaret, Charlie A1 - Leyffer, Sven T1 - Implementing a unified solver for nonlinearly constrained optimization N2 - 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. Y1 - 2026 ER - TY - JOUR A1 - Halbig, Katrin A1 - Hoen, Alexander A1 - Gleixner, Ambros A1 - Witzig, Jakob A1 - Weninger, Dieter T1 - A diving heuristic for mixed-integer problems with unbounded semi-continuous variables JF - EURO Journal on Computational Optimization Y1 - 2025 U6 - https://doi.org/10.1016/j.ejco.2025.100107 VL - 13 ER - TY - JOUR A1 - Bestuzheva, Ksenia A1 - Gleixner, Ambros A1 - Achterberg, Tobias T1 - Efficient separation of RLT cuts for implicit and explicit bilinear terms JF - Mathematical Programming Y1 - 2025 U6 - https://doi.org/10.1007/s10107-024-02104-0 VL - 210 SP - 47 EP - 74 ER - TY - CHAP A1 - Ghannam, Mohammed A1 - Gleixner, Ambros T1 - Hybrid Genetic Search for Dynamic Vehicle Routing with Time Windows T2 - Operations Research Proceedings 2023. OR 2023 Y1 - 2025 U6 - https://doi.org/10.1007/978-3-031-58405-3_35 ER - TY - JOUR A1 - Hoen, Alexander A1 - Kamp, Dominik A1 - Gleixner, Ambros T1 - MIP-DD: Delta Debugging for Mixed-Integer Programming Solvers JF - INFORMS Journal on Computing Y1 - 2025 U6 - https://doi.org/10.1287/ijoc.2024.0844 ER - TY - JOUR A1 - Mehrmann, Carolin A1 - Johny, Jacob A1 - Ebbinghaus, Petra A1 - Hammerschmidt, Martin A1 - Das, Ankita A1 - Wei, Xin A1 - Tesch, Marc F. A1 - Rabe, Martin T1 - Nano IR spectroscopy on Silicon-Supported Organic–Inorganic Hybrid Materials JF - Phys. Chem. Chem. Phys. Y1 - 2026 U6 - https://doi.org/10.1039/D5CP03815D PB - Royal Society of Chemistry (RSC) ER - TY - CHAP A1 - Pedersen, Jaap A1 - Lindner, Niels A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Comparing Branching Rules for the Quota Steiner Tree Problem with Interference T2 - Operations Research Proceedings 2025 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 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. Y1 - 2026 ER - TY - CHAP A1 - Franke, Paula A1 - Hamacher, Kay A1 - Manns, Paul T1 - Minimizing and Maximizing the Shannon Entropy for Fixed Marginals T2 - Operations Research Proceedings 2025 N2 - The mutual information (MI) between two random variables is an important correlation measure in data analysis. The Shannon entropy of a joint probability distri- bution is the variable part under fixed marginals. We aim to minimize and maximize it to obtain the largest and smallest MI possible in this case, leading to a scaled MI ratio for better comparability. We present algorithmic approaches and optimal solutions for a set of problem instances based on data from molecular evolution. We show that this allows us to construct a sensible, systematic correction to raw MI values. Y1 - 2026 ER - TY - JOUR A1 - Lelièvre, Tony A1 - Zhang, Wei T1 - Pathwise estimates for effective dynamics: the case of nonlinear vectorial reaction coordinates JF - Multiscale Modeling and Simulation N2 - Effective dynamics using conditional expectation was proposed in [F. Legoll and T. Lelièvre, Nonlinearity, 2010] to approximate the essential dynamics of high-dimensional diffusion processes along a given reaction coordinate. The approximation error of the effective dynamics when it is used to approximate the behavior of the original dynamics has been considered in recent years. As a continuation of the previous work [F. Legoll, T. Lelièvre, and S. Olla, Stoch. Process. Appl, 2017], in this paper we obtain pathwise estimates for effective dynamics when the reaction coordinate function is either nonlinear or vector-valued. Y1 - 2018 U6 - https://doi.org/10.1137/18M1186034 IS - 17 SP - 1019 EP - 1051 ER - TY - JOUR A1 - Hartmann, Carsten A1 - Schütte, Christof A1 - Zhang, Wei T1 - Jarzynski's equality, fluctuation theorems, and variance reduction: Mathematical analysis and numerical algorithms JF - Journal of Statistical Physics N2 - In this paper, we study Jarzynski's equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature, we review and generalize these nonequilibrium theorems using mathematical arguments, therefore enabling further investigations in the mathematical community. On the numerical side, variance reduction approaches such as importance sampling method are studied in order to compute free energy differences based on Jarzynski's equality. Y1 - 2018 U6 - https://doi.org/10.1007/s10955-019-02286-4 VL - 175 IS - 6 SP - 1214 EP - 1261 ER - TY - JOUR A1 - Zhang, Wei A1 - Klus, Stefan A1 - Conrad, Tim A1 - Schütte, Christof T1 - Learning chemical reaction networks from trajectory data JF - SIAM Journal on Applied Dynamical Systems (SIADS) N2 - We develop a data-driven method to learn chemical reaction networks from trajectory data. Modeling the reaction system as a continuous-time Markov chain and assuming the system is fully observed,our method learns the propensity functions of the system with predetermined basis functions by maximizing the likelihood function of the trajectory data under l^1 sparse regularization. We demonstrate our method with numerical examples using synthetic data and carry out an asymptotic analysis of the proposed learning procedure in the infinite-data limit. Y1 - 2019 U6 - https://doi.org/10.1137/19M1265880 VL - 18 IS - 4 SP - 2000 EP - 2046 ER -