@article{KoflerWaldKolbitschetal.2024, author = {Kofler, Andreas and Wald, Christian and Kolbitsch, Christoph and von Tycowicz, Christoph and Ambellan, Felix}, title = {Joint Reconstruction and Segmentation in Undersampled 3D Knee MRI combining Shape Knowledge and Deep Learning}, volume = {69}, journal = {Physics in Medicine and Biology}, number = {9}, doi = {10.1088/1361-6560/ad3797}, year = {2024}, abstract = {Task-adapted image reconstruction methods using end-to-end trainable neural networks (NNs) have been proposed to optimize reconstruction for subsequent processing tasks, such as segmentation. However, their training typically requires considerable hardware resources and thus, only relatively simple building blocks, e.g. U-Nets, are typically used, which, albeit powerful, do not integrate model-specific knowledge. In this work, we extend an end-to-end trainable task-adapted image reconstruction method for a clinically realistic reconstruction and segmentation problem of bone and cartilage in 3D knee MRI by incorporating statistical shape models (SSMs). The SSMs model the prior information and help to regularize the segmentation maps as a final post-processing step. We compare the proposed method to a state-of-the-art (SOTA) simultaneous multitask learning approach for image reconstruction and segmentation (MTL) and to a complex SSMs-informed segmentation pipeline (SIS). Our experiments show that the combination of joint end-to-end training and SSMs to further regularize the segmentation maps obtained by MTL highly improves the results, especially in terms of mean and maximal surface errors. In particular, we achieve the segmentation quality of SIS and, at the same time, a substantial model reduction that yields a five-fold decimation in model parameters and a computational speedup of an order of magnitude. Remarkably, even for undersampling factors of up to R=8, the obtained segmentation maps are of comparable quality to those obtained by SIS from ground-truth images.}, language = {en} } @article{PrauseBorndoerferGrimmetal.2024, author = {Prause, Felix and Bornd{\"o}rfer, Ralf and Grimm, Boris and Tesch, Alexander}, title = {Approximating rolling stock rotations with integrated predictive maintenance}, volume = {30}, journal = {Journal of Rail Transport Planning \& Management}, doi = {10.1016/j.jrtpm.2024.100434}, pages = {100434}, year = {2024}, abstract = {We study the solution of the rolling stock rotation problem with predictive maintenance (RSRP-PdM) 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 six 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.}, language = {en} } @article{SikorskiNiknejadWeberetal.2024, author = {Sikorski, Alexander and Niknejad, Amir and Weber, Marcus and Donati, Luca}, title = {Tensor-SqRA: Modeling the transition rates of interacting molecular systems in terms of potential energies}, volume = {160}, journal = {Journal of Chemical Physics}, arxiv = {http://arxiv.org/abs/2311.09779}, doi = {10.1063/5.0187792}, pages = {104112}, year = {2024}, abstract = {Estimating the rate of rare conformational changes in molecular systems is one of the goals of molecular dynamics simulations. In the past few decades, a lot of progress has been done in data-based approaches toward this problem. In contrast, model-based methods, such as the Square Root Approximation (SqRA), directly derive these quantities from the potential energy functions. In this article, we demonstrate how the SqRA formalism naturally blends with the tensor structure obtained by coupling multiple systems, resulting in the tensor-based Square Root Approximation (tSqRA). It enables efficient treatment of high-dimensional systems using the SqRA and provides an algebraic expression of the impact of coupling energies between molecular subsystems. Based on the tSqRA, we also develop the projected rate estimation, a hybrid data-model-based algorithm that efficiently estimates the slowest rates for coupled systems. In addition, we investigate the possibility of integrating low-rank approximations within this framework to maximize the potential of the tSqRA.}, language = {en} } @article{TjusilaBesanconTurneretal.2024, author = {Tjusila, Gennesaret and Besan{\c{c}}on, Mathieu and Turner, Mark and Koch, Thorsten}, title = {How Many Clues To Give? A Bilevel Formulation For The Minimum Sudoku Clue Problem}, volume = {54}, journal = {Operations Research Letters}, doi = {10.1016/j.orl.2024.107105}, pages = {107105}, year = {2024}, abstract = {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.}, language = {en} } @article{BreugemSchlechteSchulzetal.2023, author = {Breugem, Thomas and Schlechte, Thomas and Schulz, Christof and Bornd{\"o}rfer, Ralf}, title = {A three-phase heuristic for the Fairness-Oriented Crew Rostering Problem}, volume = {154}, journal = {Computers \& Operations Research}, doi = {10.1016/j.cor.2023.106186}, pages = {106186}, year = {2023}, abstract = {The Fairness-Oriented Crew Rostering Problem (FCRP) considers the joint optimization of attractiveness and fairness in cyclic crew rostering. Like many problems in scheduling and logistics, the combinatorial complexity of cyclic rostering causes exact methods to fail for large-scale practical instances. In case of the FCRP, this is accentuated by the additionally imposed fairness requirements. Hence, heuristic methods are necessary. We present a three-phase heuristic for the FCRP combining column generation techniques with variable-depth neighborhood search. The heuristic exploits different mathematical formulations to find feasible solutions and to search for improvements. We apply our methodology to practical instances from Netherlands Railways (NS), the main passenger railway operator in the Netherlands Our results show the three-phase heuristic finds good solutions for most instances and outperforms a state-of-the-art commercial solver.}, language = {en} } @article{BinkowskiKulligBetzetal.2024, author = {Binkowski, Felix and Kullig, Julius and Betz, Fridtjof and Zschiedrich, Lin and Walther, Andrea and Wiersig, Jan and Burger, Sven}, title = {Computing eigenfrequency sensitivities near exceptional points}, volume = {6}, journal = {Phys. Rev. Research}, arxiv = {http://arxiv.org/abs/2402.17648}, doi = {10.1103/PhysRevResearch.6.023148}, pages = {023148}, year = {2024}, language = {en} } @article{KreimeierPokuttaWaltheretal., author = {Kreimeier, Timo and Pokutta, Sebastian and Walther, Andrea and Woodstock, Zev}, title = {On a Frank-Wolfe approach for abs-smooth functions}, journal = {Optimization Methods and Software}, doi = {10.1080/10556788.2023.2296985}, language = {en} } @article{HunkenschroederPokuttaWeismantel2022, author = {Hunkenschr{\"o}der, Christoph and Pokutta, Sebastian and Weismantel, Robert}, title = {Optimizing a low-dimensional convex function over a high-dimensional cube}, journal = {SIAM Journal on Optimization}, year = {2022}, language = {en} } @article{DesignolleVertesiPokutta2024, author = {Designolle, S{\´e}bastien and V{\´e}rtesi, Tam{\´a}s and Pokutta, Sebastian}, title = {Symmetric multipartite Bell inequalities via Frank-Wolfe algorithms}, volume = {109}, journal = {Physics Review A}, number = {2}, doi = {10.1103/PhysRevA.109.022205}, year = {2024}, abstract = {In multipartite Bell scenarios, we study the nonlocality robustness of the Greenberger-Horne-Zeilinger (GHZ) state. When each party performs planar measurements forming a regular polygon, we exploit the symmetry of the resulting correlation tensor to drastically accelerate the computation of (i) a Bell inequality via Frank-Wolfe algorithms and (ii) the corresponding local bound. The Bell inequalities obtained are facets of the symmetrized local polytope and they give the best-known upper bounds on the nonlocality robustness of the GHZ state for three to ten parties. Moreover, for four measurements per party, we generalize our facets and hence show, for any number of parties, an improvement on Mermin's inequality in terms of noise robustness. We also compute the detection efficiency of our inequalities and show that some give rise to the activation of nonlocality in star networks, a property that was only shown with an infinite number of measurements.}, language = {en} } @article{EiflerGleixner2024, author = {Eifler, Leon and Gleixner, Ambros}, title = {Safe and verified Gomory mixed integer cuts in a rational MIP framework}, volume = {34}, journal = {SIAM Journal on Optimization}, number = {1}, doi = {10.1137/23M156046X}, year = {2024}, abstract = {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 [INFORMS J. Comput., 21 (2009), pp. 641-649]. 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 to exact optimality and reduce solving times by 26.8\% on the MIPLIB 2017 benchmark test set.}, language = {en} }