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Low-precision first-order method-based fix-and-propagate heuristics for large-scale mixed-integer linear optimization
No full textWe 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
Mathematische Optimierung in der OP-Planung
No full textDeutsche Krankenhäuser sehen sich derzeit mit enormen Schwierigkeiten konfrontiert. Ungefähr jede 2. Klinik muss drastische Sparmaßnahmen ergreifen, was auch die Allgemeinversorgung beeinträchtigt. Die Gründe dafür sind vielschichtig: stark gestiegene Sach- und Personalkosten bei gleicher Finanzierung, teilweiser Patientenrückgang, starke regionale Unterschiede in der Versorgung, Fachkräftemangel und fehlende Investitionen in Kern- und Zukunftsbereiche, insbesondere der Digitalisierung. Das belastet die Haushalte der Kliniken. Insbesondere die Digitalisierung und die Anwendung von Methoden der künstlichen Intelligenz und der mathematischen Optimierung könnten eine Schlüsselrolle spielen, um die komplexen Krankenhausprozesse mit Kennzahlen qualitativ zu bewerten und zu verbessern. In diesem Artikel stellen wir vier Praxisprobleme aus der OP-Planung vor und benennen welche Entscheidungen, Nebenbedingungen und Zielkriterien mit mathematischen Entscheidungsmodellen dargestellt und optimiert werden können. Hierzu erläutern wir das erweiterte Potenzial einer umfassenden Anwendung von mathematischer Optimierung im OP-Bereich
Efficient and Accurate Machine Learning Interatomic Potential for Graphene: Capturing Stress–Strain and Vibrational Properties
No full textFishexplorer: A multimodal cellular atlas platform for neuronal circuit dissection in larval zebrafish
No full textUnderstanding how neural circuits give rise to behavior requires comprehensive knowledge of neuronal morphology, connectivity, and function. Atlas platforms play a critical role in enabling the visualization, exploration, and dissemination of such information. Here, we present FishExplorer, an interactive and expandable community platform designed to integrate and analyze multimodal brain data from larval zebrafish. FishExplorer supports datasets acquired through light microscopy (LM), electron microscopy (EM), and X-ray imaging, all co-registered within a unified spatial coordinate system which enables seamless comparison of neuronal morphologies and synaptic connections. To further assist circuit analysis, FishExplorer includes a suite of tools for querying and visualizing connectivity at the whole-brain scale. By integrating data from recent large-scale EM reconstructions (presented in companion studies), FishExplorer enables researchers to validate circuit models, explore wiring principles, and generate new hypotheses. As a continuously evolving resource, FishExplorer is designed to facilitate collaborative discovery and serve the growing needs of the teleost neuroscience community
Quantum dynamics of coupled excitons and phonons in chain-like systems: tensor train approaches and higher-order propagators
No full textSource code and simulation results: High Purcell enhancement in all-TMDC nanobeam resonator designs with active monolayers for nanolasers
No full textPentraxin-3, MyD88, GLP-1, and PD-L1: Performance assessment and composite algorithmic analysis for sepsis identification
No full textThis study examines nine emerging biomarkers as possible indicators for diagnosing sepsis in emergency department patient
Exploring Interdisciplinary Research Trends through Critical Years for Interdisciplinary Citation
No full textA two-stage model for periodic timetabling with fixed line activities
No full textThe 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