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A Geometric Approach to Integrated Periodic Timetabling and Passenger Routing

Authors Fabian Löbel , Niels Lindner

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Subject Classification

ACM Subject Classification
  • Applied computing → Transportation
  • Mathematics of computing → Combinatorial optimization
  • Theory of computation → Network optimization
Keywords
  • Periodic Timetabling
  • Passenger Routing
  • Polyhedral Complexes

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Abstract

We offer a geometric perspective on the problem of integrated periodic timetabling and passenger routing in public transport. Inside the space of periodic tensions, we single out those regions, where the same set of paths provides shortest passenger routes. This results in a polyhedral subdivision, which we combine with the known decomposition by polytropes. On each maximal region of the common refinement, the integrated problem is solvable in polynomial time. We transform these insights into a new geometry-driven primal heuristic, integrated tropical neighborhood search (ITNS). Computationally, we compare implementations of ITNS and the integrated (restricted) modulo network simplex algorithm on the TimPassLib benchmark set, and contribute better solutions in terms of total travel time for all but one of the twenty-five instances for which a proven optimal solution is not yet known.

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Fabian Löbel and Niels Lindner. A Geometric Approach to Integrated Periodic Timetabling and Passenger Routing. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 2:1-2:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/OASIcs.ATMOS.2025.2

Author Details

Fabian Löbel
  • Zuse Institute Berlin, Germany
Niels Lindner
  • Freie Universität Berlin, Germany

Funding

  • Löbel, Fabian: Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – The Berlin Mathematics Research Center MATH+ (EXC-2046/1, project ID: 390685689).

References

  1. Ralf Borndörfer, Heide Hoppmann, and Marika Karbstein. Passenger routing for periodic timetable optimization. Public Transport, 9(1):115-135, 2017. URL: https://doi.org/10.1007/s12469-016-0132-0.
  2. Ralf Borndörfer, Heide Hoppmann, Marika Karbstein, and Fabian Löbel. The Modulo Network Simplex with Integrated Passenger Routing. In Andreas Fink, Armin Fügenschuh, and Martin Josef Geiger, editors, Operations Research Proceedings 2016, pages 637-644. Springer International Publishing, 2017. URL: https://doi.org/10.1007/978-3-319-55702-1_84.
  3. Ralf Borndörfer, Niels Lindner, and Sarah Roth. A concurrent approach to the periodic event scheduling problem. Journal of Rail Transport Planning & Management, 15:100175, 2020. URL: https://doi.org/10.1016/j.jrtpm.2019.100175.
  4. Enrico Bortoletto, Niels Lindner, and Berenike Masing. Tropical Neighbourhood Search: A New Heuristic for Periodic Timetabling. In Mattia D'Emidio and Niels Lindner, editors, 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022), volume 106 of Open Access Series in Informatics (OASIcs), pages 3:1-3:19, Dagstuhl, Germany, 2022. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. ISSN: 2190-6807. URL: https://doi.org/10.4230/OASIcs.ATMOS.2022.3.
  5. Enrico Bortoletto, Niels Lindner, and Berenike Masing. The Tropical and Zonotopal Geometry of Periodic Timetables. Discrete & Computational Geometry, 2024. URL: https://doi.org/10.1007/s00454-024-00686-2.
  6. Philine Gattermann, Peter Großmann, Karl Nachtigall, and Anita Schöbel. Integrating Passengers' Routes in Periodic Timetabling: A SAT approach. In Marc Goerigk and Renato F. Werneck, editors, 16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016), volume 54 of Open Access Series in Informatics (OASIcs), pages 3:1-3:15, Dagstuhl, Germany, 2016. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/OASIcs.ATMOS.2016.3.
  7. Michael Joswig and Katja Kulas. Tropical and ordinary convexity combined. Advances in Geometry, 10(2):333-352, 2010. Publisher: De Gruyter Section: Advances in Geometry. URL: https://doi.org/10.1515/advgeom.2010.012.
  8. Michael Joswig and Benjamin Schröter. Parametric Shortest-Path Algorithms via Tropical Geometry. Mathematics of Operations Research, 47(3):2065-2081, 2022. Publisher: INFORMS. URL: https://doi.org/10.1287/moor.2021.1199.
  9. Christian Liebchen. Periodic timetable optimization in public transport. PhD thesis, Technicsche Universität Berlin, 2006. Google Scholar
  10. Fabian Löbel, Niels Lindner, and Ralf Borndörfer. The Restricted Modulo Network Simplex Method for Integrated Periodic Timetabling and Passenger Routing. In Janis S. Neufeld, Udo Buscher, Rainer Lasch, Dominik Möst, and Jörn Schönberger, editors, Operations Research Proceedings 2019, pages 757-763, Cham, 2020. Springer International Publishing. URL: https://doi.org/10.1007/978-3-030-48439-2_92.
  11. Bernardo Martin-Iradi and Stefan Ropke. A column-generation-based matheuristic for periodic and symmetric train timetabling with integrated passenger routing. European Journal of Operational Research, 297(2):511-531, 2022. URL: https://doi.org/10.1016/j.ejor.2021.04.041.
  12. Berenike Masing, Niels Lindner, and Enrico Bortoletto. Computing All Shortest Passenger Routes with a Tropical Dijkstra Algorithm, 2024. arXiv:2412.14654 [math]. URL: https://doi.org/10.48550/arXiv.2412.14654.
  13. Karl Nachtigall and Jens Opitz. Solving Periodic Timetable Optimisation Problems by Modulo Simplex Calculations. In Matteo Fischetti and Peter Widmayer, editors, 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08), volume 9 of Open Access Series in Informatics (OASIcs), pages 1-15, Dagstuhl, Germany, 2008. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/OASIcs.ATMOS.2008.1588.
  14. Michiel A. Odijk. Construction of periodic timetables, Part 1: A cutting plane algorithm. Technical Report 94-61, TU Delft, 1994. Google Scholar
  15. Gert-Jaap Polinder, Marie Schmidt, and Dennis Huisman. Timetabling for strategic passenger railway planning. Transportation Research Part B: Methodological, 146:111-135, 2021. URL: https://doi.org/10.1016/j.trb.2021.02.006.
  16. Stephanie Riedmüller. A path-based model for integrated periodic timetabling and passenger routing. Master’s thesis, Freie Universität Berlin, 2023. Google Scholar
  17. Philine Schiewe, Marc Goerigk, and Niels Lindner. Introducing TimPassLib – A Library for Integrated Periodic Timetabling and Passenger Routing. Operations Research Forum, 4, 2023. URL: https://doi.org/10.1007/s43069-023-00244-1.
  18. Philine Schiewe and Anita Schöbel. Periodic Timetabling with Integrated Routing: Toward Applicable Approaches. Transportation Science, 54(6):1714-1731, 2020. Publisher: INFORMS. URL: https://doi.org/10.1287/trsc.2019.0965.
  19. Marie Schmidt. Integrating Routing Decisions in Public Transportation Problems. Springer Optimization and Its Applications. Springer New York, NY, 2014. URL: https://doi.org/10.1007/978-1-4614-9566-6.
  20. Marie Schmidt and Anita Schöbel. Timetabling with passenger routing. OR Spectrum, 37(1):75-97, 2015. URL: https://doi.org/10.1007/s00291-014-0360-0.
  21. Paolo Serafini and Walter Ukovich. A Mathematical Model for Periodic Scheduling Problems. SIAM Journal on Discrete Mathematics, 2(4):550-581, 1989. URL: https://doi.org/10.1137/0402049.
  22. Michael Siebert and Marc Goerigk. An experimental comparison of periodic timetabling models. Computers & Operations Research, 40(10):2251-2259, 2013. URL: https://doi.org/10.1016/j.cor.2013.04.002.
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