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Performance of Algorithms for Periodic Timetable Optimization

In: Computer-aided Systems in Public Transport

Author

Listed:
  • Christian Liebchen

    (TU Berlin)

  • Mark Proksch

    (intranetz GmbH)

  • Frank H. Wagner

    (Deutsche Bahn AG)

Abstract

During the last 15 years, many solution methods for the important task of constructing periodic timetables for public transportation companies have been proposed. We first point out the importance of an objective function, where we observe that in particular a linear objective function turns out to be a good compromise between essential practical requirements and computational tractability. Then, we enter into a detailed empirical analysis of various Mixed Integer Programming (MIP) procedures — those using node variables and those using arc variables — genetic algorithms, simulated annealing and constraint programming. To our knowledge, this is the first comparison of five conceptually different solution approaches for periodic timetable optimization. On rather small instances, an arc-based MIP formulation behaves best, when refined by additional valid inequalities. On bigger instances, the solutions obtained by a genetic algorithm are competitive to the solutions CPLEX was investigating until it reached a time or memory limit. For Deutsche Bahn AG, the genetic algorithm was most convincing on their various data sets, and it will become the first automated timetable optimization software in use.

Suggested Citation

  • Christian Liebchen & Mark Proksch & Frank H. Wagner, 2008. "Performance of Algorithms for Periodic Timetable Optimization," Lecture Notes in Economics and Mathematical Systems, in: Mark Hickman & Pitu Mirchandani & Stefan Voß (ed.), Computer-aided Systems in Public Transport, pages 151-180, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-73312-6_8
    DOI: 10.1007/978-3-540-73312-6_8
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    Citations

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    Cited by:

    1. Pellegrini, Paola & Rodriguez, Joaquin, 2013. "Single European Sky and Single European Railway Area: A system level analysis of air and rail transportation," Transportation Research Part A: Policy and Practice, Elsevier, vol. 57(C), pages 64-86.
    2. Chen, Zhiwei & Li, Xiaopeng & Zhou, Xuesong, 2019. "Operational design for shuttle systems with modular vehicles under oversaturated traffic: Discrete modeling method," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 1-19.
    3. Polinder, G.-J. & Cacchiani, V. & Schmidt, M.E. & Huisman, D., 2020. "An iterative heuristic for passenger-centric train timetabling with integrated adaption times," ERIM Report Series Research in Management ERS-2020-006-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    4. Polinder, G.-J. & Kroon, L.G. & Aardal, K. & Schmidt, M.E. & Molinaro, M., 2018. "Resolving infeasibilities in railway timetabling instances," ERIM Report Series Research in Management ERS-2018-002-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    5. Cacchiani, Valentina & Furini, Fabio & Kidd, Martin Philip, 2016. "Approaches to a real-world Train Timetabling Problem in a railway node," Omega, Elsevier, vol. 58(C), pages 97-110.
    6. Rolf N. Van Lieshout, 2021. "Integrated Periodic Timetabling and Vehicle Circulation Scheduling," Transportation Science, INFORMS, vol. 55(3), pages 768-790, May.
    7. Christian Liebchen, 2008. "The First Optimized Railway Timetable in Practice," Transportation Science, INFORMS, vol. 42(4), pages 420-435, November.
    8. Berenike Masing & Niels Lindner & Patricia Ebert, 2023. "Forward and Line-Based Cycle Bases for Periodic Timetabling," SN Operations Research Forum, Springer, vol. 4(3), pages 1-33, September.
    9. Hartleb, Johann & Schmidt, Marie, 2022. "Railway timetabling with integrated passenger distribution," European Journal of Operational Research, Elsevier, vol. 298(3), pages 953-966.

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