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Does Laziness Pay Off? - A Lazy-Constraint Approach to Timetabling

Authors Torsten Klug, Markus Reuther, Thomas Schlechte

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial optimization
Keywords
  • Moving Block
  • Railway Track Allocation
  • Timetabling
  • Train Routing

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Abstract

Timetabling is a classical and complex task for public transport operators as well as for railway undertakings. The general question is: Which vehicle is taking which route through the transportation network in which order? In this paper, we consider the special setting to find optimal timetables for railway systems under a moving block regime. We directly set up on our work of [T. Schlechte et al., 2022], i.e., we consider the same model formulation and real-world instances of a moving block headway system. In this paper, we present a repair heuristic and a lazy-constraint approach utilizing the callback features of Gurobi, see [Gurobi Optimization, 2022]. We provide an experimental study of the different algorithmic approaches for a railway network with 100 and up to 300 train requests. The computational results show that the lazy-constraint approach together with the repair heuristic significantly improves our previous approaches.

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Torsten Klug, Markus Reuther, and Thomas Schlechte. Does Laziness Pay Off? - A Lazy-Constraint Approach to Timetabling. In 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022). Open Access Series in Informatics (OASIcs), Volume 106, pp. 11:1-11:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/OASIcs.ATMOS.2022.11

Author Details

Torsten Klug
  • LBW Optimization GmbH, Berlin, Germany
Markus Reuther
  • LBW Optimization GmbH, Berlin, Germany
Thomas Schlechte
  • LBW Optimization GmbH, Berlin, Germany

References

  1. Ralf Borndörfer, Torsten Klug, Leonardo Lamorgese, Carlo Mannino, Markus Reuther, and Thomas Schlechte, editors. Handbook of Optimization in the Railway Industry, volume 268. Springer, 2018. URL: https://doi.org/10.1007/978-3-319-72153-8.
  2. Valentina Cacchiani, Dennis Huisman, Martin Kidd, Leo Kroon, Paolo Toth, Lucas Veelenturf, and Joris Wagenaar. An overview of recovery models and algorithms for real-time railway rescheduling. Transportation Research Part B: Methodological, 63:15-37, 2014. URL: https://doi.org/10.1016/j.trb.2014.01.009.
  3. Gurobi Optimization, LLC. Gurobi Optimizer Reference Manual, 2022. URL: https://www.gurobi.com.
  4. Steven S. Harrod. A tutorial on fundamental model structures for railway timetable optimization. Surveys in Operations Research and Management Science, 17(2):85-96, 2012. URL: https://doi.org/10.1016/j.sorms.2012.08.002.
  5. Leonardo Lamorgese and Carlo Mannino. An exact decomposition approach for the real-time Train Dispatching problem. Operations Research, 63:48-64, 2015. URL: https://doi.org/10.1287/opre.2014.1327.
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  7. Ulrich Pferschy and Rostislav Staněk. Generating subtour elimination constraints for the TSP from pure integer solutions. Central European Journal of Operations Research, 25(1):231-260, February 2016. URL: https://doi.org/10.1007/s10100-016-0437-8.
  8. Thomas Schlechte, Ralf Borndörfer, Jonas Denißen, Simon Heller, Torsten Klug, Michael Küpper, Niels Lindner, Markus Reuther, Andreas Söhlke, and William Steadman. Timetable optimization for a moving block system. Journal of Rail Transport Planning & Management, 22:100315, June 2022. URL: https://doi.org/10.1016/j.jrtpm.2022.100315.
  9. Peijuan Xu, Francesco Corman, Qiyuan Peng, and Xiaojie Luan. A train rescheduling model integrating speed management during disruptions of high-speed traffic under a quasi moving block system. Transportation Research Part B, 104:638-666, 2017. URL: https://doi.org/10.1016/j.trb.2017.05.008.
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