A Hybridised Integer Programming and Local Search Method for Robust Train Driver Schedules Planning

  • Ignacio Laplagne
  • Raymond S. K. Kwan
  • Ann S. K. Kwan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3616)


When a train arrives at a station, it often stops for some time before continuing, giving rise to a window of relief opportunities (WRO), during which the train may be handed over between drivers. Incorporating these windows into the scheduling model may help improve the robustness and efficiency of driver schedules. However, if it is formulated as a set covering problem, the incorporation of WROs would cause the resulting model to be too big to be solved in realistic times with current technology.

In this paper, we propose a combined integer programming and local search approach. In the first step, WROs are approximated, and the problem is solved using integer programming. Using the solution thus obtained as a starting point, WROs are restored and a multi-neighbourhood local search algorithm takes over. We also investigate the possibility of deriving a new set of approximations from the local search solution, and loop back to the integer programming phase.

The algorithm is tested using real-life data from a large rail network in Scotland, producing improved, operational schedules for this network.


Local Search Schedule Model Infeasible Solution Local Search Phase Train Driver 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ignacio Laplagne
    • 1
  • Raymond S. K. Kwan
    • 1
  • Ann S. K. Kwan
    • 1
  1. 1.School of ComputingUniversity of LeedsLeedsUK

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