Performance of Algorithms for Periodic Timetable Optimization

  • Christian Liebchen
  • Mark Proksch
  • Frank H. Wagner
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 600)


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.


Minimal Span Tree Mixed Integer Programming Constraint Programming Valid Inequality Cycle Base 
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 2008

Authors and Affiliations

  • Christian Liebchen
    • 1
  • Mark Proksch
    • 2
  • Frank H. Wagner
    • 3
  1. 1.Institut für MathematikTU BerlinBerlinGermany
  2. 2.intranetz GmbHBerlinGermany
  3. 3.KonzernentwicklungDeutsche Bahn AGBerlinGermany

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