During the last 15 years, there have been proposed many solution methods
for the important task of constructing periodic timetables for public transportation
companies. 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
procedures { such using nodes variables and such using arcs variables { genetic algorithms,
simulated annealing and constraint programming. To our knowledge, this
is the first comparison of five conceptually different solution approaches.
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.