TY - GEN A1 - Liebchen, Christian A1 - Proksch, Mark A1 - Wagner, Frank H. T1 - Performance of Algorithms for Periodic Timetable Optimization N2 - 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. Y1 - 2004 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/161 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-1612 ER -