Abstract
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.
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References
Barták, R. (1999). Constraint programming: A survey of solving technology. AIRONews journal IV, 4, 7–11.
Berger, F. (2002). Minimale Kreisbasen in Graphen. Technical report, Lecture on the annual meeting of the DMV, Halle.
Bixby, B. (2003). Personal communication. Rice University.
Bussieck, M. R., Winter, T., and Zimmermann, U. (1997). Discrete optimization in public rail transport. Mathematical Programming (Series B), 79, 415–444.
Deo, N., Prabhu, M., and Krishnamoorthy, M. S. (1982). Algorithms for generating fundamental cycles in a graph. ACM Transactions on Mathematical Software, 8, 26–42.
Deo, N., Kumar, N., and Parsons, J. (1995). Minimum-length fundamental-cycle set problem: A new heuristic and an SIMD implementation. Technical report CS-TR-95-04. University of Central Florida.
Emden-Weinert, T. and Proksch, M. (1999). Best practice simulated annealing for the airline crew scheduling problem. Journal of Heuristics, 5, 419–436.
Horton, J. D. (1987). A polynomial-time algorithm to find the shortest cycle basis of a graph. SIAM Journal on Computing, 16, 358–366.
ILOG SA (2004). CPLEX 8.1. http://www.ilog.com/products/cplex.
Laube, J. (2004). Taktfahrplanoptimierung mit Constraint Programming, diploma thesis, in German.
Liebchen, C. (2003). Finding short integral cycle bases for cyclic timetabling. In G. D. Battista and U. Zwick, editors, Algorithms-ESA 2003, Lecture Notes in Computer Science 2832, pages 715–726. Springer.
Liebchen, C. and Möhring, R. H. (2003). Information on MIPLIB’s timetabinstances. Technical report 049/2003, TU Berlin.
Liebchen, C. and Möhring, R. H. (2007). The modeling power of the periodic event scheduling problem: Railway timetables — and beyond. This volume.
Liebchen, C. and Peeters, L. (2002a). On cyclic timetabling and cycles in graphs. Technical report 761/2002, TU Berlin.
Liebchen, C. and Peeters, L. (2002b). Some practical aspects of periodic timetabling. In P. Chamoni, R. Leisten, A. Martin, J. Minnemann, and H. Stadtler, editors, Operations Research Proceedings 2001, pages 25–32. Springer, Berlin.
Lindner, T. (2000). Train Schedule Optimization in Public Transport. Ph.D. thesis, TU Braunschweig.
Mühlenbein, H. (1997). Genetic algorithms. In E. H. L. Aarts and J. K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 137–171. John Wiley & Sons.
Nachtigall, K. (1994). A branch and cut approach for periodic network programming. Hildesheimer Informatik-Berichte 29.
Nachtigall, K. (1996). Cutting planes for a polyhedron associated with a periodic network. Technical report, DLR Interner Bericht 17.
Nachtigall, K. (1998). Periodic network optimization and fixed interval timetables, habilitation thesis.
Nachtigall, K. and Voget, S. (1996). A genetic algorithm approach to periodic railway synchronization. Computers & Operations Research, 23, 453–463.
Odijk, M. (1997). Railway Timetable Generation. Ph.D. thesis, TU Delft.
Proksch, M. (1997). Simulated Annealing und seine Anwendung auf das Crew-Scheduling-Problem, Diploma thesis, in German.
Schrijver, A. and Steenbeek, A. (1993). Dienstregelingontwikkeling voor Nederlandse Spoorwegen N.V. Rapport Fase 1, in Dutch. Technical report, Centrum voor Wiskunde en Informatica.
Serafini, P. and Ukovich, W. (1989). A mathematical model for periodic scheduling problems. SIAM Journal on Discrete Mathematics, 2, 550–581.
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Liebchen, C., Proksch, M., Wagner, F.H. (2008). Performance of Algorithms for Periodic Timetable Optimization. In: Hickman, M., Mirchandani, P., Voß, S. (eds) Computer-aided Systems in Public Transport. Lecture Notes in Economics and Mathematical Systems, vol 600. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73312-6_8
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DOI: https://doi.org/10.1007/978-3-540-73312-6_8
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