A Matching Approach for Periodic Timetabling
The periodic event scheduling problem (PESP) is a well studied problem known as intrinsically hard, but with important applications mainly for finding good timetables in public transportation. In this paper we consider PESP in public transportation, but in a reduced version (r-PESP) in which the driving and waiting times of the vehicles are fixed to their lower bounds. This results in a still NP-hard problem which has less variables, since only one variable determines the schedule for a whole line. We propose a formulation for r-PESP which is based on scheduling the lines. This enables us on the one hand to identify a finite candidate set and an exact solution approach. On the other hand, we use this formulation to derive a matching-based heuristic for solving PESP. Our experiments on close to real-world instances from LinTim show that our heuristic is able to compute competitive timetables in a very short runtime.
PESP
Timetabling
Public Transport
Matching
Finite Dominating Set
1:1-1:15
Regular Paper
Julius
Pätzold
Julius Pätzold
Anita
Schöbel
Anita Schöbel
10.4230/OASIcs.ATMOS.2016.1
M. Goerigk. Exact and heuristic approaches to the robust periodic event scheduling problem. Public Transport, 7(1):101-119, 2015.
M. Goerigk, M. Schachtebeck, and A. Schöbel. Evaluating line concepts using travel times and robustness: Simulations with the lintim toolbox. Public Transport, 5(3), 2013.
M. Goerigk and A. Schöbel. Improving the modulo simplex algorithm for large-scale periodic timetabling. Computers and Operations Research, 40(5):1363-1370, 2013.
P. Großmann, S. Hölldobler, N. Manthey, K. Nachtigall, J. Opitz, and P. Steinke. Solving periodic event scheduling problems with sat. In H. Jiang, W. Ding, M. Ali, and X. Wu, editors, Advanced Research in Applied Artificial Intelligence, volume 7345, pages 166-175. Springer, 2012.
J. Harbering, A. Schiewe, and A. Schöbel. LinTim - Integrated Optimization in Public Transportation. Homepage. see http://lintim.math.uni-goettingen.de/.
L. Kroon, G. Maróti, M. R. Helmrich, M. Vromans, and R. Dekker. Stochastic improvement of cyclic railway timetables. Transportation Research Part B: Methodological, 42(6):553 - 570, 2008.
L.G. Kroon, D. Huisman, E. Abbink, P.-J. Fioole, M. Fischetti, G. Maroti, A. Shrijver, A. Steenbeek, and R. Ybema. The new Dutch timetable: The OR Revolution. Interfaces, 39:6-17, 2009.
C. Liebchen. Periodic Timetable Optimization in Public Transport. dissertation.de - Verlag im Internet, Berlin, 2006.
C. Liebchen. The first optimized railway timetable in practice. Transportation Science, 42(4):420-435, 2008.
M. Michaelis and A. Schöbel. Integrating line planning, timetabling, and vehicle scheduling: A customer-oriented approach. Public Transport, 1(3):211-232, 2009.
K. Nachtigall. Periodic Network Optimization and Fixed Interval Timetables. PhD thesis, University of Hildesheim, 1998.
K. Nachtigall and J. Opitz. Solving periodic timetable optimisation problems by modulo simplex calculations. In Proc. ATMOS, 2008.
K. Nachtigall and S. Voget. A genetic approach to periodic railway synchronization. Computers Ops. Res., 23(5):453-463, 1996.
M. A. Odijk. A constraint generation algorithm for the construction of periodic railway timetables. Transportation Research, 30B:455-464, 1996.
J. Pätzold. Periodic timetabling with fixed driving and waiting times. Master’s thesis, Fakultät für Mathematik und Informatik, Georg August University Göttingen, 2016. (in German).
L. Peeters and L. Kroon. A cycle based optimization model for the cyclic railway timetabling problem. In S. Voß and J. Daduna, editors, Computer-Aided Transit Scheduling, volume 505 of Lecture Notes in Economics and Mathematical systems, pages 275-296. Springer, 2001.
P. Serafini and W. Ukovich. A mathematical model for periodic scheduling problems. SIAM Journal on Discrete Mathematic, 2:550-581, 1989.
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode