Skip to main content
SpringerLink
Log in

A Cut-Based Heuristic to Produce Almost Feasible Periodic Railway Timetables

  • Conference paper
Experimental and Efficient Algorithms (WEA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 3503))

Included in the following conference series:

Abstract

We consider the problem of satisfying the maximum number of constraints of an instance of the Periodic Event Scheduling Problem (Pesp). This is a key issue in periodic railway timetable construction, and has many other applications, e.g. for traffic light scheduling.

We generalize two (in-) approximability results, which are known for Maximum-K-Colorable-Subgraph. Moreover, we present a deterministic combinatorial polynomial time algorithm. Its output violates only very few constraints for five real-world instances.

Supported by the DFG Research Center “Mathematics for key technologies” (Matheon) in Berlin.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arora, S., Karger, D., Karpinski, M.: Polynomial Time Approximation Schemes for Dense Instances of NP-hard Problems. In: Proceedings of the 27th Annual ACM Symposium on Theory of Computing, pp. 284–293. ACM Press, New York (1995)

    Google Scholar 

  2. CPLEX 8.1  ILOG SA, France (2004), http://www.ilog.com/products/cplex

  3. Crescenzi, P., Kann, V.: A compendium of NP optimization problems (2005), http://www.nada.kth.se/~viggo/problemlist/compendium.html

  4. Daduna, J.R., Voß, S.: Practical Experiences in Schedule Synchronization. In: Daduna, J.R., et al. (eds.) Computer-Aided Transit Scheduling— Proceedings of the Sixth International Workshop on Computer-Aided Scheduling of Public Transport. LNEMS, vol. 430, pp. 39–55. Springer, Heidelberg (1995)

    Google Scholar 

  5. Engelhardt-Funke, O., Kolonko, M.: Analysing stability and investments in railway networks using advanced evolutionary algorithms. International Transactions in Operational Research 11, 381–394 (2004)

    Article  MATH  Google Scholar 

  6. Goemans, M., Williamson, D.: 878-Approximation Algorithms for Max Cut and Max 2Sat. In: Proceedings of the 26th Annual ACM Symposium on Theory of Computing, pp. 422–431. ACM Press, New York (1994)

    Google Scholar 

  7. Hassin, R.: A Flow Algorithm for Network Synchronization. Operations Research 44, 570–579 (1996)

    Article  MATH  Google Scholar 

  8. Liebchen, C.: Der Berliner U-Bahn Fahrplan 2005: Realisierung eines mathematisch optimierten Angebotskonzepts. In: Tagungsbericht Heureka 2005 Optimierung in Transport und Verkehr, FGSV (2005) (in German)

    Google Scholar 

  9. Liebchen, C., Möhring, R.H.: The Modeling Power of the Periodic Event Scheduling Problem: Railway Timetables—and Beyond. Preprint 020/2004, Mathematical Institute, TU Berlin, Germany (2004)

    Google Scholar 

  10. Liebchen, C., Proksch, M., Wagner, F.H.: Performance of Algorithms for Periodic Timetable Optimization. Preprint 021/2004, Mathematical Institute, TU Berlin, Germany (2004)

    Google Scholar 

  11. Lindner, T.: Train Schedule Optimization in Public Rail Transport. Ph.D. Thesis, TU Braunschweig, Germany (2000)

    Google Scholar 

  12. Martin, A., Achterberg, T., Koch, T.: MIPLIB 2003 (2003), http://www.zib.de/miplib

  13. Nachtigall, K., Voget, S.: A genetic algorithm approach to periodic railway synchronization. Computers and Operations Research 23, 453–463 (1996)

    Article  MATH  Google Scholar 

  14. Odijk, M.: Railway Timetable Generation. Ph.D. Thesis, TU Delft, The Netherlands (1997)

    Google Scholar 

  15. Papadimitriou, C.H., Yannakakis, M.: Optimization, Approximation, and Complexity Classes. Journal of Computer and System Sciences 43, 425–440 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  16. Peeters, L.: Cyclic Railway Timetable Optimization. Ph.D. Thesis, Erasmus Universiteit Rotterdam, The Netherlands (2003)

    Google Scholar 

  17. Schrijver, A., Steenbeek, A.: Dienstregelingontwikkeling voor Nederlandse Spoorwegen N.V.—Rapport Fase 1. Report, CWI, The Netherlands. In: Dutch (1993)

    Google Scholar 

  18. Serafini, P., Ukovich, W.: A mathematical model for periodic scheduling problems. SIAM Journal on Discrete Mathematics 2, 550–581 (1989)

    MATH  MathSciNet  Google Scholar 

  19. Vitanyi, P.M.B.: How Well Can a Graph be n-Colored? Discrete Mathematics 34, 69–80 (1981)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Mathematik, TU Berlin, Sekr. MA 6-1, Straße des 17. Juni 136, D-10623, Berlin, Germany

    Christian Liebchen

Authors
  1. Christian Liebchen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. CTI and Univ. of Patras, Greece

    Sotiris E. Nikoletseas

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Liebchen, C. (2005). A Cut-Based Heuristic to Produce Almost Feasible Periodic Railway Timetables. In: Nikoletseas, S.E. (eds) Experimental and Efficient Algorithms. WEA 2005. Lecture Notes in Computer Science, vol 3503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427186_31

Download citation

  • DOI: https://doi.org/10.1007/11427186_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25920-6

  • Online ISBN: 978-3-540-32078-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation