License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/OASIcs.ATMOS.2008.1580
URN: urn:nbn:de:0030-drops-15802
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2008/1580/
Go to the corresponding OASIcs Volume Portal

Liebchen, Christian ; Swarat, Elmar

The Second Chvatal Closure Can Yield Better Railway Timetables

pdf-format:
08002.Liebchen.1580.pdf (0.1 MB)

Abstract

We investigate the polyhedral structure of the Periodic Event Scheduling Problem (PESP), which is commonly used in periodic railway timetable optimization. This is the first investigation of Chvatal closures and of the Chvatal rank of PESP instances.
In most detail, we first provide a PESP instance on only two events, whose Chvatal rank is very large. Second, we identify an instance for which we prove that it is feasible over the first Chvatal closure, and also feasible for another prominent class of known valid inequalities, which we reveal to live in much larger Chvatal closures. In contrast, this instance turns out to be infeasible already over the second Chvatal closure. We obtain the latter result by introducing new valid inequalities for the PESP, the multi-circuit cuts. In the past, for other classes of valid inequalities for the PESP, it had been observed that these do not have any effect in practical computations. In contrast, the new multi-circuit cuts that we are introducing here indeed show some effect in the computations that we perform on several real-world instances - a positive effect, in most of the cases.

BibTeX - Entry

@InProceedings{liebchen_et_al:OASIcs:2008:1580,
  author =	{Christian Liebchen and Elmar Swarat},
  title =	{{The Second Chvatal Closure Can Yield Better Railway Timetables}},
  booktitle =	{8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08) },
  series =	{OpenAccess Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-07-1},
  ISSN =	{2190-6807},
  year =	{2008},
  volume =	{9},
  editor =	{Matteo Fischetti and Peter Widmayer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1580},
  URN =		{urn:nbn:de:0030-drops-15802},
  doi =		{10.4230/OASIcs.ATMOS.2008.1580},
  annote =	{Keywords: }
}

Collection: 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08)
Issue Date: 2008
Date of publication: 24.09.2008

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI