License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/OASIcs.ATMOS.2017.11
URN: urn:nbn:de:0030-drops-79021
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7902/
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Fischer, Frank ; Schlechte, Thomas

Strong Relaxations for the Train Timetabling Problem Using Connected Configurations

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OASIcs-ATMOS-2017-11.pdf (3 MB)

Abstract

The task of the train timetabling problem or track allocation problem is to find conflict free schedules for a set of trains with predefined routes in a railway network. Especially for non-periodic instances models based on time expanded networks are often used. Unfortunately, the linear programming relaxation of these models is often extremely weak because these models do not describe combinatorial relations like overtaking possibilities very well. In this paper we extend the model by so called connected configuration subproblems. These subproblems perfectly describe feasible schedules of a small subset of trains (2-3) on consecutive track segments. In a Lagrangian relaxation approach we solve several of these subproblems together in order to produce solutions which consist of combinatorially compatible schedules along the track segments. The computational results on a mostly single track corridor taken from the INFORMS RAS Problem Solving Competition 2012 data indicate that our new solution approach is rather strong. Indeed, for this instance the solution of the Lagrangian relaxation is already integral.

BibTeX - Entry

@InProceedings{fischer_et_al:OASIcs:2017:7902,
  author =	{Frank Fischer and Thomas Schlechte},
  title =	{{Strong Relaxations for the Train Timetabling Problem Using Connected Configurations}},
  booktitle =	{17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)},
  pages =	{11:1--11:16},
  series =	{OpenAccess Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-042-2},
  ISSN =	{2190-6807},
  year =	{2017},
  volume =	{59},
  editor =	{Gianlorenzo D'Angelo and Twan Dollevoet},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7902},
  URN =		{urn:nbn:de:0030-drops-79021},
  doi =		{10.4230/OASIcs.ATMOS.2017.11},
  annote =	{Keywords: combinatorial optimization, train timetabling, Lagrangian relaxation, connected configurations}
}

Keywords: combinatorial optimization, train timetabling, Lagrangian relaxation, connected configurations
Collection: 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)
Issue Date: 2017
Date of publication: 04.09.2017

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