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Forward Cycle Bases and Periodic Timetabling

Authors Niels Lindner , Christian Liebchen , Berenike Masing

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Author Details

Niels Lindner
  • Zuse Institute Berlin, Germany
Christian Liebchen
  • Technical University of Applied Sciences Wildau, Germany
Berenike Masing
  • Zuse Institute Berlin, Germany

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Niels Lindner, Christian Liebchen, and Berenike Masing. Forward Cycle Bases and Periodic Timetabling. In 21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021). Open Access Series in Informatics (OASIcs), Volume 96, pp. 2:1-2:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


Periodic timetable optimization problems in public transport can be modeled as mixed-integer linear programs by means of the Periodic Event Scheduling Problem (PESP). In order to keep the branch-and-bound tree small, minimum integral cycle bases have been proven successful. We examine forward cycle bases, where no cycle is allowed to contain a backward arc. After reviewing the theory of these bases, we describe the construction of an integral forward cycle basis on a line-based event-activity network. Adding turnarounds to the instance R1L1 of the benchmark library PESPlib, we computationally evaluate three types of forward cycle bases in the Pareto sense, and come up with significant improvements concerning dual bounds.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Mathematics of computing → Integer programming
  • Applied computing → Transportation
  • Periodic Timetabling
  • Cycle Bases
  • Mixed Integer Programming


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