<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>8275</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2021-07-03</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Forward Cycle Bases and Periodic Timetabling</title>
    <abstract language="eng">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 \texttt{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.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-82756</identifier>
    <identifier type="doi">10.4230/OASIcs.ATMOS.2021.2</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="AcceptedDate">30.07.2021</enrichment>
    <enrichment key="SourceTitle">appeared in 21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021)</enrichment>
    <author>Niels Lindner</author>
    <submitter>Niels Lindner</submitter>
    <author>Christian Liebchen</author>
    <author>Berenike Masing</author>
    <series>
      <title>ZIB-Report</title>
      <number>21-18</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Periodic Timetabling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Cycle Bases</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mixed Integer Programming</value>
    </subject>
    <collection role="ccs" number="G.">Mathematics of Computing</collection>
    <collection role="ccs" number="J.">Computer Applications</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="lindner">Lindner, Niels</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="persons" number="masing">Masing, Berenike</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
    <collection role="projects" number="MathPlus-AA3-8">MathPlus-AA3-8</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/8275/ZR-21-18.pdf</file>
  </doc>
</export-example>
