An iterative heuristic for passenger-centric train timetabling with integrated adaption times

Gert Jaap Polinder, Valentina Cacchiani, Marie Schmidt*, Dennis Huisman

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)
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In this paper we present a method to construct a periodic timetable from a tactical planning perspective. We aim at constructing a timetable that is feasible with respect to infrastructure constraints and minimizes total perceived passenger travel time. In addition to in-train and transfer times, our notion of perceived passenger time includes the adaption time (waiting time at the origin station). Adaption time minimization allows us to avoid strict frequency regularity constraints and, at the same time, to ensure regular connections between passengers’ origins and destinations. The combination of adaption time minimization and infrastructure constraints satisfaction makes the problem very challenging. The described periodic timetabling problem can be modelled as an extension of a Periodic Event Scheduling Problem (PESP) formulation, but requires huge computing times if it is directly solved by a general-purpose solver for instances of realistic size. In this paper, we propose a heuristic approach consisting of two phases that are executed iteratively. First, we solve a mixed-integer linear program to determine an ideal timetable that minimizes the total perceived passenger travel time but neglects infrastructure constraints. Then, a Lagrangian-based heuristic makes the timetable feasible with respect to infrastructure constraints by modifying train departure and arrival times as little as possible. The obtained feasible timetable is then evaluated to compute the resulting total perceived passenger travel time, and a feedback is sent to the Lagrangian-based heuristic so as to possibly improve the obtained timetable from the passenger perspective, while still respecting infrastructure constraints. We illustrate the proposed iterative heuristic approach on real-life instances of Netherlands Railways and compare it to a benchmark approach, showing that it finds a feasible timetable very close to the ideal one.

Original languageEnglish
Article number105740
JournalComputers and Operations Research
Early online date12 Feb 2022
Publication statusPublished - Jun 2022

Bibliographical note

Funding Information:
We thank Erasmus Trustfonds for supporting this work. Furthermore, we thank G?bor Mar?ti for providing several figures used in this paper. Valentina Cacchiani acknowledges the support by the Air Force Office of Scientific Research under award number FA8655-20-1-7019.

Publisher Copyright: © 2022 The Authors


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