An Iterative Heuristic for Passenger-Centric Train Timetabling with Integrated Adaption Times

Abstract

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 average 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 mini-
mizes the average perceived passenger travel time but neglects infrastructure constraints.
Then, a Lagrangian-based heuristic makes the timetable feasible with respect to infra-
structure constraints by modifying train departure and arrival times as little as possible.
The obtained feasible timetable is then evaluated to compute the resulting average per-
ceived 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.

Keywords: public transportation planning, heuristic, integration of timetabling and passenger routing, adaption time