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

In this paper we present a method to construct a periodic timetable from a tacticalplanning perspective. We aim at constructing a timetable that is feasible with respectto infrastructure constraints and minimizes average perceived passenger travel time. Inaddition to in-train and transfer times, our notion of perceived passenger time includesthe adaption time (waiting time at the origin station). Adaption time minimization allowsus to avoid strict frequency regularity constraints and, at the same time, to ensure regularconnections between passengers’ origins and destinations. The combination of adaptiontime minimization and infrastructure constraints satisfaction makes the problem verychallenging.The described periodic timetabling problem can be modelled as an extension of a PeriodicEvent Scheduling Problem (PESP) formulation, but requires huge computing times ifit 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 heuristicso as to possibly improve the obtained timetable from the passenger perspective, whilestill respecting infrastructure constraints. We illustrate the proposed iterative heuristicapproach on real-life instances of Netherlands Railways and compare it to a benchmarkapproach, showing that it finds a feasible timetable very close to the ideal one