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 \nplanning perspective. We aim at constructing a timetable that is feasible with respect \nto infrastructure constraints and minimizes average perceived passenger travel time. In \naddition to in-train and transfer times, our notion of perceived passenger time includes \nthe adaption time (waiting time at the origin station). Adaption time minimization allows \nus to avoid strict frequency regularity constraints and, at the same time, to ensure regular \nconnections between passengers\xe2\x80\x99 origins and destinations. The combination of adaption \ntime minimization and infrastructure constraints satisfaction makes the problem very \nchallenging. \n \nThe described periodic timetabling problem can be modelled as an extension of a Peri- \nodic Event Scheduling Problem (PESP) formulation, but requires huge computing times if \nit is directly solved by a general-purpose solver for instances of realistic size. In this paper, \nwe propose a heuristic approach consisting of two phases that are executed iteratively. \nFirst, we solve a mixed-integer linear program to determine an ideal timetable that mini- \nmizes the average perceived passenger travel time but neglects infrastructure constraints. \nThen, a Lagrangian-based heuristic makes the timetable feasible with respect to infras- \ntructure constraints by modifying train departure and arrival times as little as possible. \nThe obtained feasible timetable is then evaluated to compute the resulting average per- \nceived 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 \nstill respecting infrastructure constraints. We illustrate the proposed iterative heuristic \napproach on real-life instances of Netherlands Railways and compare it to a benchmark \napproach, showing that it finds a feasible timetable very close to the ideal one