Resolving Infeasibilities in Railway Timetabling Instances

Abstract

One of the key assumptions of timetabling algorithms is that a solution exists that meets the pre-specified constraints, like driving times, transfer constraints and headway constraints. If this assumption is satisfied, in most cases a timetable can be found rapidly. Nowadays, railways are being used more intensively, which leads to a higher utilization of the network. Due to this increased utilisation, capacity conflicts occur, so that no feasible solution to the timetabling models can be found, without making subtle but non-trivial changes to the initial input. Resolving these conflicts is essential for railway companies with high utilization of infrastructure. In this paper, we consider infeasible timetabling instances together with a list of allowed modifications of the constraints. We iteratively identify local conflicts in these instances and resolve them by adapting some of the constraints, until there are no more conflicts. The adaptations of the constraints are changes in the right-hand sides that we try to make as small as possible but that resolve the infeasibility. We empirically show that our method can be improved by enriching the initial minimal conflicts found with more constraints. In order to keep the problems tractable, an iterative procedure is used to find solutions to subproblems corresponding to conflicts in the complete timetabling instance. In a case study on instances from the Dutch railway network, we show that these instances can be made feasible within a few minutes.

Solving large-scale train timetable adjustment problems under infrastructure maintenance possessions

“…In order to reduce the size of the very large constraint graphs representing the complete Dutch network, DONS applies several techniques. Peeters (2003) and Polinder (2015) describe the basic techniques of removing parallel arcs, i.e., arcs that connect the same pair of events, by intersecting their time windows. Additionally, as the running time arcs in DONS have a fixed time duration, they are combined with the subsequent dwell process, which allows to remove the arrival events from the constraint graph.…”

“…This paper extends the model developed in Van Aken et al (2017) by incorporating turnaround activities for short-turned trains, considering several procedures. Network aggregation techniques similar to the ones described in Peeters (2003) and Polinder (2015) are applied, but tailored to the TTAP. We extend the idea of removing headway constraints as described in Louwerse and Huisman (2014) to include timetable periodicity.…”

“…We adopt this approach by removing the departure-through events, and replace the events in the associated headway activities by the respective arrival-through events. This may result in parallel arcs, which are removed by intersecting the time windows as described in Peeters (2003) and Polinder (2015). The objective function (12) does not consider delays of through events, hence, its value does not change.…”

Resolving instability in railway timetabling problems

“…Resolving instability in railway timetabling problems Most of the models for solving timetabling problems (PESP) assume that it is possible to schedule all services from the line plan. Only recently, , Polinder (2015) and presented approaches for solving problems of local infeasibility in periodic timetabling problems. Polinder (2015) resolves conflicts reported in the planning model DONS Schrijver and Steenbeek (1994) by relaxing neighbouring processes.…”

“…Only recently, , Polinder (2015) and presented approaches for solving problems of local infeasibility in periodic timetabling problems. Polinder (2015) resolves conflicts reported in the planning model DONS Schrijver and Steenbeek (1994) by relaxing neighbouring processes. proposed a similar approach to support the planning model TAKT .…”