Railway Timetabling Using Lagrangian Relaxation

Publisher's full text
Ulf Brännlund
Per Olov Lindberg
Andreas Nou

We present a novel optimization approach for the timetabling problem of a railway company, i.e., scheduling of a set of trains to obtain a profit maximizing timetable, while not violating track capacity constraints. The scheduling decisions are based on estimates of the value of running different types of service at specified times. We model the problem as a very large integer programming problem. The model is flexible in that if allows for general cost functions. We have used a Lagrangian relaxation solution approach, in which the track capacity constraints are relaxed and assigned prices, so that the problem separates into one dynamic program for each physical train. The number of dual variables is very large. However, it turns out that only a small fraction of these are nonzero, wh ich one may take advantage of in the dual updating schemes. The approach has been, tested on a realistic example suggested by the Swedish National Railway Administration. This example contains 18 passenger trains and 8 freight trains to be scheduled during a day on a stretch of single track, consisting of 17 stations. The computation times are rather modest and the obtained timetables are within a few percent of optimality.

LATEST NEWS


2017-11-30

Millions for research into maritime transport and the environment

Maritime transport is a major source of emissions of harmful air pollutants and carbon dioxide. In a new project, a research team from the Swedish National Road and Transport Research Institute (VTI) and the University of Gothenburg has received SEK 6.4...


2017-11-30

New research programme for more efficient travel

The Swedish National Road and Transport Research Institute (VTI) is playing an important role in a major new research programme to find radical solutions leading to fewer trips and more efficient travel, along with tools to enable better use of roads and...


2017-11-30

Simulator used to practice emergency responses safely

Emergency responses of the police, ambulance, and rescue services are associated with a high risk of accidents, but practicing them in real traffic is neither safe nor permissible. A simulator-based method developed by the Swedish National Road and Transport...


2017-10-26

Simulation of cut-in by manually driven vehicles in platooning scenarios

A study in a VTI-driving simulator has showed that a platoon will be able to handle a cut in from a manually driven car. The results of this study have recently been presented at two conferences in Japan.


2017-10-16

ERPUG Forum

The five-year anniversary of European Road Profile Users' Group (ERPUG) Forum will take place at Ramboll head quarter, Copenhagen, Denmark October 19-20, 2017.


2017-09-29

Self-driving buses in Sweden next year?

A self-driving, fossil-free bus. This idea might become reality through a forthcoming collaborative project involving the Swedish National Road and Transport Research Institute (VTI), Linköping University and several other participants. The project group aim...