A Lagrangian heuristic algorithm for a real-world train timetabling problem

Authors:
Alberto Caprara;Michele Monaci;Paolo Toth;Pier Luigi Guida
Affiliations:
DEIS, University of Bologna, Viale Risorgimento 2, I-40136 Bologna, Italy;DEI, University of Padova Via Gradenigo 6/A, I-35131 Padova, Italy;DEIS, University of Bologna, Viale Risorgimento 2, I-40136 Bologna, Italy;Rete Ferroviaria Italiana SpA, Piazza della Croce Rossa 1, I-00195 Roma, Italy
Venue:
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
Year:
2006

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Abstract

The train timetabling problem (TTP) aims at determining an optimal timetable for a set of trains which does not violate track capacities and satisfies some operational constraints. In this paper, we describe the design of a train timetabling system that takes into account several additional constraints that arise in real-world applications. In particular, we address the following issues:*Manual block signaling for managing a train on a track segment between two consecutive stations. *Station capacities, i.e., maximum number of trains that can be present in a station at the same time. *Prescribed timetable for a subset of the trains, which is imposed when some of the trains are already scheduled on the railway line and additional trains are to be inserted. *Maintenance operations that keep a track segment occupied for a given period. We show how to incorporate these additional constraints into a mathematical model for a basic version of the problem, and into the resulting Lagrangian heuristic. Computational results on real-world instances from Rete Ferroviaria Italiana (RFI), the Italian railway infrastructure management company, are presented.