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A Lagrangian heuristic algorithm for a real-world train timetabling problem. (English) Zbl 1120.90324

Summary: 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.

##### MSC:
 90B35 Scheduling theory, deterministic 90C59 Approximation methods and heuristics