Approaches to a real-world Train Timetabling Problem in a railway node

We consider the Train Timetabling Problem (TTP) in a railway node (i.e. a set of stations in an urban area interconnected by tracks), which calls for determining the best schedule for a given set of trains during a given time horizon, while satisfying several track operational constraints. In particular, we consider the context of a highly congested railway node in which different Train Operators wish to run trains according to timetables that they propose, called ideal timetables. The ideal timetables altogether may be (and usually are) conflicting, i.e. they do not respect one or more of the track operational constraints. The goal is to determine conflict-free timetables that differ as little as possible from the ideal ones.