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Solving the Periodic Timetabling Problem using a Genetic Algorithm

In railway operations, a timetable is established to determine the departure and arrival times for the trains or other rolling stock at the different stations or relevant points inside the rail network or a subset of this network. The elaboration of this timetable is done to respond to the commercial requirements for both passenger and freight traffic, but also it must respect a set of security and capacity constraints associated with the railway network, rolling stock and legislation. Combining these requirements and constraints, as well as the important number of trains and schedules to plan, makes the preparation of a feasible timetable a complex and time-consuming process, that normally takes several months to be completed. This article addresses the problem of generating periodic timetables, which means that the involved trains operate in a recurrent pattern. For instance, the trains belonging to the same train line, depart from some station every 15 minutes or one hour. To tackle the problem, we present a constraint-based model suitable for this kind of problem. Then, we propose a genetic algorithm, allowing a rapid generation of feasible periodic timetables. Finally, two case studies are presented, the first, describing a sub-set of the Netherlands rail network, and the second a large portion of the Nord-pas-de-Calais regional rail network, both of them are then solved using our algorithm and the results are presented and discussed.