An approach to the timetabling problem in deregulated railway markets based on metaheuristic algorithms

The train timetabling problem in liberalized railway markets represents a challenge to the coordination between infrastructure managers and railway undertakings. Efficient scheduling is critical to maximizing infrastructure capacity and utilization while adhering as closely as possible to the requests of railway undertakings. These objectives ultimately contribute to maximizing the infrastructure manager's revenues. This paper sets out a modular simulation framework to reproduce the dynamics of deregulated railway systems. Ten metaheuristic algorithms using the MEALPY Python library are then evaluated in order to optimize train schedules in the liberalized Spanish railway market. In addition, an analysis of the scalability of the problem has been carried out by comparing the results with those obtained with a classical mathematical model such as SCIP in Pyomo. The results show that the Genetic Algorithm outperforms others in revenue optimization, convergence speed, and schedule adherence. Alternatives, such as Particle Swarm Optimization and Ant Colony Optimization Continuous, show slower convergence and higher variability. The results emphasize the trade-off between scheduling more trains and adhering to requested times, providing insights into solving complex scheduling problems in deregulated railway systems.