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

The train timetabling problem in liberalized railway markets represents a challenge to the coordination between infrastructure managers and railway undertakings. Efficient scheduling is critical in 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. 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.

Towards Equitable Rail Service Allocation Through Fairness-Oriented Timetabling in Liberalized Markets

Over the last few decades, European rail transport has undergone major changes as part of the process of liberalization set out in European regulations. In this context of liberalization, railway undertakings compete with each other for the limited infrastructure capacity available to offer their rail services. The infrastructure manager is responsible for the equitable allocation of infrastructure between all companies in the market, which is essential to ensure the efficiency and sustainability of this competitive ecosystem. In this paper, a methodology based on Jain, Gini and Atkinson equity metrics is used to solve the rail service allocation problem in a liberalized railway market, analyzing the solutions obtained. The results show that the proposed methodology and the equity metrics used allow for equitable planning in different competitiveness scenarios. These results contrast with solutions where the objective of the infrastructure manager is to maximize its own profit, without regard for the equitable allocation of infrastructure. Therefore, the computational tests support the methodology and metrics used as a planning and decision support tool in a liberalized railway market.

Dynamic Pricing in High-Speed Railways Using Multi-Agent Reinforcement Learning

This paper addresses a critical challenge in the high-speed passenger railway industry: designing effective dynamic pricing strategies in the context of competing and cooperating operators. To address this, a multi-agent reinforcement learning (MARL) framework based on a non-zero-sum Markov game is proposed, incorporating random utility models to capture passenger decision making. Unlike prior studies in areas such as energy, airlines, and mobile networks, dynamic pricing for railway systems using deep reinforcement learning has received limited attention. A key contribution of this paper is a parametrisable and versatile reinforcement learning simulator designed to model a variety of railway network configurations and demand patterns while enabling realistic, microscopic modelling of user behaviour, called RailPricing-RL. This environment supports the proposed MARL framework, which models heterogeneous agents competing to maximise individual profits while fostering cooperative behaviour to synchronise connecting services. Experimental results validate the framework, demonstrating how user preferences affect MARL performance and how pricing policies influence passenger choices, utility, and overall system dynamics. This study provides a foundation for advancing dynamic pricing strategies in railway systems, aligning profitability with system-wide efficiency, and supporting future research on optimising pricing policies.