A train trajectory optimization method based on the safety reinforcement learning with a relaxed dynamic reward

Abstract Train trajectory optimization (TTO) is an effective way to address energy consumption in rail transit. Reinforcement learning (RL), an excellent optimization method, has been used to solve TTO problems. Although traditional RL algorithms use penalty functions to restrict the random exploration behavior of agents, they cannot fully guarantee the safety of the process and results. This paper proposes a proximal policy optimization based safety reinforcement learning framework (S-PPO) for the train trajectory optimization, including a safe action rechoosing mechanism (SARM) and a relaxed dynamic reward mechanism (RDRM) combining a relaxed sparse reward and a dynamic dense reward. SARM guarantees that the new states generated by the agent consistently adhere to the environmental security constraints, thereby enhancing sampling efficiency and facilitating algorithm convergence. RDRM is composed of a relaxed sparse reward and a dynamic dense reward, offering a better balance between exploration and exploitation. The experimental results show that S-PPO can significantly improve the exploration ability of the algorithm, obtain better train operation trajectories than soft constraint algorithms, and the convergence process is smoother. Finally, it was demonstrated that S-PPO exhibits good adaptability across various speed limit tracks.