XRL-TO: An explainable reinforcement learning-based approach for bus timetable dynamic optimization

Bus timetable optimization is crucial for a bus-centric public transportation system. Existing bus timetable optimization methods typically produce fixed timetables based on historical passenger flows, limiting their ability to meet real-time passenger demand fluctuations. Although dynamic optimization methods based on deep reinforcement learning (DRL) have been explored recently, they often fail to accurately capture real-time passenger demand and prioritize minimizing costs at the expense of service quality. Additionally, their black-box nature limits transparency, potentially introducing redundant state features that hinder the model's ability to capture passenger demands and reduce stability. In this paper, we propose a new eXplainable Reinforcement Learning-based approach for bus Timetable dynamic Optimization (XRL-TO). Specifically, a novel Markov Decision Process (MDP) model is developed to effectively capture passenger demand and balance service quality and operating costs. An Attention-based Deep Q-Network (ADQN) is employed as the agent to process the new state representation. To enhance its transparency, a LIME-based Reinforcement Learning eXplainability method (LRLX) is proposed to analyze the decision-making process of ADQN and systematically refine the state representation, improving both the transparency and stability of XRL-TO. Experimental results on real-world data demonstrate that XRL-TO significantly reduces both operating costs and passengers’ average waiting time compared to state-of-the-art algorithms. Furthermore, LRLX substantially enhances the transparency and stability of our approach, making it highly valuable for bus timetable dynamic optimization in practice.