Optimal bus bridging service for urban rail transit disruptions with stochastic passenger demand

Disruptions in urban rail transit (URT) systems can significantly impact operational efficiency, while well-designed bus bridging service (BBS) can effectively mitigate such effects. To address the surge in travel demand caused by disruptions, this study comprehensively considers alternative transportation modes that affected passengers may adopt (including taxis, shared bicycles, bridging buses, and walking), aiming to minimize both the operational costs of bridging buses and the total travel time of passengers. A travel choice model based on the random regret minimization (RRM) theory is developed to characterize passengers' decision-making behavior following station disruptions. Demand uncertainty is represented using trapezoidal fuzzy variables, and a distributionally robust credibility optimization model is established. An innovative reinforcement learning-based parallel genetic algorithm (RPGA) is proposed for solving the model. A case study of a bidirectional disruption during the 08:00-10:00 on the section of Xi'an Metro Line 2 demonstrates that: (1) The proposed model exhibits stronger robustness under demand uncertainty, achieving a reduction of 3 dispatched vehicles and a cost saving of 9,439 RMB by moderately increasing passenger costs by 850 RMB and extending bridging time; (2) The RPGA algorithm outperforms Non-dominated Sorting Genetic Algorithm II (NSGA-II), Reinforcement Learning-based NSGA-II (RLNSGA-II), and Multi-objective Particle Swarm Optimization Algorithm (MOPSO) in hypervolume (HV), generational distance (GD), and non-dominated ratio (NDR); (3) Increasing the rated passenger capacity within a certain range can reduce average passenger delays but correspondingly raises transportation costs. This method effectively enhances the system's ability to cope with demand fluctuations and provides decision-making support for emergency scheduling in urban rail transit.