A Two-Stage Model for Optimizing Intercity Multimodal Timetables and Passenger Flow Assignment Under Multiple Uncertainty Within Urban Agglomerations

In order to maximize passenger travel satisfaction and enhance the sustainability of the intercity multimodal transportation system, this paper proposes a two-stage model for intercity multimodal timetable coordination optimization under uncertainty. In the first stage, a robust spatio-temporal graph is built to allocate intermodal passenger flows in order to determine passengers’ route selection results to minimize the total travel cost. At the same time, explicit capacity constraints and transfer behaviors are considered in order to be more realistic. In addition, passengers can take multiple transportation modes (High-speed Rail, Ordinary Rail, EMU, and Coach) in a single trip. The outputs of the first stage are subsequently integrated into the second-stage interval multi-objective timetable optimization model to determine departure times and stopping patterns under uncertain dwell and travel times. It is able to achieve the maximum reduction of passenger travelling time and waiting time within the minimum timetable adjustment, which further improves the integration level of transportation services. To ensure the diversity and convergence of model solving on the basis of retaining uncertain information, we propose an integrated algorithm PSO-IMOEA-MC involving Particle Swarm Optimization algorithm (PSO) and Interval Many-objective Evolutionary Algorithm combined with Monte Carlo (IMOEA-MC). Finally, the effectiveness of the proposed two-stage model and algorithm is validated using three intercity networks: Beijing–Zhangjiakou, Chengdu–Chongqing, and Guangzhou–Qingyuan. The results demonstrate the performance of the method in finding high-level solutions that retain more uncertainty. The findings of this study provide technical support for timetable adjustments under diverse operational scenarios.