Coordinated Optimization of Feeder Flex-Route Transit Scheduling for Urban Rail Systems

Given the distinct operational features of flex-route transit (FRT) compared to conventional fixed-route systems, this study integrates FRT with urban rail transit and proposes a collaborative optimization approach for feeder flex-route operations and scheduling. The model incorporates path planning, timetable design, and vehicle scheduling to minimize travel costs, enhance operational efficiency, and improve service quality. A mixed-integer nonlinear programming method is applied to optimize scheduling while aligning with rail timetables and passenger transfer behavior. Simulation experiments based on realistic urban transit scenarios are conducted to validate the model, optimizing key operational parameters such as departure intervals, vehicle deployment, and stop selection. The results demonstrate that the proposed approach effectively adjusts schedules and vehicle assignments to accommodate fluctuating passenger demand. This study offers both a theoretical foundation and a practical framework for integrated scheduling of feeder flex-route services, with potential applications for improving coordination and performance in multimodal public transit systems.