Festival timetable synchronization of metro trains and high-speed railway trains for late-night operations: an integrated bi-directional transfer optimization model

This paper focuses on synchronizing festival timetables between high-speed railway (HSR) and metro for late-night operations. A multi-objective model is proposed to optimize metro timetables of the last service period incorporating collaboration with HSR timetables. The model is designed to facilitate bi-directional transfers by maximizing spatial accessibility and temporal availability of metro service as well as minimizing transfer waiting times for HSR passengers. Our model can be efficiently solved using Gurobi, providing optimal solutions for large-scale metro networks within reasonable computational timeframes. A real-world case study is conducted to validate the effectiveness of our model. The results indicate that slight adjustments to metro timetables, without introducing additional trains, can yield significantly enhancements in late-night metro service for HSR passengers. Moreover, a smaller extension of service time across the entire metro network is proved to be more effective than a greater extension of service time on hub-connected metro lines.