Integrated Optimization of Train Timetabling and Rolling Stock Circulation

This technical report presents an integrated optimization model for train timetabling and rolling stock circulation in urban rail transit systems experiencing tidal passenger flow. The model aims to minimize passenger waiting time and operational costs by considering various real-world factors, including safe-headway constraints and dwell-time calculations. An improved algorithm based on NSGA-II is introduced to efficiently solve the nonlinear multi-objective optimization problem. The algorithm employs a two-layer chromosome encoding scheme, where the upper layer represents train departure times and the lower layer encodes rolling stock connections. A simulation study conducted on Beijing Metro Line 6 demonstrates that the optimized flexible scheme significantly reduces operational costs by 18.2% while only increasing passenger waiting time by approximately 9%. The findings confirm the model's effectiveness in enhancing service quality and resource utilization under tidal passenger flow conditions, thereby addressing the operational challenges faced during peak periods.