Integrated optimization of train stopping plans and timetabling for urban rail transit based on dynamic demand

This study addresses the higher demand of passengers during peak hours in urban rail transit by proposing an integrated optimization of train stopping plans and timetabling to reduce overcrowding and the total waiting time. A nonlinear integer programming model is developed, incorporating passenger demand, operation costs, train capacity, and station congestion levels. The decision variables include the stopping plan and departure headways. The objective is to minimize total operation time, average operation time, and waiting time, while reducing congestion variance across stations. A case study using the NSGA-II algorithm shows that the optimized solution significantly alleviates station congestion compared to the all-stop plan. Additionally, it reduces average operation time, total operation time, and waiting time by 3.42%, 9.40%, and 10.44%, respectively, demonstrating the model's feasibility and effectiveness.