Weekly train timetabling integrating stop planning for high-speed rail lines

In high-speed rail (HSR) train planning and scheduling, traditional approaches often focus on passenger demand over short periods, such as one or two hours or a single day, while overlooking demand fluctuations over an entire week. This study proposes an integrated model for weekly train timetabling and stop planning, aiming to optimize both train stops and schedules across different times of day and days of the week. To improve computational efficiency for large-scale, real-world applications, a Lagrangian relaxation algorithm is developed. Case studies based on Chinese HSR lines demonstrate that the proposed model and algorithm outperform both the commercial solver CPLEX and the conventional sequential approach of line planning followed by timetabling. The weekly timetable generated by the proposed algorithm significantly reduces train and passenger traveling costs by improving traveling speeds and the proportion of passengers traveling within their preferred periods compared to current practical timetables, making it widely applicable to a wide range of HSR lines.