Train Timetabling With Stop Planning and Passenger Distributing Integration Orientated by Railway Capacity and Passenger Service

In the process of railway operation planning, it is essential to take into account both railway capacity and origin to destination (OD) passenger demand. Stop plan plays a vital role in generating a train timetable with maximum railway capacity and ensuring high-quality service to transport passengers. Therefore, we are addressing the challenge of optimizing both the stop plan and timetable for a group of trains on a railway line, focusing on railway capacity estimation and passenger demand satisfaction. To provide realistic and precise passenger distribution, the preferences of different categories of passengers are given due regard. A classic time-space network describes the integrated problem, based on which a mathematical model is formulated to minimize train occupancy time on the high-speed railway line and maximize passenger kilometers at the same time. A decomposition approach based on Lagrangian relaxation (LR) is suggested to address the problem, which decomposes the integrated scheduling problem into two sub-problems: a train timetabling sub-problem, and a stop planning and passenger distributing sub-problem by dualizing constraints linking the two. A heuristic approach based on genetic algorithms is designed to obtain feasible solutions. The proposed model and approach are shown to generate good solutions efficiently. A series of real-world instances are conducted on the Beijing-Shanghai high-speed railway line in China, and the experimental outcomes show the benefits of optimizing the stop plan. Other related analyses are discussed by comparing results with different total number of stops, heterogeneous and homogeneous cases.