Train timetable and stopping plan generation based on cross-line passenger flow in high-speed railway network

Considering the real scenario in China, in order to decrease passenger transfer, cross-line trains are scheduled extensively for the large number of cross-line passenger flow. Therefore, in this paper, we propose a more practical approach aiming to schedule more trains within a limit time horizon by both main-line train and cross-line train scheduling optimization (train timetable and stopping plan optimization). We find that the train scheduling and passenger assignment problems are multi-commodity flow problems. The trains (as the users) share the railway capacities (as the resource) in a high-speed railway network, and the passengers (as the users) share the train carrying capacities (as the resource). Thus, based on this, we formulate two space-time networks-train and passenger space-time networks-to present the train operation and the passenger flow, respectively. In addition, we regard train disturbances in different directions as different train headways at cross-line stations to optimize train scheduling practically. Sequentially, a mixed-integer linear programing model with headway and coupling constraints is formulated. To solve the model efficiently for a large-scale application, we decompose the problem into two space-time path-searching sub-problems based on the passenger and train space-time networks by the Lagrangian relaxation and alternating direction method of multipliers decomposition methods. Finally, we adopt the Taiyuan-Dezhou and Zhengzhou-Beijing high-speed railway networks in a practical experiment, and an experiment without cross-line operation is designed to test the effect of cross-line operation. The results show the proposed approach can obtain a no-conflict timetable and all the passenger demand can be satisfied, meanwhile, the capacity can improve 20.7% when the cross-line operation is not considered.