Joint Optimization of Time-Dependent Line Planning and Differential Pricing with Passenger Train Choice in High-Speed Railway Networks

Line planning problems and differential pricing problems are complementary processes in the railway system, but these two problems were generally considered separate processes in most of the existing literature. This paper studies a time-dependent line planning problem and differential pricing problem with passenger train choice in high-speed railway networks under elastic origin-destination-period demand. After clearly and flexibly describing the organization cost of operators, the price cost, and the time cost of passengers in a physical infrastructure-based directed graph, a non-linear joint optimization model is designed with a diversity of optimization goals of maximizing the total revenue of railway operators minus the total travel cost of passengers. An algorithm based on a simulated annealing framework is designed to solve the joint optimization model, and six neighborhood search strategies are designed by combining the features of the studied problem and designed model closely to improve the efficiency of the solution search. The results based on both a toy railway network and a real-world railway network show that the optimized time-dependent line plan and differential price plan are beneficial to increasing the total revenue of railway operators and improving the travel service of railway passengers.