Optimizing Train Timetable Based on Departure Time Preference of Passengers for High-Speed Rails

Passengers would like to choose the most suitable train based on their travel preferences, expenses, and train timetable in the high-speed railway corridor. Meanwhile, the railway department will constantly adjust the train timetable according to the distribution of passenger flows during a day to achieve the optimal operation cost and energy consumption saving plan. The question is how to meet the differential travel needs of passengers and achieve sustainable goals of service providers. Therefore, it is necessary to design a demand-oriented and environment-friendly high-speed railway timetable. This paper formulates the optimization of train timetable for a given high-speed railway corridor, which is based on the interests of both passengers and transportation department. In particular, a traveling time-space network with virtual departure arc is constructed to analyze generalized travel costs of passengers of each origin-destination (OD), and bilevel programming model is used to optimize the problem. The upper integer programming model regards the minimization of the operating cost, which is simplified to the minimum traveling time of total trains, as the goal. The lower level is a user equilibrium model which arranges each OD passenger flow to different trains. A general advanced metaheuristic algorithm embedded with the Frank–Wolfe method is designed to implement the bilevel programming model. Finally, a real-world numerical experiment is conducted to verify the effectiveness of both the model and the algorithm.