Optimization of train timetables in high-speed railway corridors considering passenger departure time and seat-class preferences

There are a number of trains running in high-speed railway (HSR) corridors throughout the day, which results in diverse passenger travel choices. Passengers can select their preferred train according to their favorite departure time and seat class based on a fixed train timetable, that is, the selection differences from departure time to seat classes are dramatic. The train timetable determines the distribution of passenger flow on trains, and the requirement distribution in turn affects the train timetable. To address this game relationship, this paper develops a method to optimize uneven running train timetables with a given total number of trains considering passenger departure time and seat-class preferences. We analyze the impact of departure time and seat class on passenger choice behaviors and build a time-space-seat 3-dimensional network to account for these choices. Then, the impedance function of each type of arc in the network is designed. In addition, a bi-level programming model is constructed to optimize the train timetable in the HSR corridor; the upper-level model calculates train departure time, arrival time and dwelling time at each station and determines the assignment of car lists with different seat classes for each train. The lower-level model is used to distribute the passenger flow to each train. Combined with the user equilibrium principle, a complex genetic algorithm embedded with the Frank–Wolfe method is designed to reasonably distribute passenger flows to each train. Finally, we take the Lanzhou-Xi'an HSR as an example to test both the model and the algorithm. The results show that the optimal train timetable can meet the requirements of both seat class and departure time with appropriate solution time limitations.