Huang Zhipeng, Yang Limin, Li Jinlian, Zhang Tao, Qu Zixian, Miao Yusen
School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou, China.
Key Laboratory of Railway Industry on Plateau Railway Transportation Intelligent Management and Control, Lanzhou Jiaotong University, Lanzhou, China.
PLoS One. 2025 Jun 18;20(6):e0326170. doi: 10.1371/journal.pone.0326170. eCollection 2025.
High-speed railway timetables are typically based on origin-destination (OD) passenger demand, establishing departure times and intervals for trains. Utilizing this data, operators systematically develop daily train timetables that are consistent across a defined operational cycle. However, this approach often overlooks individual passenger preferences for departure times, fares, and seat classes, leading to low occupancy rates for some trains while others remain difficult to book. In this article, with the number of trains predetermined and considering the diverse demands of passengers, we addresses these challenges by analyzing passenger preferences and optimizing train stopping patterns and adjacent train departure intervals. We propose a time-space-state three-dimensional network (TSSN) that integrates preferences for travel time, fares, and seat classes. Impedance functions for various network arcs are developed, incorporating these three key attributes of travel demand and transforming the passenger travel choice issue into a path selection problem within the TSSN. A bi-level programming model is formulated: the upper level optimizes train operations and fare structures, while the lower level employs user equilibrium (UE) theory to distribute OD passenger demands across trains. Using the Lanzhou-Xi'an high-speed railway corridor as a case study, we apply a genetic algorithm combined with a nested Frank-Wolfe method to solve the model. The resulting timetable balances the interests of high-speed rail operators and passengers, incorporating non-uniform departure intervals to better meet diverse travel needs. Ultimately, this approach enhances the scientific rigor and practicality of high-speed railway scheduling while accommodating passenger preferences effectively.
高速铁路时刻表通常基于起讫点（OD）客运需求来确定列车的出发时间和间隔。利用这些数据，运营方系统地制定出在规定运营周期内保持一致的每日列车时刻表。然而，这种方法往往忽视了乘客对出发时间、票价和座位等级的个人偏好，导致一些列车的上座率较低，而另一些列车仍然一票难求。在本文中，在列车数量预先确定的情况下，并考虑到乘客的多样化需求，我们通过分析乘客偏好并优化列车停站模式和相邻列车出发间隔来应对这些挑战。我们提出了一种时空状态三维网络（TSSN），该网络整合了对旅行时间、票价和座位等级的偏好。针对各种网络弧段开发了阻抗函数，纳入了出行需求的这三个关键属性，并将乘客出行选择问题转化为TSSN内的路径选择问题。构建了一个双层规划模型：上层优化列车运营和票价结构，下层采用用户均衡（UE）理论在列车之间分配OD客运需求。以兰新高铁走廊为例，我们应用遗传算法结合嵌套弗兰克 - 沃尔夫方法来求解该模型。所得的时刻表平衡了高铁运营方和乘客的利益，采用不均匀的出发间隔以更好地满足多样化的出行需求。最终，这种方法提高了高速铁路调度的科学性和实用性，同时有效地兼顾了乘客偏好。
