The results of the series of experiments.

In recent years, with increasing passenger travel demand, high-speed railways have developed rapidly. The stop planning and timetabling problems are the core contents of high-speed railway transport planning and have important practical significance for improving efficiency of passenger travel and railway operation Dong et al. (2020). This study proposes a collaborative optimization approach that can be divided into two phases. In the first phase, a mixed-integer nonlinear programming model is constructed to obtain a stop plan by minimizing the total passenger travel time. The constraints of passenger origin-destination (OD) demand, train capacity, and stop frequency are considered in the first phase. In the second phase, the train timetable is optimized after the stop plan is obtained. A multiobjective mixed-integer linear optimization model is formulated by minimizing the total train travel time and the deviation between the expected and actual departure times from the origin station for all trains. Multiple types of trains and more refined headways are considered in the timetabling model. Finally, the approach is applied to China’s high-speed railway, and the GUROBI optimizer is used to solve the models in the above two stages. By analyzing the results, the total passenger travel time and train travel time decreased by 2.81% and 3.34% respectively. The proposed method generates a more efficient solution for the railway system.

近年来，随着旅客出行需求持续增长，高速铁路实现了迅猛发展。停站规划（stop planning）与列车时刻表编制（timetabling）问题是高速铁路运输规划的核心内容，对于提升旅客出行效率与铁路运营效能具有重要的现实意义（Dong等，2020）。本研究提出了一种可划分为两个阶段的协同优化方法。第一阶段构建混合整数非线性规划模型（mixed-integer nonlinear programming model），以最小化旅客总出行时间为目标生成停站方案，该阶段考量了旅客起讫点（Origin-Destination, OD）需求、列车载客容量及停站频次等约束条件。第二阶段则在确定停站方案后对列车时刻表进行优化，构建了以最小化总列车运行时间，以及所有列车从始发站的实际发车时刻与预期发车时刻偏差为目标的多目标混合整数线性规划模型（multiobjective mixed-integer linear optimization model）。该时刻表编制模型兼顾了多类型列车与更精细化的列车间隔（headways）。最后，本方法被应用于中国高速铁路场景，并采用GUROBI优化器求解上述两个阶段的模型。通过对求解结果进行分析，旅客总出行时间与列车总运行时间分别降低了2.81%与3.34%。所提出的方法可为铁路系统生成更为高效的优化方案。