This paper incorporates the shortest passenger travel paths into the first train timetabling problem in urban rail transit networks. We first propose a path-based first train timetabling problem, which is formulated as a mixed-integer nonlinear programming model to reduce the travel time for passengers. To solve this model, we present a tailored branch-and-bound combined with the timetable-based Dijkstra algorithm. To further enhance the efficiency of the exact algorithm, we design a rolling time heuristic algorithm as a substitute for the branch-and-bound algorithm. Then, we proved that the rolling time heuristic combined with the timetable-based Dijkstra algorithm achieves 97.86% and 99.39% reductions in CPU time while sacrificing only 0.007% and 0.057% of optimality gap by two numerical experiments. Finally, the results based on two test networks with different structures demonstrate that the path-based first train timetabling model effectively improves passenger travel efficiency. Specifically, the travel times are reduced by 744 mins and 761 mins, while the transfer waiting times are reduced by 37.87% and 58.91% compared to the existing timetables. Moreover, the results also demonstrate that loop line networks will increase the difficulty of timetabling and lead to many passengers taking detours. To further enhance the efficiency of commuting for passengers who take the first train, URT operators may consider relaxing the limitations on the departure time of the depot stations.

中文翻译：

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城市轨道交通线网首班车时刻表及旅客换乘路径问题

本文将最短乘客出行路径纳入城市轨道交通网络中的第一个列车时刻表问题。我们首先提出基于路径的首班车时刻表问题，将其表述为混合整数非线性规划模型，以减少乘客的出行时间。为了解决这个模型，我们提出了一种与基于时间表的 Dijkstra 算法相结合的定制分支定界算法。为了进一步提高精确算法的效率，我们设计了滚动时间启发式算法来替代分支定界算法。然后，我们通过两个数值实验证明，滚动时间启发式与基于时间表的 Dijkstra 算法相结合，可以减少 97.86% 和 99.39% 的 CPU 时间，同时仅牺牲 0.007% 和 0.057% 的最优性差距。最后，基于两个不同结构的测试网络的结果表明，基于路径的首班车时刻表模型有效提高了旅客出行效率。其中，与现有时刻表相比，行车时间分别减少了744分钟和761分钟，换乘等待时间分别减少了37.87%和58.91%。此外，研究结果还表明，环线网络会增加时刻表的难度，导致许多乘客绕路。为进一步提高首班车乘客的通勤效率，城铁运营商可考虑放宽对车辆段车站发车时间的限制。