First train timetabling and passenger transfer routing problems in urban rail transit networks

Abstract

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.