Timetable synchronization of the last several trains at night in an urban rail transit network

To improve passenger accessibility and reduce the travel time cost at night, this paper aims to optimize the synchronization of the last several trains’ timetables on each line of an urban rail transit (URT) network. A space-time network is constructed to describe the train flow and passenger flow in the URT network, based on which an integer programming model is formulated. To effectively solve the proposed model, we decompose the problem into two levels and propose an iterative algorithm. In the upper level, an adaptive large neighbourhood search (ALNS) method is developed to generate new train timetables in the URT network, which are then evaluated by the passenger flow problem in the lower level, and the optimization-evaluation iteration continues until the termination conditions are met. The method and algorithm are applied to a large-scale instance using data for the Wuhan URT network at night, which involve 9 urban rail transit lines and over 119,000 passengers, and the results show that the number of inaccessible passengers is reduced by 27.53%, and the average travel time cost is reduced by 2.70%, compared with the original timetable. Then, the experimental results on a small-scale instance show that the proposed algorithm can find a near-optimal solution in a short time, which illustrates the effectiveness and efficiency of the ALNS method.