Energy-Efficient Scheduling of the First Train With Deadheading in Urban Railway Networks

Due to the inherent complexity of the urban rail transit systems, transfers between lines are generally unavoidable for passengers. In order to solve the problem of long transfer waiting time during the first train period, the operation of first train with deadheading is proposed for the first train scheduling. The first train scheduling problem is to search for an optimal schedule by adjusting the total number of skipped stations and the headway of the first deadheading train. First, the scheduling of the energy-efficient first train is formulated as a mixed integer nonlinear programming model, which aims to minimize the total waiting time and the total energy consumption. Second, an efficient variable neighborhood simulated annealing algorithm is designed to solve the model. Numerical experiments on a sample network and the Nanjing Railway network are applied to verify the performance of the proposed method. The results show that the operation of deadheading first trains is an efficient strategy to reduce the total waiting time and the total energy consumption. Moreover, the number of transfer directions with long waiting times decreases significantly.