A Cooperative Scheduling Model for Timetable Optimization in Subway Systems

TLDR

In subway systems, regenerative braking can recover energy that is largely fed back to the overhead line, but the recovered energy is typically insufficient to power accelerating trains, so only train synchronization is considered. The study proposes a cooperative scheduling approach that optimizes timetables to allow braking trains to directly supply energy to accelerating trains by defining overlapping times for peak and off‑peak periods. An integer‑programming model maximizing overlapping time under headway and dwell constraints is formulated, and a binary‑encoded genetic algorithm is used to solve it, with six numerical examples based on Beijing Yizhuang subway data. The model increases overlapping time by 22.06 % during peak hours and 15.19 % during off‑peak hours.

Abstract

In subway systems, the energy put into accelerating trains can be reconverted into electric energy by using the motors as generators during the braking phase. In general, except for a small part that is used for onboard purposes, most of the recovery energy is transmitted backward along the conversion chain and fed back into the overhead contact line. To improve the utilization of recovery energy, this paper proposes a cooperative scheduling approach to optimize the timetable so that the recovery energy that is generated by the braking train can directly be used by the accelerating train. The recovery that is generated by the braking train is less than the required energy for the accelerating train; therefore, only the synchronization between successive trains is considered. First, we propose the cooperative scheduling rules and define the overlapping time between the accelerating and braking trains for a peak-hours scenario and an off-peak-hours scenario, respectively. Second, we formulate an integer programming model to maximize the overlapping time with the headway time and dwell time control. Furthermore, we design a genetic algorithm with binary encoding to solve the optimal timetable. Last, we present six numerical examples based on the operation data from the Beijing Yizhuang subway line in China. The results illustrate that the proposed model can significantly improve the overlapping time by 22.06% at peak hours and 15.19% at off-peak hours.