Timetable Optimization for Regenerative Energy Utilization in Subway Systems

In subway systems, kinetic energy can be converted into electrical one by using regenerative braking systems. If regenerative energy (RE) is fully used, the energy demands from power grid can be dramatically reduced. Since energy storage systems usually have a high cost, they are not considered in this work. Thus, RE has to be immediately utilized by accelerating trains; otherwise, it is wasted into heat via resistors. Timetable optimization methods are often used to coordinate accelerating and braking trains at a station, such that RE can be optimally used by the former. To improve RE utilization (REU) in a subway line, we propose a timetable optimization problem and establish its mathematical model. Many realistic constraints with the decision variables, i.e., headway time and dwell time, are considered. Then we design an improved artificial bee colony (IABC) algorithm to solve the problem. Several numerical experiments are conducted based on the actual data from a subway line in Beijing, China. The correctness of the mathematical model and effectiveness of IABC are shown by comparing it with commercial software CPLEX and a genetic algorithm, respectively. The impact of the decision variables on REU is analyzed, which helps to improve the timetable currently used in this subway line. We also test the robustness of the optimized timetable when certain disturbance takes place.