A Subway Train Timetable Optimization Approach Based on Energy-Efficient Operation Strategy

With the rising energy prices and environment concerns, energy-efficient operation is paid more and more attention in the subway systems, which is one of the effective ways to reduce the operation cost and then improve the operation efficiency. There are many researches for energy-efficient operation on designing a reasonable timetable or optimizing the speed profile, but all of them are studied separately. To achieve a better performance on energy saving, we present an integrated algorithm for optimizing the timetable for the entire route together with the speed profiles between successive stations, which is named as integrated timetable. First, we give an analytical algorithm to get the optimal switching points for each section by using the Pontryagin maximum principle. For dealing with the variable speed limits, we calculate the reserve time, i.e., the difference between the pre-determined trip time and the minimum trip time, and then design an algorithm to distribute it among different sections with constant speed limits. Finally, we extend the algorithm to solve the integrated timetable. We also give some numerical examples to illustrate the validity of the algorithm based on the data from the Beijing YiZhuang subway line in China. It is recorded that the energy consumption for interstation trip can be reduced by 10.3% on average, and the total energy reduction for the entire trip is 14.5% by using the integrated timetable. Besides, it takes about 0.15 seconds to generate the integrated timetable, which means that the algorithm is quick enough to be used in the automatic train operation (ATO) system for real-time control.