Optimizing the train timetable for a subway system

With the development of subway systems, the utilization of regenerative braking energy has become an important issue. Focusing on the dynamic coordination of trains when regenerative braking energy is available, this paper proposes a new strategy, in which the regenerative energy generated by braking trains is used directly by accelerating trains. First, a mathematical model is formulated to optimize the metro timetable to maximize the utilization of regenerative braking energy. The model is a nonlinear integer programming problem that searches for the optimal headway and dwell time at each station. Furthermore, a simulated annealing algorithm is used to solve the optimal timetable. Finally, the Island Line of MTR (the mass transit system in Hong Kong) is taken as an example to illustrate the efficiency of the model and solution method. The results show that the utilization of regenerative braking energy can be improved by between 4 and 12% depending on the energy conversion rate. It is shown that a larger energy conversion rate results in a larger improvement.