A robust and energy-efficient train timetable for the subway system

In the subway system, passenger crowding in peak hours is likely to cause train delays that easily propagate to following trains, resulting in a lower efficiency of the system. Consequently, this paper focuses on determining a robust timetable for the trains on the one hand, i.e., finding a better timetable to avoid delay propagation as much as possible in case of a crowded subway system. On the other hand, this paper considers the energy efficiency, i.e., reducing the total energy consumption during operations by selecting appropriate speed profiles and maximizing the utilization of regenerative braking energy. A related mathematical optimization model is formulated with the objective of maximizing the robustness and minimizing the total energy consumption. In order to solve this model, an efficient algorithm, i.e., simulation-based variable neighborhood search algorithm, is presented to obtain a good timetable in reasonable amount of time. Finally, experiments are implemented to show the performance of the proposed algorithm.