Real-time train regulation in the metro system with energy storage devices: An efficient decomposition algorithm with bound contraction

Focusing on the energy-conservation train operation issues, this paper proposes an effective real-time train regulation scheme for metro systems with energy storage devices. Specifically, to minimize train timetable deviation, passenger waiting and energy consumption, we formulate a mixed-integer nonlinear programming model to generate energy-efficient train regulation strategies. This model explicitly considers the train traffic, passenger load and storage, immediate and delayed uses of regenerative energy. Carefully tailored to the proposed model, we devise an efficient decomposition algorithm to split the original problem into small-scale subproblems. In the algorithm, specific values of binary variables, passenger-flow estimates and logic-based cuts are consecutively identified and updated. Besides, bound contraction and bilinear-specific warming start procedures are particularly designed for further acceleration. Numerical experiments are conducted to validate the proposed model and method. Our energy-efficient train regulation strategies can improve train departure punctuality, headway regularity, reduce passenger waiting times, and achieve energy savings. Furthermore, the solution algorithm exhibits promising computational efficiency in real-world experiments, thereby facilitating an online implementation.