Efficient iterative optimization to real-time train regulation in urban rail transit networks combined with Benders decomposition method

Considering the rapid expansion of urban rail transit networks and increasing transfer demands, this paper investigates the design of real-time train regulation strategies for urban rail networks under disturbances. Specifically, a mixed-integer nonlinear programming (MINLP) model is constructed in a rolling horizon (RH) framework to reduce train deviations and passenger waiting times, which involves complex coupling relationships among network-wide non-transfer passengers, transfer passengers and train traffics of different lines. To effectively address the model complexity and adapt to the real-time nature of this issue, we proposed an efficient iterative optimization (IO) approach to split the original problem into a smaller-scale regulation issue and a computationally cheap passenger loading procedure, which can efficiently treat the introduced nonconvexity of the exact modelling scheme. Besides, tailored to the mixed-integer property of the model, the generalized Benders decomposition (GBD) technique is incorporated into our algorithm. Furthermore, to verify the effectiveness of our method, we describe the detailed implementation of a series of numerical experiments on a small-scale and a real-world case. Computational results show that our regulation method can effectively contribute to the reliability of train systems, improving operational efficiency and service level. Besides, it performs promising computational efficiency in dealing with large-scale real-world cases, applicable for real-time applications.