Real-time metro train rescheduling under uncertainties: A hybrid machine learning and integer L-shaped approach

Metro trains inevitably encounter faults during operation, leading to disturbances or disruptions. Considering the uncertainties in both the scenario type (such as delay, out-of-service, and rescue) and the duration of these disturbances or disruptions, this paper investigates the real-time train rescheduling problem in the context of Industry 5.0. A risk-averse two-stage stochastic programming model is formulated to generate rescheduling solutions for each possible uncertainty realization and ensure their seamless transition. In this model, the first stage makes rescheduling decisions that are independent of uncertainty realizations, such as the number of dispatched backup trains and whether to short-turn trains during fault handling. The second stage adopts all dispatching measures applicable to metro lines and makes additional rescheduling decisions. To integrate human factors into decision-making, the general conservative attitude of dispatchers towards risk management is captured using a mean-conditional value-at-risk criterion. Under the traditional integer L-shaped framework, the model is decomposed into a first-stage master problem and several second-stage subproblems. Aligning with the technological advancements of Industry 5.0, supervised machine learning is used to predict the objective values of the subproblems instead of solving them explicitly, thereby enabling the rapid addition of approximate optimality cuts and improving computational efficiency. Numerical experiments are conducted on the Beijing Yizhuang Metro Line. The computational results show that the proposed solution approach reduces the average computation time by 99.02% compared to GUROBI, and the developed stochastic model lowers the average objective value by over 22% compared to the practical strategy, contributing to the development of intelligent and resilient metro systems.