Integrated train rescheduling and speed management in a railway network: A meso-micro approach based on direct multiple shooting and alternating direction method of multipliers

The performance of high-speed railway systems is often affected by unavoidable disruptions, which impact the reliability of train operations and passenger satisfaction. In contrast to most existing studies, which focus on either train rescheduling or speed management in separate or sequential frameworks, this paper addresses the integrated train rescheduling and speed management problem during severe disruptions, considering power supply constraints on a bidirectional railway network. Specifically, this problem incorporates detailed train speed control into the rescheduling process and involves train rerouting strategies and flexible stops to mitigate disruption effects. To characterize the integrated problem, we develop a three-dimensional space–time-state network, where each arc corresponds to a detailed driving strategy. We then propose a mixed-integer nonlinear programming (MINLP) model to simultaneously optimize the train schedule (i.e., train order, departure and arrival times, and routes) and train speed profiles, with the goal of reducing both total passenger delays and train energy consumption. To efficiently solve the integrated model, we propose a two-stage approach based on the direct multiple shooting method and the alternating direction method of multipliers (ADMM). This approach is implemented by combining offline and online computing to meet real-time requirements. The effectiveness and efficiency of the proposed model and algorithm are verified through numerous experiments using real-world data from Chinese high-speed railways. Experimental results demonstrate that our integrated approach improves energy efficiency by an average of 19.40% in complete section blockage scenarios and 7.69% in temporary speed restriction scenarios, compared to methods that do not incorporate speed management.