A Two-Step Optimization Framework for Real-Time Train Rescheduling in an Urban Rail Transit Line

The operation of urban rail transit is inevitably affected by disturbances in practice, causing the original train timetable and rolling stock circulation to be infeasible. This paper addresses the real-time train rescheduling problem through a novel two-step optimization framework. To realign train operations with the original plan, the first step manages traffic flow by optimizing dispatching measures, including retiming, cancellation, short-turning, and backup rolling stock utilization. To maintain the highest possible service quality during the transition period, the second step introduces stop-skipping and further fine-tunes the train timetable. Both steps are formulated as mixed-integer nonlinear programming models, and the second-step model is heuristically decomposed. For computational tractability, mathematical models are transformed using some linearization techniques and then solved according to the prescribed procedure. Numerical experiments based on a small-scale case and real-world data of the Beijing Yizhuang Metro Line show that the proposed two-step optimization framework can satisfy the real-time requirements and outperform the current rescheduling method employed in the automatic train supervision system. Furthermore, the framework is proven to be applicable to different disturbance durations and locations.