Real-time train rescheduling optimization with combined cross-line strategies for urban rail network

In urban rail network systems, delays not only disrupt planned train schedules on local lines but also propagate across other lines. These delays are frequently updated in response to dynamic operating environments, creating a demand for real-time rescheduling decisions. To tackle these real-time delays with cost-effective operations and high service quality, this study investigates a real-time train rescheduling problem that incorporates cross-line operations in urban rail network systems. A mixed-integer linear programming (MILP) model is formulated under a customized rolling horizon framework to reduce penalties associated with skipped stops, destination delays, and trip frequencies, in which six strategies are involved in rescheduling trains in dynamically disturbed operating environments. To solve this model, an adaptive large neighborhood search (ALNS) algorithm is developed under the rolling horizon framework to generate train schedules and rolling stock circulation plans. To test the performance of the proposed approaches, a series of numerical experiments are conducted both on small-scale and real-life cases with performance analyses based on the INFORMS RAS 2022 (Railway Applications Section) dataset. From the computational results, we observe that the cross-line operations are helpful to improve the flexibility of rolling stock units. In addition, under the rolling horizon framework, longer individual decision horizons could perform better overall objectives owing to the larger prediction horizons by considering more trips.