Coordinated Optimization of Late-Night Metro Timetables with Selective Skip-Stop Strategy: A Hybrid GWO-CNN Approach Balancing OD Accessibility and Maintenance Needs

Urban metro systems face increasing pressure to reconcile passenger service quality with infrastructure maintenance demands during late-night operations. This study proposes a coordinated optimization framework that integrates train timetabling with a flexible and selective skip-stop strategy. A mixed-integer programming model is formulated to jointly maximize passenger Origin–Destination (OD) accessibility and extend available maintenance windows. To solve the high-dimensional and computationally intensive model efficiently, a hybrid GWO-CNN algorithm is designed, where a Convolutional Neural Network (CNN)-based surrogate model replaces the time-consuming fitness evaluation process in the Grey Wolf Optimizer (GWO). A real-world case study on the Beijing metro network demonstrates that the proposed method increases OD accessibility by 23.60% and extends maintenance window by 8310 s. Compared to the conventional GWO, the GWO-CNN algorithm achieves superior solution quality with a 98.4% reduction in computation time. Sensitivity analyses further reveal the trade-offs between skip-stop rates, objective weight settings, and optimization outcomes, offering practical insights for metro operators in tailoring late-night scheduling strategies to both passenger demand and maintenance priorities.