Integrated optimization of holiday high-speed railway timetables considering air-rail connections and additional trains

Holiday travel surges strain high-speed railway (HSR) corridors and air-rail hubs, making weekday timetables inadequate for local and intermodal passengers. A multi-objective model integrates holiday and air-rail demand, capacity constraints, and additional-train activation to maximize service utility, minimize operating costs, and preserve timetable stability. Passenger utilities are represented by trapezoidal transfer-time and Gaussian travel-time-matching functions for air-rail and local passengers, respectively. An NSGA-II algorithm with train-priority-based conflict resolution repairs infeasible timetables through time shifting, bounded backtracking, and local sequence reordering. A May Day case study on the Nanjing South–Shanghai Hongqiao HSR section shows that the share of air-rail passengers within the (0.8, 1.0] utility interval increases from 86.67% to 95.16%, while most existing train departure deviations remain within 0–10 min. Sensitivity analysis indicates diminishing marginal benefits from additional train insertion under high demand.