Optimization Model of Express–Local Train Schedules under Cross-Line Operation of Suburban Railway

Cross-line operation is a key direction for the integrated development of multi-level rail transit systems in urban agglomerations. Optimizing train operation under cross-line conditions is essential for improving the overall efficiency and service quality of rail networks. This paper addresses the joint problem of suburban railway cross-line operation and express–local train coordination. This paper develops a train scheduling optimization framework that jointly selects service patterns and departure schedules, with the objective of reducing overall costs, including passenger travel time and operating expenses. To solve the model efficiently, an extended Adaptive Large Neighborhood Search (ALNS) algorithm is developed. The proposed approach provides a practical framework for timetable planning in complex cross-line rail systems and contributes to enhancing integrated transit operations.