Integrated Optimization of Train Stop Planning and Scheduling on Metro Lines With Express/Local Mode

Train stopping patterns and schedules play critical roles in the service design of metro lines with express/local mode. Previous studies on express/local mode generally handle the design of train stopping patterns and schedules independently, which cannot ensure the overall optimality of service provision. In this paper, a mixed integer nonlinear programming model is developed to collaboratively adjust train stopping patterns and schedules in order to minimize passenger travel time in express/local mode. With two types of train services provided, overtaking is allowed and a diverse set of passenger route choices is also incorporated into the proposed model. Linearization techniques are applied to transform this model from nonlinear to linear, which enables the proposed model to be handled by commercial linear solvers. To enhance computing efficiency in large-scale problems, a guided branch-and-cut algorithm is designed. The numerical examples on a test line and a real-world metro line are implemented to demonstrate the effectiveness of the proposed model and approach. The proposed approach is compared to existing approaches to identify the benefits of integrating train stop planning and scheduling decisions. Based on the computational time and the objective value, the guided branch-and-cut algorithm outperforms the direct use of the CPLEX solver.