Robust Optimization of Flexible Train Formation Strategy and Passenger Flow Control in Urban Rail Transit

Abstract To address the mismatch between transport capacity and passenger demand in metro operations, this study investigates the coordinated optimization of flexible train formation and passenger flow control. First, under deterministic passenger demand, a coordinated optimization model is developed to determine flexible train formations and passenger flow control strategies, with the objectives of minimizing average passenger waiting time, the maximum number of stranded passengers, and train operating costs. Second, considering passenger demand uncertainty, a weak robust optimization model is established by introducing an expected protection level mechanism to reduce unmet passenger demand under demand fluctuations. The resulting models are solved using an enhanced genetic algorithm. A case study based on Hangzhou Metro Line 4 is conducted to evaluate the effectiveness and operational implications of the proposed approach. The results show that the coordinated strategy achieves a better balance between service performance and operating costs than the single-strategy and fixed-formation strategies. Compared with the flexible-formation-only strategy, the coordinated strategy reduces the average passenger waiting time, train operating costs, and the maximum number of stranded passengers by 13.26%, 4.30%, and 51.70%, respectively. Additionally, compared with fixed 6-car operation without passenger flow control, it reduces train operating costs and the maximum number of stranded passengers by 19.10% and 28.58%, respectively, while maintaining a comparable service level. Overall, the proposed approach improves the match between transport capacity and passenger demand, providing a theoretical reference and decision support basis for peak-period capacity allocation and passenger flow regulation.