To enhance the overall capacity utilization of HSR networks and promote balanced capacity utilization across different lines, this study considers optimizing the capacity utilization of HSR networks by adjusting the travel routes of direct trains. Based on the arc-path modeling framework for multi-commodity network flows, the problem was formulated as a dual-objective mixed-integer linear programming model to minimize the total travel time and enhance the balance of capacity utilization across the railway network, with consideration of the unique train routes, the matching of paired train routes, section capacity, operating mileage, and maximum operating time per train trip limitations. Then, the model was transformed into a single-objective function using the weighted-sum approach. A case study based on actual data from China’s HSR network and train line plans in early 2024 was conducted to demonstrate the effectiveness of the proposed method. The results show that the proposed method can control the total travel time while significantly reducing the number of sections with over-utilized capacity and improve the balance of railway network capacity utilization. The method can thus provide decision support for the efficient utilization of HSR network capacity.
Bao et al. (Tue,) studied this question.