Mathematical Modeling and Optimization of a Two-Layer Metro-Based Underground Logistics System Network: A Case Study of Nanjing

With the surge in urban logistics demand, traditional surface transportation faces challenges, such as traffic congestion and environmental pollution. Leveraging metro systems in metropolitan areas for both passenger commuting and underground logistics presents a promising solution. The metro-based underground logistics system (M-ULS), characterized by extensive coverage and independent right-of-way, has emerged as a potential approach for optimizing urban freight transport. However, existing studies primarily focus on single-line scenarios, lacking in-depth analyses of multi-tier network coordination and dynamic demand responsiveness. This study proposes an optimization framework based on mixed-integer programming and an improved ICSA to address three key challenges in metro freight network planning: balancing passenger and freight demand, optimizing multi-tier node layout, and enhancing computational efficiency for large-scale problem solving. By integrating E-TOPSIS for demand assessment and an adaptive mutation mechanism based on a normal distribution, the solution space is reduced from five to three dimensions, significantly improving algorithm convergence and global search capability. Using the Nanjing metro network as a case study, this research compares the optimization performance of independent line and transshipment-enabled network scenarios. The results indicate that the networked scenario (daily cost: CNY 1.743 million) outperforms the independent line scenario (daily cost: CNY 1.960 million) in terms of freight volume (3.214 million parcels/day) and road traffic alleviation rate (89.19%). However, it also requires a more complex node configuration. This study provides both theoretical and empirical support for planning high-density urban underground logistics systems, demonstrating the potential of multimodal transport networks and intelligent optimization algorithms.