Immune-Inspired Multi-Objective PSO Algorithm for Optimizing Underground Logistics Network Layout with Uncertainties: Beijing Case Study

With the rapid acceleration of global urbanization and the advent of smart city initiatives, large metropolises confront the dual challenges of surging logistics demand and constrained surface transportation resources. Traditional surface logistics networks struggle to support sustainable urban development in high-density areas due to traffic congestion, high carbon emissions, and inefficient last-mile delivery. This paper addresses the layout optimization of a hub-and-spoke underground space logistics system (ULS) network for smart cities under stochastic scenarios by proposing an immune-inspired multi-objective particle swarm optimization (IS-MPSO) algorithm. By integrating a stochastic robust Capacity–Location–Allocation–Routing (CLAR) model, the approach concurrently minimizes construction costs, maximizes operational efficiency, and enhances underground corridor load rates while embedding probability density functions to capture multidimensional uncertainty parameters. Case studies in Beijing’s Fifth Ring area demonstrate that the IS-MPSO algorithm reduces the total objective function value from 9.8 million to 3.4 million within 500 iterations, achieving stable convergence in an average of 280 iterations. The optimized ULS network adopts a “ring–synapse” topology, elevating the underground corridor load rate to 59% and achieving a road freight alleviation rate (RFAR) of 98.1%, thereby shortening the last-mile delivery distance to 1.1 km. This research offers a decision-making paradigm that balances economic efficiency and robustness for the planning of underground logistics space in smart cities, contributing to the sustainable urban development of high-density regions and validating the algorithm’s effectiveness in large-scale combinatorial optimization problems.