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

Hongbin Yu, An Shi (), Qing Liu (), Jianhua Liu, Huiyang Hu and Zhilong Chen
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Hongbin Yu: College of Architecture and Urban Planning, Beijing University of Technology, Beijing 100124, China
An Shi: School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China
Qing Liu: College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China
Jianhua Liu: School of Safety Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
Huiyang Hu: School of Safety Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
Zhilong Chen: College of Defense Engineering, Army Engineering University of PLA, Nanjing 210007, China

Sustainability, 2025, vol. 17, issue 10, 1-34

Abstract: 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.

Keywords: urban underground space; sustainable city logistics; underground logistics systems; multi-objective optimization; hub-and-spoke network; stochastic programming (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2025
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