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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Hongbin Yu & An Shi & Qing Liu & Jianhua Liu & Huiyang Hu & Zhilong Chen, 2025. "Immune-Inspired Multi-Objective PSO Algorithm for Optimizing Underground Logistics Network Layout with Uncertainties: Beijing Case Study," Sustainability, MDPI, vol. 17(10), pages 1-34, May.
    • Handle: RePEc:gam:jsusta:v:17:y:2025:i:10:p:4734-:d:1661036
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    References listed on IDEAS

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    1. Hairui Wei & Anlin Li & Nana Jia, 2020. "Research on Optimization and Design of Sustainable Urban Underground Logistics Network Framework," Sustainability, MDPI, vol. 12(21), pages 1-22, November.
    2. Ahmadi-Javid, Amir & Amiri, Elahe & Meskar, Mahla, 2018. "A Profit-Maximization Location-Routing-Pricing Problem: A Branch-and-Price Algorithm," European Journal of Operational Research, Elsevier, vol. 271(3), pages 866-881.
    3. Hu, Yucong & Liu, Qingyang & Li, Sitong & Wu, Weitiao, 2025. "Robust emergency logistics network design for pandemic emergencies under demand uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 196(C).
    4. Shahooei, Sirwan & Farooghi, Ferika & Zahedzahedani, Seyed Ehsan & Shahandashti, Mohsen & Ardekani, Siamak, 2018. "Application of underground short-haul freight pipelines to large airports," Journal of Air Transport Management, Elsevier, vol. 71(C), pages 64-72.
    5. Shi, Yi & Vanhaverbeke, Lieselot & Xu, Jiuping, 2024. "Electric vehicle routing optimization for sustainable kitchen waste reverse logistics network using robust mixed-integer programming," Omega, Elsevier, vol. 128(C).
    6. Qing Liu & Yicun Chen & Wanjie Hu & Jianjun Dong & Bo Sun & Helan Cheng, 2023. "Underground Logistics Network Design for Large-Scale Municipal Solid Waste Collection: A Case Study of Nanjing, China," Sustainability, MDPI, vol. 15(23), pages 1-28, November.
    7. Di, Zhen & Yang, Lixing & Shi, Jungang & Zhou, Housheng & Yang, Kai & Gao, Ziyou, 2022. "Joint optimization of carriage arrangement and flow control in a metro-based underground logistics system," Transportation Research Part B: Methodological, Elsevier, vol. 159(C), pages 1-23.
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