Research on Multi-Objective Distributionally Robust Optimization of Intra-City Metro Logistics Network

doi:10.3778/j.issn.1002-8331.2401-0396

Abstract

Abstract: Based on the advantages of underground system’s high efficiency, environmental protection and spare capacity that can be fully utilized in off-peak hours, this paper integrates two transport modes of ground vehicles and underground metro, studies the design of the logistics network of intra-city express delivery, and constructs a multi-objective optimization model based on distributionally robust optimization (DRO) method. The model takes into account the uncertain express demand and uncertain metro passenger flow to optimize the layout of the metro logistics network, in order to reduce the total operating cost of the logistics system and minimize the interference of express transport on metro passenger transport. Since the constructed multi-objective DRO model is a semi-infinite chance constrained optimization model, in order to solve the optimization model efficiently, this paper derives a safe approximation form that can be solved by CPLEX directly, and designs a NSGA-II algorithm to solve the large-scale optimization problem. Finally, a series of extended numerical experiments are carried out with the Shanghai metro network as a typical case to verify the effectiveness of the proposed multi-objective DRO model and NSGA-II algorithm in the design of metro-based intra-city express logistics network. The effects of discount factor, maximum allowed service time and tolerance level on the Pareto front are revealed through parameter sensitivity analysis.

Key words: hub location, underground logistics system, demand uncertainty, distributionally robust optimization, NSGA-II

摘要： 基于地铁系统的高效、环保和非高峰时段可以充分利用的空闲运力优势，整合地面车辆和地下地铁两种运输方式，研究了同城快递物流网络设计问题，构建了一种基于分布鲁棒优化（distributionally robust optimization， DRO）方法的多目标优化模型。该模型考虑了不确定快递需求和不确定地铁客流量情形来对地铁物流网络进行最优布局，以降低物流系统总运营成本及最大程度减少快递运输对地铁乘客运输的干扰。由于构建的多目标DRO模型是一个半无限机会约束优化模型，为了有效求解该优化模型，推导了可用CPLEX直接求解的安全逼近形式，并设计了一种NSGA-II算法来求解大规模优化问题。以上海地铁网络为典型案例开展了一系列扩展数值实验，验证了所提出的多目标DRO模型及NSGA-II算法在基于地铁的同城快递物流网络设计中的有效性。通过参数敏感性分析，揭示了折扣系数、允许的最大服务时间和容忍水平对Pareto前沿面的影响。

关键词: 枢纽选址, 地铁物流系统, 不确定性需求, 分布鲁棒优化, NSGA-II

GUO Shihao, HU Qingmi. Research on Multi-Objective Distributionally Robust Optimization of Intra-City Metro Logistics Network[J]. Computer Engineering and Applications, 2024, 60(21): 297-307.

郭士豪, 胡青蜜. 同城地铁物流网络多目标分布鲁棒优化研究[J]. 计算机工程与应用, 2024, 60(21): 297-307.

References

[1] COULOMBEL N, DABLANC L, GARDRAT M, et al. The environmental social cost of urban road freight: evidence from the Paris region[J]. Transportation Research Part D: Transport and Environment (S1361-9209), 2018, 63: 514-532.
[2] MU?OZ-VILLAMIZAR A, SANTOS J, MONTOYA-TORRES J R, et al. Measuring environmental performance of urban freight transport systems: a case study[J]. Sustainable Cities and Society, 2020, 52: 101844.
[3] KIKUTA J, ITO T, TOMIYAMA I, et al. New subway-integrated city logistics szystem[J]. Procedia-Social and Behavioral Sciences, 2012, 39: 476-489.
[4] DI Z, YANG L, SHI J, et al. Joint optimization of carriage arrangement and flow control in a metro-based underground logistics system[J]. Transportation Research Part B: Methodological, 2022, 159: 1-23.
[5] MOTRAGHI A, MARINOV M V. Analysis of urban freight by rail using event based simulation[J]. Simulation Modelling Practice and Theory, 2012, 25: 73-89.
[6] CHEN Z, DONG J, REN R. Urban underground logistics system in China: opportunities or challenges? [J]. Underground Space (S2467-9674), 2017, 2(3): 195-208.
[7] VISSER J. The development of underground freight transport: an overview[J]. Tunnelling and Underground Space Technology (S0886-7798), 2018, 80: 123-127.
[8] DIZIAIN D, TANIGUCHI E, DABLANC L. Urban logistics by rail and waterways in France and Japan[J]. Procedia-Social and Behavioral Sciences, 2014, 125:159-170.
[9] 韩秉志. “地铁运快递”还有潜力可挖[N].经济日报, 2023-10-22(006).
HAN B Z. There’s still potential for “subway delivery”[N]. Economic Daily, 2023-10-22(006).
[10] KAYI?O?LU B, AKGüN ?. Multiple allocation tree of hubs location problem for non-complete networks[J]. Computers & Operations Research, 2021, 136: 105478.
[11] 李俊, 张煜, 计三有, 等.不确定箱重下内河集装箱班轮航线配载决策[J].交通运输系统工程与信息, 2018, 18(2):208-215.
LI J, ZHANG Y, JI S Y, et al. Inland container liner route stowage planning decision with uncertain container weight[J]. Journal of Transportation Systems Engineering and Information Technology, 2018, 18(2): 208-215.
[12] 许闯来, 胡坚堃, 黄有方.不确定需求下快递配送网络鲁棒优化[J].计算机工程与应用, 2020, 56(3): 272-278.
XU C L, HU J K, HUANG Y F. Robust optimization of express delivery network with uncertain demand[J]. Computer Engineering and Applications, 2020, 56(3): 272-278.
[13] 夏东阳, 马继辉, 张文义. 考虑双重不确定性的公交时刻表分布鲁棒优化模型[J].控制与决策, 2023, 38(4): 1056-1064.
XIA D Y, MA J H, ZHANG W Y. A distributionally robust optimization model for the bus timetabling problem under two-fold uncertainties[J]. Control and Decision, 2023, 38(4): 1056-1064.
[14] YIN F, CHEN Y, SONG F, et al. A new distributionally robust p-hub median problem with uncertain carbon emissions and its tractable approximation method[J]. Applied Mathematical Modelling, 2019, 74: 668-693.
[15] 许双松, 刘康琳.基于分布式鲁棒优化的高铁快捷货物运输网络优化设计方法[J/OL].中国管理科学, 2023:1-11[2023?10?19]. https://doi.org/10.16381/j.cnki.issn1003-207x. 2022.1547.
XU S S, LIU K L. Hub-and-spoke network optimization method of China railway highspeed express based on distributed robust optimization[J/OL]. Chinese Journal of Management Science, 2023:1-11[2023-10-19]. https://doi.org/10.16381/j.cnki.issn1003-207x.2022.1547.
[16] ZHANG P, LIU Y, YANG G, et al. A multi-objective distributionally robust model for sustainable last mile relief network design problem[J]. Annals of Operations Research, 2022, 309: 689-730.
[17] SHANG X, YANG K, JIA B, et al. Distributionally robust cluster-based hierarchical hub location problem for the integration of urban and rural public transport system[J]. Computers & Industrial Engineering, 2021, 155: 107181.
[18] BEN-TAL A, EL GHAOUI L, NEMIROVSKI A. Robust optimization[M]. [S.l.]: Princeton University Press, 2009.
[19] 郑长江, 陈宜恒, 沈金星. 基于地铁的地上地下闭环物流配送路径优化[J]. 华东交通大学学报, 2022, 39(1): 89-98.
ZHENG C J, CHEN Y H, SHEN J X. Distribution routing optimization of ground-underground closed-loop logistics based on metro network[J]. Journal of East China Jiaotong University, 2022, 39(1): 89-98.