考虑模糊不确定的地铁货运系统成网布局规划

doi:10.16182/j.issn1004731x.joss.21-0206

摘要/Abstract

摘要：

为解决不确定条件下依托地铁开展城市地下物流的网络设计与优化问题，提出双层地铁-货运系统(metro-based underground logistics system，M-ULS)设施构成，建立地下货运环境效益期望下的M-ULS网络流量配置模型，以综合成本和系统利用率为目标，构建M-ULS网络选址-分配-路径模糊随机规划模型并提出其线性精确化方法，设计离散二进制混沌遗传粒子群算法和精确算法进行组合寻优。结果表明：与确定性情景相比，模糊随机情景下的M-ULS最佳布局方案更加保守，地下物流的环境外部效益可以抵消10%~12%的网络建设运营成本。

关键词: 城市地下物流系统, 地铁, 选址与布局, 粒子群算法, 需求不确定

Abstract:

Aming at the network design and optimization of metro-based urban underground logistics under uncertainties, the facility components of two-tier metro-based underground logistics system (M-ULS) are proposed. Focus on the comprehensive costs and system utilization rate, a M-ULS network flow assignment model is established based on the expectation of environmental benefits of underground freight transport. a M-ULS network location-allocation-routing fuzzy random programming model is established, and a crisp linearization method is presented. A solution portfolio combining discrete binary chaos particle swarm optimization-genetic algorithm and exact algorithms is designed for combinatorial optimization. Effectiveness of the presented models and algorithms is verified in real-life cases. Results show that the best M-ULS layout schemes in fuzzy random scenarios are more conservative than those in deterministic scenarios. The external environment benefits of underground logistics can offset 10%~12% of costs in network construction and operations.

Key words: urban underground logistics systems, metro, location and layout, particle swarm optimization algorithm, demand uncertainty

中图分类号:

TP391.9

胡万杰, 董建军, 任睿, 陈志龙. 考虑模糊不确定的地铁货运系统成网布局规划[J]. 系统仿真学报, 2022, 34(8): 1725-1740.

Wanjie Hu, Jianjun Dong, Rui Ren, Zhilong Chen. Layout Planning of Metro-based Underground Logistics System Network Considering Fuzzy Uncertainties[J]. Journal of System Simulation, 2022, 34(8): 1725-1740.

图/表 15

图1

图2

图3

表1

模糊随机变量构造

变量	左边界	右边界	均值	方差
$D ̂ i k$	$m i k 1$	$n i k 1$	$d i k$	$ρ i k$
$R ̂ j$	$m j 2$	$n j 2$	$r j$	—
$E ̂ i$	$m i 3$	$n i 3$	$e i$	—
$C ̂ h$	$m h 4$	$n h 4$	$c h$	—
$U ̂ j$	$m j 5$	$n j 5$	$u j$	—
$V ̂ t$	$m t 6$	$n t 6$	$v t$	—
$P ̂ s$	$m s 7$	$n s 7$	$p s$	—
$Q ̂ h$	$m h 8$	$n h 8$	$q h$	—
$W ̂ j$	$m j 9$	$n j 9$	$w j$	—

表1

图4

图5

图6

图7

表2

算法各步骤的理论复杂度

算子	时间复杂度	计算量级
总计		×10⁸
选择-交叉-变异	$O (n 2 + 2 n)$	×10⁴
混沌局部搜索	$O (3 n)$	×10²
粒子群状态更新	$O (2 n)$	×10²
选址-分配	$O (n ⋅ \| I \|)$	×10⁴
一级路径优化	$O (n ⋅ \| J ¯ \| ⋅ \| K \| ⋅ \| S \|)$	×10⁵
K-MST	$O (n ⋅ \| I \| ⋅ \| J ¯ \|)$	×10⁵
FWA	$O (n ⋅ \| I \| ⋅ \| J ¯ \| + n ⋅ \| J ¯ \| ⋅ L)$	×10⁶

表2

表3

表4

模型仿真参数取值

参数	值	参数	值
$σ ˙ j$ /(万件/d)	11	$η$ /%	55
$σ ¨ j$ /(万件/d)	4	$φ$ /(万件/车)	0.02
$H t$ /(万件/d)	60	$ζ C O 2$ /(万元/t)	0.071
$ς$ /(万件/d)	2	$ζ C O$ /(万元/t)	0.359
$r j$ /(亿元)	3	$ζ N O x$ /(万元/t)	10.32
$e i$ /(亿元)	3 000	$ζ P M$ /(万元/t)	26.34
$c h$ /(万元/km)	4 000	$ζ V O C$ /(万元/t)	0.703
$θ$ /d	36 500	$κ$ /(L/km)	0.125
$u j$ /(元/件)	0.1	$ε$ /(万元/L)	7.1×10^-4
$v t$ /(元/件)	0.07	$O C O 2$ /(t/km)	2.8×10^-4
$p s$ /(元/(件·km))	0.006	$O C O$ /(t/km)	1.7×10^-6
$q h$ /(元/(件·km))	0.002 4	$O N O x$ /(t/km)	1.01×10^-6
$w j$ /(元/件)	0.05	$O P M$ /(t/km)	1.2×10^-7
$γ$ /(元/件)	0.5	$O V O C$ /(t/km)	3.4×10^-7

表4

表5

不确定参数取值分布

变量	左边界控制量	右边界控制量	方差
$R ̂ j$	U(0.126, 0.215)	U(0.225, 0.38)	—
$E ̂ i$	U(0.011, 0.018)	U(0.035, 0.059)	—
$C ̂ h$	U(0.011, 0.018)	U(0.013, 0.022)	—
$U ̂ j$	U(0.027, 0.047)	U(0.045, 0.076)	—
$P ̂ s$	U(0.001, 0.002)	U(0.002, 0.003)	—
$Q ̂ h$	U(0.001, 0.002)	U(0.001, 0.002)	—
$V ̂ t$	U(0.018, 0.031)	U(0.018, 0.03)	—
$W ̂ j$	U(0.011, 0.019)	U(0.01, 0.017)	—
$D ̂ i k k = 1$	U(0.12, 0.32)× $d i k k = 1$	U(0.24, 0.4)× $d i k k = 1$	U(37, 595)
$D ̂ i k k = 2$	U(0.15, 0.48)× $d i k k = 2$	U(0.2, 0.3)× $d i k k = 2$	U(9, 149)
$D ̂ i k k = 3$	U(0.15, 0.25)× $d i k k = 3$	U(0.2, 0.35)× $d i k k = 3$	U(15, 189)
$D ̂ i k k = 4$	U(0.2, 0.4)× $d i k k = 4$	U(0.18, 0.42)× $d i k k = 4$	U(5, 205)

表5

图8

图9

表6

不确定条件下的地铁货运网络最优配置

$δ$ /%	站点数量	一级网络运输成本	二级网络运输成本	站点平均运营成本	站点平均负载率/%	空置惩罚成本	地下转运成本	节点建设成本	管道建设成本	管道里程/km	库存成本	总目标成本
50	10	5.59	1.10	0.99	87.85	0.14	1.86	12.72	8.57	104	1.17	40.04
60	11	6.36	1.34	1.07	92.76	0.08	1.92	15.09	11.78	143	1.87	49.22
70	13	8.16	1.61	1.05	93.60	0.26	3.02	18.67	14.50	177	2.04	60.89
80	16	9.83	1.82	1.04	92.87	0.02	4.02	22.37	14.73	179	2.22	69.55
90	18	10.93	2.11	1.04	92.24	0.78	3.87	26.65	16.19	197	2.83	80.94
100	22	13.67	2.34	0.95	84.07	1.08	5.93	32.88	17.08	208	2.45	93.46

表6

参考文献 28

1	黄海军, 高自友, 田琼, 等. 新型城镇化导向下的城市群综合交通系统管理[J]. 中国科学基金, 2018, 32(2): 214-223.
	Huang Haijun, Gao Ziyou, Tian Qiong, et al. The Management Theory and Method of the Comprehensive Transportation System in City Agglomeration under the New Urbanization Trend[J]. Bulletin of National Natural Science Foundation of China, 2018, 32(2): 214-223.
2	国家邮政局. 2020年邮政行业运行情况[EB/OL]. [2021-01-14]. .
3	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.
4	北京市交通发展研究院. 2019 年北京市交通发展年度报告[EB/OL]. [2021-01-14]. .
5	钱七虎. 利用地下空间助力发展绿色建筑与绿色城市[J]. 隧道建设, 2019, 39(11): 1737-1747.
	Qian Qihu. Exploiting Underground Space to Promote Green Building and Green City Development[J]. Tunnel Construction, 2019, 39(11): 1737-1747.
6	中共中央国务院. 交通强国建设纲要[EB/OL]. (2019-09-19) [2021-01-14]..
7	钱七虎, 郭东军. 城市地下物流系统导论[M]. 北京: 人民交通出版社, 2007.
	Qian Qihu, Guo Dongjun. Introduction to Urban Underground Logistics System[M]. Beijing: China Communications Press, 2007.
8	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.
9	Visser J. The Development of Underground Freight Transport: An Overview[J]. Tunnelling and Underground Space Technology (S0886-7798), 2018, 80: 123-127.
10	陈志龙, 郭东军. 第五类运输和供应系统——北京建设地下物流系统的战略构想[J]. 北京规划建设, 2005(3):77-80.
	Chen Zhilong, Guo Dongjun. The Fifth Type of Transportation and Supply System - A Strategic Conception of Beijing Underground Logistics System[J]. Beijing Planning and Construction, 2005(3): 77-80.
11	范益群, 游克思. 地下集装箱物流系统在港城融合发展中的应用[J]. 地下空间与工程学报, 2018, 14(增1): 49-54.
	Fan Yiqun, You Kesi. Application of Underground Container Freight Transportation on Integration Development of City and Port[J]. Chinese Journal of Underground Space and Engineering, 2018, 14(S1): 49-54.
12	Hu W, Dong J, Hwang B G, et al. Using System Dynamics to Analyze the Development of Urban Freight Transportation System Based on Rail Transit: A Case Study of Beijing[J]. Sustainable Cities and Society (S2210-6707), 2020, 53: 101923.
13	Cleophas C, Cottrill C, Ehmke J F, et al. Collaborative Urban Transportation: Recent Advances in Theory and Practice[J]. European Journal of Operational Research (S0377-2217), 2019, 273(3): 801-816.
14	李彤, 王众托. 大型城市地下物流网络优化布局的模拟植物生长算法[J]. 系统工程理论与实践, 2013, 33(4): 971-980.
	Li Tong, Wang Zhongtuo. Optimization Layout of Underground Logistics Network in Big Cities with Plant Growth Simulation Algorithm[J]. System Engineering Theory & Practice, 2013, 33(4): 971-980.
15	周芳汀, 张锦, 周国华. 带时间窗的地铁配送网络路径优化问题[J]. 交通运输系统工程与信息, 2018, 18(5): 88-94.
	Zhou Fangting, Zhang Jin, Zhou Guohua. Subway-Based Distribution Network Routing Optimization Problem with Time Windows[J]. Journal of Transportation Systems Engineering and Information Technology, 2018, 18(5): 88-94.
16	任睿, 胡万杰, 董建军, 等. 轴辐式城市地铁-货运系统网络布局优化[J]. 系统仿真学报, 2021, 33(7): 1699-1712.
	Ren Rui, Hu Wanjie, Dong Jianjun, et al. Optimization of Urban Metro-based Underground Logistics System Network with Hub-and-spoke Layout [J]. Journal of System Simulation, 2021, 33(7): 1699-1712.
17	Dong J, Hu W, Yan S, et al. Network Planning Method for Capacitated Metro-Based Underground Logistics System[J]. Advances in Civil Engineering (S1687-8094), 2018(6): 6958086.
18	Zhao L, Li H, Li M, et al. Location Selection of Intra-City Distribution Hubs in the Metro-Integrated Logistics System[J]. Tunnelling and Underground Space Technology (S0886-7798), 2018, 80: 246-256.
19	Behiri W, Belmokhtar-Berraf S, Chu C. Urban Freight Transport Using Passenger Rail Network: Scientific Issues and Quantitative Analysis[J]. Transportation Research Part E: Logistics and Transportation Review (S1366-5545), 2018, 115: 227-245.
20	Nadizadeh A, Hosseini Nasab H. Solving the Dynamic Capacitated Location-Routing Problem with Fuzzy Demands by Hybrid Heuristic Algorithm[J]. European Journal of Operational Research(S0377-2217), 2014, 238(2): 458-470.
21	Yang K, Yang L, Gao Z. Planning and Optimization of Intermodal Hub-and-Spoke Network Under Mixed Uncertainty[J]. Transportation Research Part E: Logistics and Transportation Review (S1366-5545), 2016, 95: 248-266.
22	Wang R, Yang K, Yang L, et al. Modeling and Optimization of a Road-Rail Intermodal Transport System Under Uncertain Information[J]. Engineering Applications of Artificial Intelligence (S0952-1976), 2018, 72: 423-436.
23	Shavarani S M, Mosallaeipour S, Golabi M, et al. A Congested Capacitated Multi-Level Fuzzy Facility Location Problem: An Efficient Drone Delivery System[J]. Computers & Operations Research (S0305-0548), 2019, 108: 57-68.
24	崔利刚, 任海利, 邓洁, 等. 基于模糊随机需求的B2C多品采配协同模型及其粒子群算法求解[J]. 管理工程学报, 2020, 34(6): 183-190.
	Cui Ligang, Ren Haili, Deng Jie, et al. A Particle Swarm Algorithm for a Novel B2C Multi-Item Replenishment and Delivery Coordination Model with Fuzzy Random Demands[J]. Journal of Industrial Engineering and Engineering Management, 2020, 34(6): 183-190.
25	刘彦奎, 白雪洁, 杨凯. 参数可信性优化方法[M]. 北京: 科学出版社, 2017.
	Liu Yankui, Bai Xuejie, Yang Kai. Parameter Credibility Optimization Method[M]. Beijing: Science Press, 2017.
26	Hu W, Dong J, Hwang B G, et al. Hybrid Optimization Procedures Applying for Two-Echelon Urban Underground Logistics Network Planning: A Case Study of Beijing[J]. Computers & Industrial Engineering (S0360-8352), 2020, 144: 106452.
27	刘玉敏, 高松岩. 一种改进的粒子群优化算法及其算法测试[J]. 数学的实践与认识, 2019, 49(9): 237-247.
	Liu Yumin, Gao Songyan. An Improved Particle Swarm Optimization Algorithm and Its Algorithm Test[J]. Mathematics in Practice and Theory, 2019, 49(9): 237-247.
28	陈一村, 郭东军, 陶西贵, 等. 城市地下物流系统货运需求量预测分析[J]. 地下空间与工程学报, 2021, 17(6): 1687-1694, 1741.
	Chen Yicun, Guo Dongjun, Tao Xigui, et al. Forecast Analysis of Freight Demand Volume in the Urban Underground Logistics System[J]. Chinese Journal of Underground Space and Engineering, 2021, 17(6): 1687-1694, 1741.

[1]	张莉, 张惠珍, 刘冬, 陆雨欣. 考虑紧迫度的应急物资调度及粒子群算法求解[J]. 系统仿真学报, 2022, 34(9): 1988-1998.
[2]	朱依婷, 闫云, 何兆成. 公交与社会车辆混合的中观交通建模与仿真[J]. 系统仿真学报, 2022, 34(9): 2019-2027.
[3]	冯飞波, 闫兴德, 郑宝强, 尹晓峰, 周梦真, 蒋鑫. 蓄电‒氢储混合储能系统的配电网双层优化[J]. 系统仿真学报, 2022, 34(7): 1405-1416.
[4]	马立新, 程颍. 计及可中断负荷的园区综合能源系统优化调度[J]. 系统仿真学报, 2022, 34(4): 817-825.
[5]	张凯庆, 嵇启春. 速度时变的多中心半开放式车辆路径问题研究[J]. 系统仿真学报, 2022, 34(4): 836-846.
[6]	陈魁, 毕利, 王文雅. 柔性作业车间AGV与机器双资源集成调度研究[J]. 系统仿真学报, 2022, 34(3): 461-469.
[7]	孙晓安, 栾小丽, 刘飞. 基于智能优化灰色模型的电子固废预测[J]. 系统仿真学报, 2022, 34(3): 536-542.
[8]	魏腾飞, 潘庭龙. 基于改进PSO优化LSTM网络的短期电力负荷预测[J]. 系统仿真学报, 2021, 33(8): 1866-1874.
[9]	牛侃, 李冰, 付强. 基于混沌扰动机制粒子群算法的战场频率分配方法[J]. 系统仿真学报, 2021, 33(8): 1905-1913.
[10]	孟建军, 王终军, 胥如迅, 李德仓. 基于模糊复合策略的高速列车主动悬挂控制研究[J]. 系统仿真学报, 2021, 33(7): 1554-1564.
[11]	魏瑞轩, 吴子沉. 无人机集群实时任务分配方法研究[J]. 系统仿真学报, 2021, 33(7): 1574-1581.
[12]	任睿, 胡万杰, 董建军, 陈志龙. 轴辐式城市地铁-货运系统网络布局优化[J]. 系统仿真学报, 2021, 33(7): 1699-1712.
[13]	刘晓琳, 吴竟祎. 飞机舵机电液加载系统控制补偿器设计与仿真[J]. 系统仿真学报, 2021, 33(5): 1031-1038.
[14]	汪润鸿, 王红军, 邹湘军, 曾泽钦, 李慧, 黄钊丰, 刘伟良. 基于混合粒子群算法的组合式变速箱传动比优化研究[J]. 系统仿真学报, 2021, 33(4): 825-836.
[15]	陈魁, 毕利. 改进粒子群算法在考虑运输时间下的FJSP研究[J]. 系统仿真学报, 2021, 33(4): 845-853.