考虑生物危险源扩散的疫区应急物资调配模型

doi:10.16265/j.cnki.issn1003-3033.2023.11.0434

摘要/Abstract

摘要：

为解决传染性生物危险源扩散后疫区应急物资选址-分配问题,构建多目标优化应急物资调配模型。该模型以最小化配送时间、最小化疫区物资未满足程度为目标函数,结合考虑潜伏期、重复感染率的易感者-潜伏者-感染者-康复者(SEIRS)传染病动力学模型,建立物资需求方程,预测各疫区实时物资需求;针对应急救援过程中疫情扩散对应急物资调配方案的影响,使用改进非支配排序遗传算法(NSGA)-II求解模型。通过k-means算法预选址,实现适用于现有疫区的配送中心选址方案动态更新,进一步联合决策配送中心各类车辆派遣数、各类物资配送量;并以武汉市2020年疫情数据作为算例对比分析。结果表明:该模型计算效率较高,相较于传统NSGA-II算法,在收敛性、多样性和稳定性上具有性能优势,所得应急物资调配方案调配时间更短,疫区未满足程度更小,验证了模型的有效性。

关键词: 生物危险源扩散, 疫区应急物资, 调配模型, 多目标优化, 应急救援, 改进非支配排序遗传算法(NSGA)-II

Abstract:

In order to solve the problem of location selection and deployment of emergency supplies in epidemic areas after the spread of infectious biohazards, a multi-objective optimal emergency materials allocation model was established. Two kinds of objective functions, the minimization of distribution time and the minimization of the unsatisfied degree of materials, in the epidemic area were applied to this model. The Susceptible-Exposed-Infectious-Recovered-Susceptible(SEIRS) model, considering the incubation period and the repeated infection rate, was combined to establish the material demand equation and predict the real-time material demand in the epidemic area. In view of the impact of the spread of the epidemic on the allocation plan of emergency materials during the emergency rescue process, an impoved NSGA-II algorithm solution model was designed. The k-means algorithm was used for pre-location to realize the dynamic update of the location plan of the distribution center applicable to the existing epidemic area. Then, further joint decisions on the dispatch number of various vehicles and the distribution amount of various materials in the distribution center were made. Taking the epidemic data of Wuhan city in 2020 as an example, comparative analysis shows that the model has high computational efficiency, and has performance advantages in convergence, diversity and stability compared with the traditional NSGA-II algorithm. The obtained emergency materials allocation plan has a shorter deployment time and less unmet degree in the epidemic area, which verifies the effectiveness of the model.

Key words: biohazard diffusion, emergency supplies in epidemic areas, allocation model, multi-objective optimization, emergency rescue, improved non-dominated sorting genetic algorithm(NSGA)-II

张民波, 钟子逸, 闫瑾, 王翠灵, 王子超, 李春欣. 考虑生物危险源扩散的疫区应急物资调配模型[J]. 中国安全科学学报, 2023, 33(11): 206-213.

ZHANG Minbo, ZHONG Ziyi, YAN Jin, WANG Cuiling, WANG Zichao, LI Chunxin. Model of emergency supplies allocation in epidemic areas considering spread of biohazard diffusion[J]. China Safety Science Journal, 2023, 33(11): 206-213.

图/表 10

图1

图2

表1

候选配送中心

B	城市名	地理坐标	S_ik/件			$E i v$ /辆
B	城市名	地理坐标	k₁	k₂	k₃	v₁	v₂	v₃
b₁	天门	(60°39'N,113°10'E)	4 692	898	1 832	10	10	10
b₂	孝感	(30°56'N,113°54'E)	3 867	1 204	2 512	6	15	13
b₃	黄石	(30°12'N,115°06'E)	4 521	559	1 934	10	10	11
b₄	赤壁	(113°88'N,29°72'E)	2 899	956	2 484	8	9	7
b₅	信阳	(32°13'N,114°07'E)	3 078	854	2 388	7	12	9
b₆	钟祥	(31°10'N,112°34'E)	2 983	736	2 096	9	11	13
b₇	荆州	(112°24'N,30°33'E)	4 581	951	1 873	10	15	9
b₈	荆门	(31°02'N,112°12'E)	3 260	1 026	2 144	11	9	12
b₉	洪湖	(29°48'N,113°27'E)	6 125	653	2 065	7	12	11
b₁₀	咸宁	(29°53'N,114°17'E)	4 862	987	2 254	11	9	15
b₁₁	庐山	(29°42'N,116°26'E)	3 228	688	2 317	7	9	10
b₁₂	抚州	(27°95'N,116°36'E)	4 120	856	2 057	10	10	11
b₁₃	黄冈	(30°27'N,114°52'E)	4 934	1 089	3 048	15	10	14
b₁₄	麻城	(31°10'N,115°01'E)	4 057	1 109	2 138	9	10	8
b₁₅	景德镇	(29°17'N,117°13'E)	3 545	837	2 067	8	9	9
b₁₆	婺源	(29°25'N,117°85'E)	3 659	964	2 218	9	11	12
b₁₇	宜昌	(30°42'N,111°17'E)	4 122	1 046	1 849	12	8	9
b₁₈	南昌	(28°40'N,115°55'E)	5 879	1 264	2 403	10	12	17
b₁₉	安庆	(30°53'N,117°05'E)	3 477	1 187	2 123	9	13	10
b₂₀	随州	(31°42'N,113°22'E)	2 954	983	2 377	10	10	10
b₂₁	黄山	(30°01'N,118°01'E)	3 255	874	2 050	8	16	12
b₂₂	上饶	(25°27'N,117°58'E)	3 843	1 033	1 963	10	9	11
b₂₃	鄂州	(30°23'N,114°52'E)	6 089	922	3 089	11	14	13
b₂₄	岳阳	(29°22'N,113°06'E)	4 229	1 127	987	10	11	9

表1

图3

图4

表2

表3

表4

应急物资调度方案

配送中心	疫区	$e i k 1$ /辆			$e i k 2$ /辆			$e i k 3$ /辆			$Q i j k 1$ / 件	$Q i j k 2$ / 件	$Q i j k 3$ / 件
配送中心	疫区	v₁	v₂	v₃	v₁	v₂	v₃	v₁	v₂	v₃	$Q i j k 1$ / 件	$Q i j k 2$ / 件	$Q i j k 3$ / 件
b₁₄	j₁	3	5	2	1	2	1	1	0	2	3750	850	1800
b₁	j₁	3	5	4	2	0	1	1	1	0	4 250	750	1 400
b₉	j₁	4	5	5	0	1	1	0	3	0	5 000	350	1 800
b₄	j₁	1	2	4	2	0	0	1	2	0	2 200	600	2 000
b₂	j₁	2	3	5	0	2	3	0	3	1	3 300	850	2 300
b₂₃	j₁	4	5	7	1	1	1	1	2	1	5 500	650	2500
b₁₃	j₁	3	4	5	2	0	1	2	0	2	4 150	750	2 600
b₁₀	j₁	4	2	7	1	1	1	1	1	1	4 450	650	1 900
b₁₁	j₂	1	2	6	0	2	0	1	1	1	2 700	400	1 900
b₁₈	j₂	2	3	7	1	0	2	0	2	0	3 800	600	1 200
b₁₅	j₂	3	2	2	1	1	1	0	3	0	2 700	650	1 800
b₃	j₂	2	4	4	1	1	1	1	1	0	3 400	450	1400

表4

图5

图6

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