﻿ 城镇应急物资储备库动态多重覆盖模型
 北京航空航天大学学报(社会科学版)  2019, Vol. 32 Issue (1): 57-64 PDF

Dynamic Multiple Coverage Model of Urban Emergency Material Depository
WANG Feifei, HOU Yunxian, LI Shisen
School of Economics and Management, China Agricultural University, Beijing 100083, China
Abstract: This article studies emergency material depository layout optimization, which plays an important role in urban emergency rescue. First, considering that the road condition has an important impact on the effect of emergency rescue, the concept of road damage risk factor is introduced in this article to build satisfaction attenuation function based on the thought of demand satisfaction decreasing within the coverage radius. Second, on account of the supply ability limitation of emergency material depository and the dynamic process of emergency rescue, this article proposes a dynamic multiple coverage model of urban emergency material depository from the perspective of supply and demand and time dimension. Using an improved immune optimization algorithm, the objective of this model is to maximize the total demand satisfaction and minimize the total distribution distance. Third, the validity of the model and algorithm is verified by numerical examples to provide advice for decision makers of the emergency material depository layout optimization.
Keywords: emergency material depository     layout optimization     dynamic     multiple coverage     immune optimization algorithm

(二) 满意度衰减函数

 (1)

(三) 基于满意度衰减函数的动态多重覆盖模型

I={I1, I2, …, Im} 和J ={J1, J2, …, Jn}分别为应急需求点和候选应急物资储备库的集合；s为应急救援活动开展阶段(s=1, 2, …, q)；pss阶段需开放的应急物资储备库数量；Qiss阶段应急需求点i的需求量；dij为应急需求点i与候选应急物资储备库j间距离；uijss阶段候选应急物资储备库j对应急需求点i的物资供应量；f ijss阶段候选急物资储备库j对应急需求点i的满意度水平；xijs为0, 1变量，当xijs为1时，表示s阶段应急需求点i被应急物资储备库j覆盖，否则为0；yjs为0, 1变量，当yjs为1时，表示候选应急物资储备库在s阶段被选中，否则为0。

 (2)
 (3)

S·T·

 (4)
 (5)
 (6)
 (7)

λ1λ2分别为目标函数Z1Z2的权系数，且λ1+λ2=1，则上节所建模型可转换为如下形式：

 (8)

S·T·：(4)~(7)

(二) 算法选择[23]

1.抗体编码和抗体群的产生

2.抗体亲和度评价函数

3.免疫操作

(1) 选择，文章选用常用的轮盘赌法进行选择操作。

(2) 交叉，采用单点交叉法进行交叉操作。

(3) 变异，选择常用的随机选择变异位进行变异操作。

4.终止条件

5.免疫优化算法具体步骤

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