基于群体划分的冠状病毒群体免疫优化算法

基于群体划分的冠状病毒群体免疫优化算法

李博群, 孙志锋

A Coronavirus Herd Immunity Optimizer Based on Swarm Division

LI Boqun, SUN Zhifeng

表1 基准测试函数

Tab.1 Function of benchmark test

函数名称	函数表达式	搜索范围
Sphere	F₁(x)= $\overset{D}{\sum_{j = 1}} x_{j}^{2}$	[-100, 100]
Schwefel P2.21	F₂(x)= $\underset{j = 1,2, \dots, D}{m a x} \|x_{j}\|$	[-100, 100]
Schwefel P2.22	F₃(x)= $\overset{D}{\sum_{j = 1}} \|x_{j}\|$ + $\overset{D}{\prod_{j = 1}} \|x_{j}\|$	[-10, 10]
Noise	F₄(x)= $\overset{D}{\sum_{j = 1}}$ j $x_{j}^{4}$ +random[0, 1)	[-100, 100]
Rastrigin	F₅(x)= $\overset{D}{\sum_{j = 1}} [x_{j}^{2} - 10 c o s (2 π x_{j}) + 10]$	[-5.12, 5.12]
Griewank	F₆(x)= $\frac{1}{4000} \overset{D}{\sum_{j = 1}} x_{j}^{2}$ - $\overset{D}{\prod_{j = 1}}$ cos $\frac{x_{j}}{\sqrt{j}}$ +1	[-600, 600]
Salomon	F₇(x)=-cos(2π $\sqrt{\overset{D}{\sum_{j = 1}} x_{j}^{2}}$ )+0.1 $\sqrt{\overset{D}{\sum_{j = 1}} x_{j}^{2}}$ +1	[-100, 100]
Ackley	F₈(x)=-20exp(-0.2 $\sqrt{\frac{1}{D} \overset{D}{\sum_{j = 1}} x_{j}^{2}}$ )-exp[ $\frac{1}{D} \overset{D}{\sum_{j = 1}}$ cos(2πx_j)]+20+e	[-32, 32]
Shifted Griewank	F₉(x)= $\frac{1}{4000} \overset{D}{\sum_{j = 1}}$ (x_j-o_j)²- $\overset{D}{\prod_{j = 1}}$ cos $\frac{x_{j} - o_{j}}{\sqrt{j}}$ +1	[-600, 600]
Shifted Ackley	F₁₀(x)=-20exp(-0.2 $\sqrt{\frac{1}{D} \overset{D}{\sum_{j = 1}} (x_{j} - o_{j})^{2}}$ )-exp[ $\frac{1}{D} \overset{D}{\sum_{j = 1}}$ cos 2π(x_j-o_j)]+20+e	[-32, 32]
Shifted+Rotated Rastrigin	F₁₁(x)= $\overset{D}{\sum_{j = 1}} [z_{j}^{2} - 10 c o s (2 π z_{j}) + 10]$ , z=M[0.051 2(x-o)]	[-100, 100]
Shifted+Rotated Levy	F₁₂(x)=sin²(πw₁)+ $\overset{D - 1}{\sum_{j = 1}}$ (w_j-1)² $[1 + 10 s i n^{2} (π w_{j} - 1)]$ +(w_D-1)² $[1 + s i n^{2} (2 π w_{D})]$ , w_j=1+ $\frac{z_{j} - 1}{4}$ , z=M[0.051 2(x-o)]	[-100, 100]