function chromo_offspring = cross_mutation( chromo_parent,f_num,x_num,x_min,x_max,pc,pm,yita1,yita2,fun )
%模拟二进制交叉与多项式变异
[pop,~]=size(chromo_parent);
suoyin=1;
for i=1:pop
%%%模拟二进制交叉
%初始化子代种群
%随机选取两个父代个体
parent_1=round(pop*rand(1));
if (parent_1<1)
parent_1=1;
end
parent_2=round(pop*rand(1));
if (parent_2<1)
parent_2=1;
end
%确定两个父代个体不是同一个
while isequal(chromo_parent(parent_1,:),chromo_parent(parent_2,:))
parent_2=round(pop*rand(1));
if(parent_2<1)
parent_2=1;
end
end
chromo_parent_1=chromo_parent(parent_1,:);
chromo_parent_2=chromo_parent(parent_2,:);
off_1=chromo_parent_1;
off_2=chromo_parent_1;
if(rand(1)<pc)
%进行模拟二进制交叉
u1=zeros(1,x_num);
gama=zeros(1,x_num);
for j=1:x_num
u1(j)=rand(1);
if u1(j)<0.5
gama(j)=(2*u1(j))^(1/(yita1+1));
else
gama(j)=(1/(2*(1-u1(j))))^(1/(yita1+1));
end
off_1(j)=0.5*((1+gama(j))*chromo_parent_1(j)+(1-gama(j))*chromo_parent_2(j));
off_2(j)=0.5*((1-gama(j))*chromo_parent_1(j)+(1+gama(j))*chromo_parent_2(j));
%使子代在定义域内
if(off_1(j)>x_max(j))
off_1(j)=x_max(j);
elseif(off_1(j)<x_min(j))
off_1(j)=x_min(j);
end
if(off_2(j)>x_max(j))
off_2(j)=x_max(j);
elseif(off_2(j)<x_min(j))
off_2(j)=x_min(j);
end
end
%计算子代个体的目标函数值
off_1(1,(x_num+1):(x_num+f_num))=object_fun(off_1,f_num,x_num,fun);
off_2(1,(x_num+1):(x_num+f_num))=object_fun(off_2,f_num,x_num,fun);
end
%%%多项式变异
if(rand(1)<pm)
u2=zeros(1,x_num);
delta=zeros(1,x_num);
for j=1:x_num
u2(j)=rand(1);
if(u2(j)<0.5)
delta(j)=(2*u2(j))^(1/(yita2+1))-1;
else
delta(j)=1-(2*(1-u2(j)))^(1/(yita2+1));
end
off_1(j)=off_1(j)+delta(j);
%使子代在定义域内
if(off_1(j)>x_max(j))
off_1(j)=x_max(j);
elseif(off_1(j)<x_min(j))
off_1(j)=x_min(j);
end
end
%计算子代个体的目标函数值
off_1(1,(x_num+1):(x_num+f_num))=object_fun(off_1,f_num,x_num,fun);
end
if(rand(1)<pm)
u2=zeros(1,x_num);
delta=zeros(1,x_num);
for j=1:x_num
u2(j)=rand(1);
if(u2(j)<0.5)
delta(j)=(2*u2(j))^(1/(yita2+1))-1;
else
delta(j)=1-(2*(1-u2(j)))^(1/(yita2+1));
end
off_2(j)=off_2(j)+delta(j);
%使子代在定义域内
if(off_2(j)>x_max(j))
off_2(j)=x_max(j);
elseif(off_2(j)<x_min(j))
off_2(j)=x_min(j);
end
end
%计算子代个体的目标函数值
off_2(1,(x_num+1):(x_num+f_num))=object_fun(off_2,f_num,x_num,fun);
end
off(suoyin,:)=off_1;
off(suoyin+1,:)=off_2;
suoyin=suoyin+2;
end
chromo_offspring=off;
end
import numpy as np
import random
"""
SBX 模拟二进制交叉
SBX主要是模拟基于二进制串的单点交叉工作原理,将其作用于以实数表示的染色体。
两个父代染色体经过交叉操作产生两个子代染色体,使得父代染色体的有关模式信息在子代染色体中得以保留。
输入:
population 种群规模
alfa 交叉概率
numRangeList 决策变量上限
mu是一个(0,1)的随机数
"""
def cross(population, alfa, numRangeList, mu=1):
N = population.shape[0]
V = population.shape[1]
populationList = range(N)
for _ in range(N):
r = random.random()
if r < alfa:
p1, p2 = random.sample(populationList, 2)
beta = np.array([0] * V)
randList = np.random.random(V)
for j in range(V):
if randList.any() <= 0.5:
beta[j] = (2.0 * randList[j]) ** (1.0 / (mu + 1))
else:
beta[j] = (1.0 / (2.0 * (1 - randList[j]))) ** (1.0 / (mu + 1))
# 随机选取两个个体
old_p1 = population[p1,]
old_p2 = population[p2,]
# 交叉
new_p1 = 0.5 * ((1 + beta) * old_p1 + (1 - beta) * old_p2)
new_p2 = 0.5 * ((1 - beta) * old_p1 + (1 + beta) * old_p2)
# 上下界判断
new_p1 = np.max(np.vstack((new_p1, np.array([0] * V))), 0)
new_p1 = np.min(np.vstack((new_p1, numRangeList)), 0)
new_p2 = np.max(np.vstack((new_p2, np.array([0] * V))), 0)
new_p2 = np.min(np.vstack((new_p2, numRangeList)), 0)
# 将交叉后的个体返回给种群
population[p1,] = new_p1
population[p2,] = new_p2
if __name__ == '__main__':
random.seed(0)
np.random.seed(0)
xN = 10
yN = 5
alfa = 0.9
population = np.random.rand(xN * yN).reshape(xN, yN) * 1.0
print('交叉前:')
print(population)
# 交叉
cross(population, alfa, np.array([1] * 5))
print('交叉后:')
print(population)
SBX(Simulated binary crossover)模拟二进制交叉算子和DE(differential evolution)差分进化算子
SBX的python实现