模拟退火算法(SA)、遗传算法(GA)、布谷鸟算法(CS)、人工蜂群算法(ABC)学习笔记—附MATLAB注释代码
clear
close
clc
%varnum 变量个数
%eps 精度
%lb ub 变量范围
%n 种群大小
%pc 交叉概率
%pm 变异概率
%M 动态线性变换
f = @(x) 11*sin(6*x) + 7*cos(5*x);%待求函数最大值优化问题的函数
%f = @(x) x*sin(10*pi*x)+2;
ezplot(f)
hold on
h = plot(0,0,'*');
varnum = 1;%%变量个数
n = 200; %%种群大小
eps = 1e-2;
pc = 0.9;%%交叉一般是0.4-0.9
pm = 0.01;%%变异概率
maxgen = 200;%%种群数量
q = 0.2;%%排序选择中的最好的个体选择概率
lb =-pi;%%函数自变量下限
ub =pi;%%函数自变量上限
%%初始化种群
for i = 1:varnum
L(i) = ceil(log2(ub(i)-lb(i)) / eps +1);%%ceil函数:朝正无穷大方向取整,L是每个自变量的编码长度
end
LS = sum(L);%%多个自变量时,是每个自变量的长度之和;LS是自变量组成的二进制编码总位长
pop = randi([0 1],n,LS);%%生成n行LS列的随机数,生成0或者1
spoint = cumsum([0 L]);%%cumsum计算数组各行的累加值
for iter = 1:maxgen
%% 将二进制转化为十进制
for i = 1:n
for j = 1:varnum
startpoint = spoint(j) + 1;
endpoint = spoint(j+1);
real(i,j) = decode(pop(i,startpoint:endpoint),lb(j),ub(j));
end
end
%% 计算适应度值
fitvalue = fitnessfun(real);
fval = objfun(real);
h.XData = real;
h.YData = fval;
pause(0.051)
%%轮盘赌选择
%%[dad,mom] = selection(pop,fitvalue);
%%排序选择
%%选择
[dad,mom] = sortselection(pop,fitvalue,q);
%%交叉
newpop = crossover(dad,mom,pc);
%%变异
newpop = mutation(newpop,pm);
pop = newpop;
end
for i = 1:n
for j = 1:varnum
startpoint = spoint(j) + 1;
endpoint = spoint(j+1);
real(i,j) = decode(pop(1,startpoint:endpoint),lb(j),ub(j));%%把最后的种群计算成十进制数
end
end
fitvalue = fitnessfun(real);%%计算适应度的值
[bestfitness,bestindex] = max(fitvalue)%%找到最好的适应度
bestindividual = real(bestindex,:)
fval = objfun(bestindividual)%%计算最好的目标函数值
plot(bestindividual,fval,'*')%%绘制点
function fitvalue = fitnessfun(x)
Cmin = 0.01;
[row,~] = size(x);
for i = 1:row
fval = objfun(x(i,:));
if fval + Cmin > 0
fitvalue(i) = fval + Cmin;
else
fitvalue(i) = 0;
end
end
function real = decode(pop,lb,ub)
%% pop种群
%% varnum 变量个数
[~,col] = size(pop);
for j = col:-1:1
temp(j) = 2^(j-1)*pop(j);%%计算二进制数
end
temp = sum(temp);
real = lb + temp *(ub - lb)/(2^col-1);
end
function [dad,mom] = selection(pop,fitvalue)
%%轮盘赌选择算法
%% 计算累加概率
PP = cumsum(fitvalue ./ sum(fitvalue) );
[row,~] = size(pop);
%% 选择出row个个体,轮盘赌的方式
for i = 1:row
for j = 1:row
r = rand;
if r <= PP(j)
dad(i,:) = pop(j,:);
break;
end
end
mom(i,:) = pop(randi([1 row]),:);
end
function [dad,mom] = sortselection(pop,fitvalue,q)
[row,~] = size(pop);
[~,Sindex] = sort(fitvalue,'descend');%%按照适应度高低排序
pop = pop(Sindex,:);
%%每个个体被选中的概率
P = q*(1-q).^((1:row)-1)/(1-(1-q)^row);
%%种群被选中的累计概率
PP = cumsum(P);
%%选择出row个个体
for i = 1:row
for j = 1:row
r = rand;
if r <= PP(j)
dad(i,:) = pop(j,:);
break;
end
end
mom(i,:) = pop(randi([1 row]),:);
end
function newpop = crossover(dad,mom,pc)
[row,col] = size(dad);
for i = 1:row
if rand < pc %%生成的随机数小于交叉概率
cpoint = randi([1 col-1]);%%交叉点
%%把交叉点之前的父代和交叉点之后的母代进行组合
newpop(i,:) = [dad(i,1:cpoint) mom(i,cpoint+1:end)];
else
newpop(i,:) = dad(i,:);
end
end
function newpop = mutation(pop,pm)
[row,col] = size(pop);
newpop = zeros(row,col);
for i = 1:row
mpoint = randi([1 col]);%%变异的点
if rand < pm
newpop(i,:) = ~pop(1,mpoint);%%变异的位置取反
else
newpop(i,:) = pop(i,:);%%不发生变异
end
end
function fval = objfun(x)
%目标函数
fval = 11*sin(6*x) + 7*cos(5*x);
%fval = x*sin(10*pi*x)+2;
两个算子的选择结果稍微有点不一样,根据图像显然可见,在横坐标1.3附近取得最大值,排序选择的结果比较好
1.轮盘赌选择算子结果:
[外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接
2.排序选择算子结果
遗传算法(Genetic Algorithm)MATLAB案例详细解析代码以及PPT.zip