function GAconstrain
% Genetic Algorithm(real coding)
% By: Javad Ivakpour
% E-mail: javad7@gmail.com
% May 2006
% Goal: find maximum of function that introduced in fun00.m file in current
% directory and can be plotted in plot00
% this file is also include the random serach for comparision
tic
clc
figure(1)
clf
clear all
format long
%------------------------ parameters ------------------------
% befor using this function you must specified your function in fun00.m
% file in current directory and then set the parameters
var=2; % Number of variables (this item must be equal to the
% number of variables that is used in the function in
% fun00.m file)
n=100; % Number of population
m0=30; % Number of generations that max value remains constant
% (use for termination criteria)
nmutationG=20; %number of mutation children(Gaussian)
nmutationR=20; %number of mutation children(random)
nelit=2; %number of elitism children
valuemin=ones(1,var)*-5*pi; % min possible value of variables
valuemax=ones(1,var)*5*pi; % max possible value of variables
A=[1 1;-0.5 +1;1 -1;-1 -1]; % constrains: Ax+B>0
B=[5*pi 0 5*pi +5*pi+10];
%-------------------------------------------------------------------------
[r,c]=size(A);
if c~=var
disp('Number of columns in A must be equivalent to var')
A
var
return
end
nmutation=nmutationG+nmutationR;
sigma=(valuemax-valuemin)/10; %Parameter that related to Gaussian
% function and used in mutation step
max1=zeros(nelit,var);
parent=zeros(n,var);
cu=[valuemin(1) valuemax(1) valuemin(2) valuemax(2)];
for l=1:var
p(:,l)=valuemin(l)+rand(n,1).*(valuemax(l)-valuemin(l));
end
initial=p;
m=m0;
maxvalue=ones(m,1)*-1e10;
maxvalue(m)=-1e5;
g=0;
meanvalue(m)=0;
%------------- **** termination criteria ****-------------
while abs(maxvalue(m)-maxvalue(m-(m0-1)))>0.001*maxvalue(m) &...
(abs(maxvalue(m))>1e-10 & abs(maxvalue(m-(m0-1)))>1e-10)...
& m<10000 & abs(maxvalue(m)-meanvalue(m))>1e-5 | m<20
sigma=sigma./(1.05);% reducing the sigma value
% ------ **** % reducing the number of mutation()random **** ----
g=g+1;
if g>10 & nmutationR>0
g=0;
nmutationR=nmutationR-1;
nmutation=nmutationG+nmutationR;
end
%------------- **** function evaluation ****-------------
for i=1:n
y(i)=fun00(p(i,:));
flag(i)=0;
end
if var==2
figure(1)
hold off
plot00(cu)
hold on
plot3(p(:,1),p(:,2),y,'ro')
title({'Genetic Algorithm: constrained problem'...
,'Performance of GA ( o : each individual)',...
'blue o:possible solution & red o impossible solution ',...
'black o: best solution'},'color','b')
end
s=sort(y);
maxy=max(y);
miny=min(y);
for i=1:n
k=length(B);
for j=1:k
x=p(i,:);
if (A(j,:)*x'+B(j))<=0
y(i)=miny;
flag(i)=1;
end
end
end
if var==2
for i=1:n
if flag(i)==0
plot3(p(i,1),p(i,2),y(i),'bo')
end
end
end
s=sort(y);
maxvalue1(1:nelit)=s(n:-1:n-nelit+1);
if nelit==0
maxvalue1(1)=s(n);
for i=1:n
if y(i)==maxvalue1(1)
max1(1,:)=p(i,:);
end
end
end
for k=1:nelit
for i=1:n
if y(i)==maxvalue1(k)
max1(k,:)=p(i,:);
end
end
end
if var==2
hold on
plot3(max1(1,1),max1(1,2),maxvalue1(1),'kh')
end
y=y-min(y)*1.02;
sumd=y./sum(y);
meanvalue=y./(sum(y)/n);
%------------- **** Selection: Rolette wheel ****-------------
for l=1:n
sel=rand;
sumds=0;
j=1;
while sumds<sel
sumds=sumds+sumd(j);
j=j+1;
end
parent(l,:)=p(j-1,:);
end
p=zeros(n,var);
%------------- **** regeneration ****-------------
for l=1:var
%------------- **** cross-over ****-------------
for j=1:ceil((n-nmutation-nelit)/2)
t=rand*1.5-0.25;
p(2*j-1,l)=t*parent(2*j-1,l)+(1-t)*parent(2*j,l);
p(2*j,l)=t*parent(2*j,l)+(1-t)*parent(2*j-1,l);
end
%------------- **** elitism ****-------------
for k=1:nelit
p((n-nmutation-k+1),l)=max1(k,l);
end
%------------- **** mutation ****-------------
for i=n-nmutation+1:n-nmutationR
phi=1-2*rand;
z=erfinv(phi)*(2^0.5);
p(i,l)=z*sigma(l)+parent(i,l);
end
for i=n-nmutationR+1:n
p(i,1:var)=valuemin(1:var)+rand(1,var).*(valuemax(1:var)...
-valuemin(1:var));
end
for i=1:n
for l=1:var
if p(i,l)<valuemin(l)
p(i,l)=valuemin(l);
elseif p(i,l)>valuemax(l)
p(i,l)=valuemax(l);
end
end
end
end
p;
m=m+1;
max1;
maxvalue(m)=maxvalue1(1);
maxvalue00(m-m0)=maxvalue1(1);
mean00(m-m0)=sum(s)/n;
meanvalue(m)=mean00(m-m0);
figure(1)
if var~=2
hold off
plot(maxvalue00)
hold on
plot(mean00,'g')
hold on
title({'Performance of GA',...
'best value GA:blue, mean value GA:green',''}...
,'color','b')
xlabel('number of generations')
ylabel('value')
end
pause(0.001)
end
clc
disp(' Genetic Algorithm(real coding) ')
disp(' By: Javad Ivakpour ')
disp(' E-mail: javad7@gmail.com ')
disp('**************************************')
num_of_fun_evaluation=n*m
max_point_GA=max1(1,:)
maxvalue_GA=maxvalue00(m-m0)
if var==2
figure(1)
hold on
plot3(max1(1,1),max1(1,2),maxvalue1,'yp')
hold on
end
figure(2)
title('Performance of GA(best value)','color','b')
xlabel('number of generations')
ylabel('max value of best solution')
hold on
plot(maxvalue00)
hold on
toc