SA_2.m

% written by Mojtaba Eslami

clear all

ul = -5; % lower bound of design variables
uh = 5; % higher bound of design variables

x = [ul:0.1:uh];
y = [ul:0.1:uh];
for i=1:length(x)
    for j=1:length(y)
        f(i,j) = 20+x(i)^2+y(j)^2-10*(cos(2*pi*x(i))+cos(2*pi*y(j)));
    end
end

figure(1);clf;hold on
contour(x,y,f,10)
xlabel('x_1')
ylabel('x_2')

axis([ul uh ul uh])
colormap(gray)

c = .5; % temperature reduction factor
n = 50; % % number of iterations before temperature reduction (n is used instead of the parameter m)


% estimating the value of T
x1 = ul+rand(10,1)*uh; % ten random numbers are generated for x1
x2 = ul+rand(10,1)*uh; % ten random numbers are generated for x2

f = 20+x1.^2+x2.^2-10*(cos(2*pi*x1)+cos(2*pi*x2));
T = abs(mean(f));

p = 1; %cycle number
i = 1; %iteration number
vicinity_radius = 2;


X = ul+(uh-ul)*rand(2,1);
X_best = X;
fbest(1) = 1000;

while p<200
    f = 20+X(1).^2+X(2).^2-10*(cos(2*pi*X(1))+cos(2*pi*X(2)));
    
    X_new(1) = max(X(1)-vicinity_radius,ul)+rand*(min(X(1)+vicinity_radius,uh)-max(X(1)-vicinity_radius,ul));
    X_new(2) = max(X(2)-vicinity_radius,ul)+rand*(min(X(2)+vicinity_radius,uh)-max(X(2)-vicinity_radius,ul));
        
    f_new = 20+X_new(1).^2+X_new(2).^2-10*(cos(2*pi*X_new(1))+cos(2*pi*X_new(2)));
    
    % accept or reject X_new using Metropolis criterion
    if f_new<f
        X = X_new;
        
        %saving the results
        if f_new<min(fbest)
            X_best = X;
            fbest(p) = min(min(fbest),f_new);
        end
        
    elseif exp(-(f_new-f)/T)<rand
        X = X_new;
    end
    
        
    i = i+1;
    
    if i>=n
        fbest(p) = min(fbest);
        p = p+1;
        i = 1;
        T = c*T;
    end
    
end

X_best

figure(1)
plot(X_best(1),X_best(2),'k.')

figure(2)
plot(fbest,'k.')
xlabel('cycle number')
ylabel('min f(x_1,x_2)')