EMO_2.m

% electro-magnetism algorithm
% written by Mojtaba Eslami

clear all

n = 2;
MaxIter = 100*n;
LSIter = 10;
m = 40;
delta = 0.01;
lk = -5.12;
uk = 5.12;

Length = delta*(uk-lk);

% generation of initial random vectors
for i=1:m 
    lambda = rand(2,1);
    x(:,i) = lk+lambda*(uk-lk);
    f(i) = 20+x(1,i)^2+x(2,i)^2-10*cos(2*pi*x(1,i))-10*cos(2*pi*x(2,i));
end

X = [-5.12:0.01:5.12];
Y = [-5.12:0.01:5.12];
for i=1:length(X)
    for j=1:length(Y)
        fun(i,j) = 20+X(i)^2+Y(j)^2-10*cos(2*pi*X(i))-10*cos(2*pi*Y(j));
    end
end
figure(1);clf;hold on
contour(X,Y,fun,10)
plot(x(1,:),x(2,:),'k.')
xlabel('x_1')
ylabel('x_2')
colormap(gray)
axis([-5.12 5.12 -5.12 5.12])
    
f_best(1) = min(f);

iteration = 1;
while iteration<MaxIter
    f_best(iteration) = min(f);

    % local search procedure
    counter = 1;
    for i=1:m
        lambda1 = rand;
        while counter<LSIter
            y = x(:,i);
            lambda2 = rand(2,1);
            if lambda1>0.5
                y = y+lambda2*Length;
            else
                y = y-lambda2*Length;
            end
            
            if 20+y(1,i)^2+y(2,i)^2-10*cos(2*pi*y(1,i))-10*cos(2*pi*y(2,i))<f(i)
                x(:,i) = y;
                counter = LSIter-1;
                f(i) = 20+x(1,i)^2+x(2,i)^2-10*cos(2*pi*x(1,i))-10*cos(2*pi*x(2,i));
            end
            counter = counter+1;
        end
    end
    index = find(f==min(f));
    x_best = x(:,index);
    
    % calculation of the total force vector
    for i=1:m
        q(i) = exp(-n*(f(i)-f(index))/sum(f-f(index)));
        F = zeros(2,m);
    end
    for i=1:m
        for j=1:m
            if f(j)<f(i)
                F(:,i) = F(:,i)+(x(:,j)-x(:,i))*q(i)*q(j)/(norm(x(:,j)-x(:,i))^2);
            elseif j~=i
                F(:,i) = F(:,i)-(x(:,j)-x(:,i))*q(i)*q(j)/(norm(x(:,j)-x(:,i))^2);
            end
        end
    end
    
    % movement according to the total force
    for i=1:m
        if i~=index
            lambda = rand;
            F(:,i) = F(:,i)/norm(F(:,i));
            for k=1:n
                if F(k,i)>0
                    x(k,i) = x(k,i)+lambda*F(k,i)*(uk-x(k,i));
                else
                    x(k,i) = x(k,i)+lambda*F(k,i)*(x(k,i)-lk);
                end
            end
        end
    end
    iteration = iteration+1;
    
    for i=1:m 
        f(i) = 20+x(1,i)^2+x(2,i)^2-10*cos(2*pi*x(1,i))-10*cos(2*pi*x(2,i));
    end

end

x_best

figure(2);clf;hold on
contour(X,Y,fun,10)
plot(x(1,:),x(2,:),'k.')
xlabel('x_1')
ylabel('x_2')
colormap(gray)
axis([-5.12 5.12 -5.12 5.12])
plot(x(1,:),x(2,:),'k.')

figure(3)
plot(f_best,'k.')
xlabel('iteration number')
ylabel('min f(x_1,x_2)')