ABC_2.m

% written by Mojtaba Eslami
clear all

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

x = [ul:0.01:uh];
y = [ul:0.01: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)

figure(2);clf;hold on
contour(x,y,f,10)
xlabel('x_1')
ylabel('x_2')

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

SN = 30; % number of bees in colony
n = 2;   % number of varibles of the optimization problem
a = .1;

% initialization
x = ul+(uh-ul)*rand(n,SN);

figure(1)
plot(x(1,:),x(2,:),'k.')

lim = 10;

for k=1:1000
    
    % setting the position of employed bees
    for z=1:SN
        temp = ceil(SN*rand);
        v(1,z) = x(1,z)+(-a+2*a*rand).*(x(1,z)-x(1,ceil(SN*rand)));
        while temp==z
            temp = ceil(SN*rand);
            v(1,z) = x(1,z)+(-a+2*a*rand).*(x(1,z)-x(1,ceil(SN*rand)));
        end
        
        temp = ceil(SN*rand);
        v(2,z) = x(2,z)+(-a+2*a*rand).*(x(2,z)-x(2,ceil(SN*rand)));
        while temp==z
            temp = ceil(SN*rand);
            v(2,z) = x(2,z)+(-a+2*a*rand).*(x(2,z)-x(2,ceil(SN*rand)));
        end
    end
    
    % calculation of the fitness function
    temp1 = 20+x(1,:).^2+x(2,:).^2-10*(cos(2*pi*x(1,:))+cos(2*pi*x(2,:)));
    
    % onlooker bees
    for z=1:length(temp1)
        if temp1(z)>=0
            fitness(z) = 1/(1+temp1(z));
        else
            fitness(z) = 1+abs(temp1(z));
        end
    end
    
    pm = fitness/sum(fitness);
    
    % saving the best results obtained so far
    fbest(k) = min(20+x(1,:).^2+x(2,:).^2-10*(cos(2*pi*x(1,:))+cos(2*pi*x(2,:))));
    
    % calculation of the best solution obtained so far
    if fbest(k)<=min(fbest)
        x_best = v(:,find(fitness==max(fitness),1));
    else
        fbest(k) = min(fbest);
    end
    
    % implementation of the roulette-wheel
    for z = 1:SN 
        s = 0;
        temp = rand;
        count = 0;
        while s<temp
            s = s+pm(count+1);
            count = count+1;
        end
        x(:,z) = v(:,count); %assignment of the new positions
    end
    
    
    
    % check if the bees find better solutions or not. If not, they should be
    % changed to scout bees
    if k>lim && all(diff(fbest(end-lim:end)))==0
        x = ul+(uh-ul)*rand(n,SN);
    end
end

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

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

x_best