SCA.m

%  Sine Cosine Algorithm (SCA)  
%
%  Source codes demo version 1.0                                                                      
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%  Developed in MATLAB R2011b(7.13)                                                                   
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%  Author and programmer: Seyedali Mirjalili                                                          
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%         e-Mail: ali.mirjalili@gmail.com                                                             
%                 seyedali.mirjalili@griffithuni.edu.au                                               
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%       Homepage: http://www.alimirjalili.com                                                         
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%  Main paper:                                                                                        
%  S. Mirjalili, SCA: A Sine Cosine Algorithm for solving optimization problems
%  Knowledge-Based Systems, DOI: http://dx.doi.org/10.1016/j.knosys.2015.12.022
%_______________________________________________________________________________________________
% You can simply define your cost function in a seperate file and load its handle to fobj 
% The initial parameters that you need are:
%__________________________________________
% fobj = @YourCostFunction
% dim = number of your variables
% Max_iteration = maximum number of iterations
% SearchAgents_no = number of search agents
% lb=[lb1,lb2,...,lbn] where lbn is the lower bound of variable n
% ub=[ub1,ub2,...,ubn] where ubn is the upper bound of variable n
% If all the variables have equal lower bound you can just
% define lb and ub as two single numbers

% To run SCA: [Best_score,Best_pos,cg_curve]=SCA(SearchAgents_no,Max_iteration,lb,ub,dim,fobj)
%______________________________________________________________________________________________


function [Destination_position,Destination_fitness,Convergence_curve]=SCA(N,Max_iter,lb,ub,dim,fobj)
% tic
if(max(size(ub)) == 1)
   ub = ub.*ones(1,dim);
   lb = lb.*ones(1,dim);  
end
%Initialize the set of random solutions
X=initialization_SSA(N,dim,ub,lb);

Destination_position=zeros(1,dim);
Destination_fitness=inf;
Objective_values = zeros(1,size(X,1));

Convergence_curve=[];

% Calculate the fitness of the first set and find the best one
for i=1:size(X,1)
    Objective_values(1,i)=fobj(X(i,:));
    if i==1
        Destination_position=X(i,:);
        Destination_fitness=Objective_values(1,i);
    elseif Objective_values(1,i)<Destination_fitness
        Destination_position=X(i,:);
        Destination_fitness=Objective_values(1,i);
    end
    
    All_objective_values(1,i)=Objective_values(1,i);
end

Convergence_curve(1) = Destination_fitness;

%Main loop
l=2; % start from the second iteration since the first iteration was dedicated to calculating the fitness
while l<=Max_iter+1
    
    % Eq. (3.4)
    a = 2;
    r1=a-l*((a)/Max_iter); % r1 decreases linearly from a to 0
    
    % Update the position of solutions with respect to destination
    for i=1:size(X,1) % in i-th solution
        for j=1:size(X,2) % in j-th dimension
            
            % Update r2, r3, and r4 for Eq. (3.3)
            r2=(2*pi)*rand();
            r3=2*rand;
            r4=rand();
            
            % Eq. (3.3)
            if r4<0.5
                % Eq. (3.1)
                X(i,j)= X(i,j)+(r1*sin(r2)*abs(r3*Destination_position(j)-X(i,j)));
            else
                % Eq. (3.2)
                X(i,j)= X(i,j)+(r1*cos(r2)*abs(r3*Destination_position(j)-X(i,j)));
            end
            
        end
    end
    
    for i=1:size(X,1)
         
       for j=1:dim
           if X(i,j)>ub(j)
               X(i,j)=ub(j);
           end
           if X(i,j)<lb(j)
               X(i,j)=lb(j);
           end
       end
        
        % Calculate the objective values
        Objective_values(1,i)=fobj(X(i,:));
        % Update the destination if there is a better solution
        if Objective_values(1,i)<Destination_fitness
            Destination_position=X(i,:);
            Destination_fitness=Objective_values(1,i);
        end
    end


    Convergence_curve(l)=Destination_fitness;
    l=l+1;
end
% toc
% disp(['The runtime of SCA: ',num2str(toc)]);