A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGA-II in Matlab

optimalfront.m

% FUNCTION TO FIND THE PARETO FRONT


function s = optimalfront(j)
L=length(j);    % Number of elements to compare
n=zeros(1,L);   % Number of times an object is dominated
h=[];           % First Pareto front
s=zeros(L);     % Show which elements are dominated by p
for p=1:1:L
       for q=1:1:L
           % P domina a Q
            if (j(1,p)<=j(1,q) && j(2,p)<=j(2,q)) && (j(1,p)<j(1,q) || j(2,p)<j(2,q))
                s(q,p)=1;
            % Q domina a P
            elseif (j(1,q)<=j(1,p) && j(2,q)<=j(2,p)) && (j(1,q)<j(1,p) || j(2,q)<j(2,p))
                n(p)=n(p)+1;
            end    
       end 
       if n(p)==0
           temp=[p;j(1,p);j(2,p)];
           h=[h temp];
       end
   
end
fop={h};
i=1;
flag=1; % Indicates that there is an optimal front i

while flag==1
    h=[];
    for p=1:1:size(fop{i},2);
            for q=1:1:L
                a=fop{i};
                a=a(1,p);
                    if s(q,a)==1
                       n(q)=n(q)-1;
                       if n(q)==0
                               temp=[q;j(1,q);j(2,q)];
                               h=[h temp];
                       end
                   end
            end
    end
    i=i+1;
    if size(h,1)~=0
        fop{i}=h;
    else
        flag=0;
    end
end

This algorithm was created by Kalyanmoy Deb, Samir Agrawal, Amrit Pratap, and T Meyarivan in this paper http://link.springer.com/chapter/10.1007%2F3-540-45356-3_83. This gist is only the implementation in Matlab

Thanks for the code. It helped a lot.