非支配排序算法通用MATLAB代码

function [FrontNO,MaxFNO] = NDSort(PopObj,nSort)
%NDSort - Do non-dominated sorting on the population by ENS
 
%
 
%   FrontNO = NDSort(A,s) does non-dominated sorting on A, where A is a
 
%   matrix which stores the objective values of all the individuals in the
 
%   population, and s is the number of individuals being sorted at least.
 
%   FrontNO(i) means the number of front of the i-th individual.
 
%
 
%   [FrontNO,K] = NDSort(...) also returns the maximum number of fronts,
 
%   except for the value of inf.
 
%
 
%   In particular, s = 1 stands for find only the first non-dominated
 
%   front, s = size(A,1)/2 stands for sort only half of the population
 
%   (which is often used in the algorithm), and s = inf stands for sort the
 
%   whole population.
 
%
 
%   Example:
 
%       [FrontNO,MaxFNO] = NDSort(PopObj,1)
 
 
    [N,M] = size(PopObj);
    
    FrontNO = inf(1,N);
    MaxFNO  = 0;
    [PopObj,rank] = sortrows(PopObj);
    while sum(FrontNO<inf) < min(nSort,N)
        MaxFNO = MaxFNO + 1;
        for i = 1 : N
            if FrontNO(i) == inf
                Dominated = false;
                for j = i-1 : -1 : 1
                    if FrontNO(j) == MaxFNO
                        m = 2;
                        while m <= M && PopObj(i,m) >= PopObj(j,m)
                            m = m + 1;
                        end
                        Dominated = m > M;
                        if Dominated || M == 2
                            break;
                        end
                    end
                end
                if ~Dominated
                    FrontNO(i) = MaxFNO;
                end
            end
        end
    end
    FrontNO(rank) = FrontNO;
end