非支配排序代码matlab

非支配排序（Non-dominated sorting）是多目标优化中常用的一种技术。Matlab中可以使用NSGA-II工具箱进行非支配排序，代码如下：

% 定义目标函数
function [y1,y2] = myObjectives(x1,x2)
    y1 = x1.^2;
    y2 = (x1-2).^2 + x2.^2;
end

% 定义非支配排序算法
function result = nonDominatedSorting(population)
    N = length(population);
    F = cell(N,1);
    n = zeros(N,1);
    S = cell(N,1);
    rank = zeros(N,1);
    for p=1:N
        S{p} = [];
        n(p) = 0;
        for q=1:N
            if dominates(population(p,:),population(q,:))
                S{p} = [S{p},q];
            elseif dominates(population(q,:),population(p,:))
                n(p) = n(p) + 1;
            end
        end
        if n(p) == 0
            rank(p) = 1;
            F{1} = [F{1},p];
        end
    end
    i = 1;
    while ~isempty(F{i})
        Q = [];
        for p=F{i}
            for q=S{p}
                n(q) = n(q) - 1;
                if n(q) == 0
                    rank(q) = i+1;
                    Q = [Q,q];
                end
            end
        end
        i = i + 1;
        F{i} = Q;
    end
    result.rank = rank;
    result.F = F(1:i-1);
end

% 定义支配关系
function result = dominates(a,b)
    result = all(a <= b) && any(a < b);
end

% 测试非支配排序
population = rand(50,2);
result = nonDominatedSorting(population);
for i=1:length(result.F)
    disp(result.F{i})
end