nsga2算法中合并子代和父代种群，然后进行排序精英选择的matlab代码示例

以下是一个简单的NSGA-II算法的Matlab代码示例，包括合并种群、非支配排序、拥挤度距离计算和选择：

function [pop] = nsga2(pop, pop_child, n, m)
% pop: 父代种群
% pop_child: 子代种群
% n: 种群大小
% m: 目标函数个数

% 合并种群
pop = [pop; pop_child];

% 非支配排序
front = nondominated_sort(pop, n, m);

% 计算拥挤度距离
cd = crowding_distance(pop, front, n, m);

% 选择
pop = selection(pop, front, cd, n, m);
end

function [front] = nondominated_sort(pop, n, m)
% 非支配排序

% 初始化
front(1).f = [];
sp(1:n) = 0;
np(1:n) = 0;

for i=1:n
    front(i).f = [];
    sp(i) = 0;
    np(i) = 0;
end

% 计算支配关系
for i=1:n
    for j=1:n
        if i~=j
            dom = dominance(pop(i,:), pop(j,:), m);
            if dom == 1
                sp(i) = sp(i) + 1;
            elseif dom == -1
                np(i) = np(i) + 1;
            end
        end
    end
    if sp(i) == 0
        front(1).f = [front(1).f i];
    end
end

% 非支配排序
i = 1;
while ~isempty(front(i).f)
    Q = [];
    for j=1:length(front(i).f)
        p = front(i).f(j);
        for k=1:n
            if (p~=k) && (sp(k)>0)
                sp(k) = sp(k) - 1;
                if sp(k) == 0
                    Q = [Q k];
                end
            end
        end
    end
    i = i + 1;
    front(i).f = Q;
end
end

function [dom] = dominance(x, y, m)
% 判断x是否支配y

dom = 0;
less_eq_cnt = 0;
less_cnt = 0;

for i=1:m
    if x(i) <= y(i)
        less_eq_cnt = less_eq_cnt + 1;
    end
    if x(i) < y(i)
        less_cnt = less_cnt + 1;
    end
end

if less_cnt == 0 && less_eq_cnt < m
    dom = 1; % x支配y
end

if less_cnt < m && less_eq_cnt == m
    dom = -1; % y支配x
end
end

function [cd] = crowding_distance(pop, front, n, m)
% 计算拥挤度距离

cd = zeros(n,1);

for f=1:length(front)
    fsize = length(front(f).f);
    if fsize > 0
        for i=1:m
            temp = pop(front(f).f,:);
            temp = sortrows(temp,i);
            cd(front(f).f(1)) = Inf;
            cd(front(f).f(fsize)) = Inf;
            for j=2:fsize-1
                cd(front(f).f(j)) = cd(front(f).f(j)) + (temp(j+1,i) - temp(j-1,i))/(temp(fsize,i) - temp(1,i));
            end
        end
    end
end
end

function [pop] = selection(pop, front, cd, n, m)
% 选择

pop_new = [];
next_front = 1;
cnt = 0;

while cnt < n
    if ~isempty(front(next_front).f)
        if cnt + length(front(next_front).f) <= n
            % 将此层全部选入
            temp = pop(front(next_front).f,:);
            pop_new = [pop_new; temp];
            cnt = cnt + length(front(next_front).f);
            next_front = next_front + 1;
        else
            % 按照拥挤度距离排序，并选取前n-cnt个
            temp = pop(front(next_front).f,:);
            [~,index] = sort(cd(front(next_front).f),'descend');
            temp = temp(index,:);
            pop_new = [pop_new; temp(1:n-cnt,:)];
            cnt = n;
        end
    else
        break;
    end
end

pop = pop_new;
end

其中，`pop`和`pop_child`分别为父代和子代种群，`n`为种群大小，`m`为目标函数个数。`nondominated_sort`函数计算非支配排序，`dominance`函数判断支配关系，`crowding_distance`函数计算拥挤度距离，`selection`函数进行选择。最后，将`pop`作为算法的输出即可。

请注意，该示例代码仅供参考，具体实现可能需要根据实际情况进行调整。