NSGA-Ⅱ算法 matlab代码

NSGA-II（Non-dominated Sorting Genetic Algorithm II）是一种常用的多目标优化算法，它是基于遗传算法的一种改进算法。NSGA-II算法通过非支配排序和拥挤度距离来维护种群的多样性，从而有效地解决了多目标优化问题。下面是NSGA-II算法的Matlab代码实现：

function [pop,fit] = nsga2(pop,fit,n,m,popsize,pcross,pmut)

% NSGA-II算法
% 输入：
% pop - 种群
% fit - 种群适应度
% n - 变量个数
% m - 目标个数
% popsize - 种群大小
% pcross - 交叉概率
% pmut - 变异概率
% 输出：
% pop - 新种群
% fit - 新种群适应度

% 计算拥挤度距离
function d = crowding_distance(f)
    [m,n] = size(f);
    d = zeros(m,1);
    for i = 1:n
        [~,idx] = sort(f(:,i));
        d(idx(1)) = inf;
        d(idx(end)) = inf;
        for j = 2:m-1
            d(idx(j)) = d(idx(j)) + (f(idx(j+1),i)-f(idx(j-1),i))/(f(idx(end),i)-f(idx(1),i));
        end
    end
end

% 非支配排序
function [F,S] = non_domination_sort(f)
    [m,n] = size(f);
    F{1} = [];
    S{1} = zeros(m,1);
    n(1) = 0;
    for p = 1:m
        S{1}(p) = 0;
        for q = 1:m
            if all(f(q,:)<=f(p,:)) && any(f(q,:)<f(p,:))
                S{1}(p) = S{1}(p) + 1;
            end
        end
        if S{1}(p) == 0
            F{1} = [F{1} p];
            n(1) = n(1) + 1;
        end
    end
    i = 1;
    while ~isempty(F{i})
        Q = [];
        for p = F{i}
            for q = 1:m
                if all(f(q,:)<=f(p,:)) && any(f(q,:)<f(p,:))
                    S{1}(q) = S{1}(q) - 1;
                    if S{1}(q) == 0
                        Q = [Q q];
                        n(i+1) = n(i+1) + 1;
                    end
                end
            end
        end
        i = i + 1;
        F{i} = Q;
    end
end

% 选择操作
function [pop,fit] = selection(pop,fit,n,m,popsize)
    [m,n] = size(fit);
    F = non_domination_sort(fit);
    newpop = [];
    newfit = [];
    i = 1;
    while length(newpop) + length(F{i}) <= popsize
        % 按拥挤度距离排序
        cd = crowding_distance(fit(F{i},:));
        [~,idx] = sort(cd,'descend');
        newpop = [newpop; pop(F{i}(idx),:)];
        newfit = [newfit; fit(F{i}(idx),:)];
        i = i + 1;
    end
    if length(newpop) < popsize
        cd = crowding_distance(fit(F{i},:));
        [~,idx] = sort(cd,'descend');
        newpop = [newpop; pop(F{i}(idx(1:popsize-length(newpop))),:)];
        newfit = [newfit; fit(F{i}(idx(1:popsize-length(newpop))),:)];
    end
    pop = newpop;
    fit = newfit;
end

% 交叉操作
function pop = crossover(pop,pcross)
    [m,n] = size(pop);
    for i = 1:2:m
        if rand < pcross
            j = randi(n-1);
            pop(i:i+1,j+1:end) = pop(i+1:-1:i,j+1:end);
        end
    end
end

% 变异操作
function pop = mutation(pop,pmut)
    [m,n] = size(pop);
    for i = 1:m
        if rand < pmut
            j = randi(n);
            pop(i,j) = rand;
        end
    end
end

% 主程序
pop = rand(popsize,n);
fit = zeros(popsize,m);
for i = 1:popsize
    fit(i,:) = objfun(pop(i,:));
end
for i = 1:100
    pop = [pop; crossover(pop,pcross)];
    pop = mutation(pop,pmut);
    for j = popsize+1:size(pop,1)
        fit(j,:) = objfun(pop(j,:));
    end
    [pop,fit] = selection(pop,fit,n,m,popsize);
end

end

其中，objfun是目标函数，需要根据具体问题进行定义。在使用该代码时，需要将objfun替换为自己定义的目标函数，并设置好其他参数。此外，该代码实现了非支配排序、拥挤度距离和选择操作，可以有效地维护种群的多样性。