nsga2算法matlab代码

以下是NSGA-II算法的Matlab代码示例：

function [pop,front]=nsga2(pop,np,pc,pm,max_gen)

%初始化
pop=initialize_pop(np);
pop=evaluate_pop(pop);
pop=fast_nondominated_sort(pop);
[pop,crowd]=crowding_distance(pop);

%迭代开始
for i=1:max_gen
    %选择操作
    mating_pool=tournament_selection(pop,np);
    %交叉操作
    offspring=crossover(mating_pool,pc);
    %变异操作
    offspring=mutate(offspring,pm);
    %评估新一代个体
    offspring=evaluate_pop(offspring);
    %合并父代和子代种群
    combined_pop=[pop,offspring];
    %快速非支配排序
    combined_pop=fast_nondominated_sort(combined_pop);
    %计算拥挤度
    [combined_pop,crowd]=crowding_distance(combined_pop);
    %选择下一代个体
    pop=selection(combined_pop,np,crowd);
end

%最终的非支配层和拥挤度计算
pop=fast_nondominated_sort(pop);
[pop,front]=crowding_distance(pop);
end

%快速非支配排序
function pop=fast_nondominated_sort(pop)
n=length(pop);
for i=1:n
    pop(i).S=[];
    pop(i).n=0;
    for j=1:n
        if i~=j
            if dominates(pop(i),pop(j))
                pop(i).S=[pop(i).S,j];
            elseif dominates(pop(j),pop(i))
                pop(i).n=pop(i).n+1;
            end
        end
    end
    if pop(i).n==0
        pop(i).rank=1;
    end
end
front=1;
while ~isempty(find([pop.rank]==front, 1))
    Q=[];
    for i=1:n
        if pop(i).rank==front
            for j=1:length(pop(i).S)
                pop(pop(i).S(j)).n=pop(pop(i).S(j)).n-1;
                if pop(pop(i).S(j)).n==0
                    pop(pop(i).S(j)).rank=front+1;
                    Q=[Q,pop(i).S(j)];
                end
            end
        end
    end
    front=front+1;
end
end

%计算拥挤度
function [pop,crowd]=crowding_distance(pop)
n=length(pop);
for i=1:n
    pop(i).crowd=0;
end
for m=1:length(pop(1).obj)
    [pop,ord]=sort_population(pop,m);
    pop(ord(1)).crowd=inf;
    pop(ord(end)).crowd=inf;
    fmax=pop(end).obj(m);
    fmin=pop(1).obj(m);
    for i=2:n-1
        pop(i).crowd=pop(i).crowd+(pop(i+1).obj(m)-pop(i-1).obj(m))/(fmax-fmin);
    end
end
crowd=[pop.crowd];
end

%选择操作
function mating_pool=tournament_selection(pop,np)
n=length(pop);
mating_pool=repmat(pop(1),1,np);
for i=1:np
    p=randperm(n,2);
    if pop(p(1)).rank<pop(p(2)).rank
        mating_pool(i)=pop(p(1));
    elseif pop(p(1)).rank>pop(p(2)).rank
        mating_pool(i)=pop(p(2));
    else
        if pop(p(1)).crowd>pop(p(2)).crowd
            mating_pool(i)=pop(p(1));
        else
            mating_pool(i)=pop(p(2));
        end
    end
end
end

%交叉操作
function offspring=crossover(mating_pool,pc)
n=length(mating_pool);
offspring=repmat(mating_pool(1),1,n);
for i=1:2:n
    if rand<pc
        p=randperm(n,2);
        [offspring(i),offspring(i+1)]=cross(mating_pool(p(1)),mating_pool(p(2)));
    else
        offspring(i)=mating_pool(i);
        offspring(i+1)=mating_pool(i+1);
    end
end
end

%变异操作
function offspring=mutate(offspring,pm)
n=length(offspring);
for i=1:n
    if rand<pm
        offspring(i)=mut(offspring(i));
    end
end
end

%选择下一代个体
function pop=selection(combined_pop,np,crowd)
[~,ord]=sort_population(combined_pop,1);
pop=[];
i=1;
while length(pop)<np
    if combined_pop(ord(i)).rank==1
        pop=[pop,combined_pop(ord(i))];
    else
        break
    end
    i=i+1;
end
if length(pop)<np
    [~,ord]=sort(crowd(ord(i:end)),'descend');
    pop=[pop,combined_pop(ord(i-1+ord(1:np-length(pop))))];
end
end

%排序操作
function [pop,ord]=sort_population(pop,m)
fvals=[pop.obj];
[~,ord]=sort(fvals(m,:));
pop=pop(ord);
end

%判断是否支配
function flag=dominates(a,b)
flag=all(a.obj<=b.obj) && any(a.obj<b.obj);
end