nsga-2算法

function f = non_domination_sort(x,M,V) [xsize,ysize]=size(x); front = 1; F(front).f = []; individual = []; for i = 1:xsize individual(i).n = 0; individual(i).p = []; for j=1:xsize less=0; equal=0; more=0; for k =1:M if (x(i,V + k) < x(j,V + k)) less=less+1; elseif (x(i,V + k) == x(j,V + k)) equal=equal+1; else more=more+1; end end if less==0 && equal ~=M individual(i).n = individual(i).n+1; elseif more==0 && equal ~=M individual(i).p=[individual(i).p j]; end end if individual(i).n == 0 x(i,M + V + 1) = 1; F(front).f = [F(front).f i]; end end while ~isempty(F(front).f) Q = []; for i = 1 : length(F(front).f) if ~isempty(individual(F(front).f(i)).p) for j = 1 : length(individual(F(front).f(i)).p) individual(individual(F(front).f(i)).p(j)).n = ... individual(individual(F(front).f(i)).p(j)).n - 1; if individual(individual(F(front).f(i)).p(j)).n == 0 x(individual(F(front).f(i)).p(j),M + V + 1) = ... front + 1; Q = [Q individual(F(front).f(i)).p(j)]; end end end end front = front + 1; F(front).f = Q; end %?注意这里是否要删除F(front).f的最后一个,因为最后一个为空 [temp,index_of_fronts] = sort(x(:,M + V + 1)); %temp是矩阵x第M+V+1列元素的升序排序后结果，x保持不变，index_of_fronts是temp中每一项对应x中的索引 for i = 1 : length(index_of_fronts) sorted_based_on_front(i,:) = x(index_of_fronts(i),:); %矩阵x中所有行按front排序 end current_index = 0; %% 拥挤距离 % Find the crowding distance for each individual in each front %对每一层 for front = 1 : (length(F) - 1)%前面length(F)最后一个数为空，所以这里要减1 %objective = []; distance = 0; y = []; previous_index = current_index + 1; %取出该层 for i = 1 : length(F(front).f) y(i,:) = sorted_based_on_front(current_index + i,:); end current_index = current_index + i; % Sort each individual based on the objective sorted_based_on_objective = []; for i = 1 : M %对每一个目标函数值进行升序排序 [sorted_based_on_objective, index_of_objectives] = sort(y(:,V + i)); sorted_based_on_objective = []; for j = 1 : length(index_of_objectives) sorted_based_on_objective(j,:) = y(index_of_objectives(j),:); end f_max = sorted_based_on_objective(length(index_of_objectives), V + i); f_min = sorted_based_on_objective(1, V + i); y(index_of_objectives(length(index_of_objectives)),M + V + 1 + i) = Inf; y(index_of_objectives(1),M + V + 1 + i) = Inf; for j = 2 : length(index_of_objectives) - 1 next_obj = sorted_based_on_objective(j + 1,V + i); previous_obj = sorted_based_on_objective(j - 1,V + i); if (f_max - f_min == 0) y(index_of_objectives(j),M + V + 1 + i) = Inf; else y(index_of_objectives(j),M + V + 1 + i) = (next_obj - previous_obj)/(f_max - f_min); end end end distance = []; distance(:,1) = zeros(length(F(front).f),1); for i = 1 : M distance(:,1) = distance(:,1) + y(:,M + V + 1 + i); end y(:,M + V + 2) = distance; y = y(:,1 : M + V + 2); z(previous_index:current_index,:) = y; end f = z();