GA 算法 参数整定与对比

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% global rin yout timef pop = 500; %种群数量 gen = 100; %迭代次数 M = 2; %目标数量 V = 3; %维度 MinX(1) = 0*ones(1); %Kp MaxX(1) = 30*ones(1); MinX(2) = 0*ones(1); %Kp MaxX(2) = 1.0*ones(1); MinX(3) = 0*ones(1); %Kp MaxX(3) = 1.0*ones(1); min_range = [MinX(1) MinX(2) MinX(3)]; %下界 max_range = [MaxX(1) MaxX(2) MaxX(3)]; %上界 %% 初始化 chromosome = initialize_variables(pop, M, V, min_range, max_range); %对初始化种群进行非支配快速排序和拥挤度计算 chromosome = non_domination_sort_mod(chromosome, M, V); %% 主程序循环 for i = 1 : gen pool = round(pop/2); %交配池大小 tour = 2; %竞标赛，参赛选手个数 %竞标赛选择适合繁殖的父代 parent_chromosome = tournament_selection(chromosome, pool, tour); mu = 20; mum = 20; offspring_chromosome = genetic_operator(parent_chromosome,M, V, mu, mum, min_range, max_range); [main_pop,~] = size(chromosome); [offspring_pop,~] = size(offspring_chromosome); clear temp intermediate_chromosome(1:main_pop,:) = chromosome; intermediate_chromosome(main_pop + 1 : main_pop + offspring_pop,1 : M+V) = offspring_chromosome; intermediate_chromosome = non_domination_sort_mod(intermediate_chromosome, M, V); chromosome = replace_chromosome(intermediate_chromosome, M, V, pop); if ~mod(i,100) clc; fprintf('%d generations completed\n',i); end end figure(1); if M == 2 plot(chromosome(:,V + 1),chromosome(:,V + 2),'*'); xlabel('f_1'); ylabel('f_2'); title('Pareto Optimal Front'); elseif M == 3 plot3(chromosome(:,V + 1),chromosome(:,V + 2),chromosome(:,V + 3),'*'); xlabel('f_1'); ylabel('f_2'); zlabel('f_3'); title('Pareto Optimal Surface'); end figure(2); plot(timef,rin,'r',timef,yout,'b'); xlabel('Time(s)');ylabel('rin,yout'); %% //*******子程序initialize_variables**********// function f = initialize_variables(N, M, V, min_range, max_range) min = min_range; max = max_range; K = M + V; for i = 1 : N for j = 1 : V f(i,j) = min(j) + (max(j) - min(j))*rand(1); end Kpidi=f(i,:); %单个可行解 f(i,V + 1: K) = evaluate_objective(Kpidi, M, V); end end %% //*******子程序non_domination_sort_mod**********// function f = non_domination_sort_mod(x, M, V) [N, ~] = size(x); clear m front = 1; F(front).f = []; individual = []; for i = 1 : N individual(i).n = 0; individual(i).p = []; for j = 1 : N dom_less = 0; dom_equal = 0; dom_more = 0; for k = 1 : M if (x(i,V + k) < x(j,V + k)) dom_less = dom_less + 1; elseif (x(i,V + k) == x(j,V + k)) dom_equal = dom_equal + 1; else dom_more = dom_more + 1; end end if dom_less == 0 && dom_equal ~= M individual(i).n = individual(i).n + 1; elseif dom_more == 0 && dom_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 [temp,index_of_fronts] = sort(x(:,M + V + 1)); for i = 1 : length(index_of_fronts) sorted_based_on_front(i,:) = x(index_of_fronts(i),:); end current_index = 0; %% Crowding distance for front = 1 : (length(F) - 1) distance = 0; y = []; previous_index = current_index + 1; for i = 1 : length(F(front).f) y(i,:) = sorted_based_on_front(current_index + i,:); end current_index = current_index + i; sorted_based_on_objective = []; for i = 1 : M [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(); end %% //*******子程序tournament_selection**********// function f = tournament_selection(chromosome, pool_size, tour_size) [pop, variables] = size(chromosome); rank = variables - 1; distance = variables; for i = 1 : pool_size for j = 1 : tour_size candidate(j) = round(pop*rand(1)); if candidate(j) == 0 candidate(j) = 1; end if j > 1 while ~isempty(find(candidate(1 : j - 1) == candidate(j))) candidate(j) = round(pop*rand(1)); if candidate(j) == 0 candidate(j) = 1; end end end end for j = 1 : tour_size c_obj_rank(j) = chromosome(candidate(j),rank); c_obj_distance(j) = chromosome(candidate(j),distance); end min_candidate = ... find(c_obj_rank == min(c_obj_rank)); if length(min_candidate) ~= 1 max_candidate = ... find(c_obj_distance(min_candidate) == max(c_obj_distance(min_candidate))); if length(max_candidate) ~= 1 max_candidate = max_candidate(1); end f(i,:) = chromosome(candidate(min_candidate(max_candidate)),:); else f(i,:) = chromosome(candidate(min_candidate(1)),:); end end end %% //*******子程序genetic_operator**********// function f = genetic_operator(parent_chromosome, M, V, mu, mum, l_limit, u_limit) [N,m] = size(parent_chromosome); clear m p = 1; was_crossover = 0; was_mutation = 0; for i = 1 : N % With 90 % probability perform crossover if rand(1) < 0.9 % Initialize the children to be null vector. child_1 = []; child_2 = []; % Select the first parent parent_1 = round(N*rand(1)); if parent_1 < 1 parent_1 = 1; end % Select the second parent parent_2 = round(N*rand(1)); if parent_2 < 1 parent_2 = 1; end % Make sure both the parents are not the same. while isequal(parent_chromosome(parent_1,:),parent_chromosome(parent_2,:)) parent_2 = round(N*rand(1)); if parent_2 < 1 parent_2 = 1; end end % Get the chromosome information for each randomnly selected % parents parent_1 = parent_chromosome(parent_1,:); parent_2 = parent_chromosome(parent_2,:); % Perform corssover for each decision variable in the chromosome. for j = 1 : V % SBX (Simulated Binary Crossover). % For more information about SBX refer the enclosed pdf file. % Generate a random number u(j) = rand(1); if u(j) <= 0.5 bq(j) = (2*u(j))^(1/(mu+1)); else bq(j) = (1/(2*(1 - u(j))))^(1/(mu+1)); end % Generate the jth element of first child child_1(j) = ... 0.5*(((1 + bq(j))*parent_1(j)) + (1 - bq(j))*parent_2(j)); % Generate the jth element of second child child_2(j) = ... 0.5*(((1 - bq(j))*parent_1(j)) + (1 + bq(j))*parent_2(j)); % Make sure that the generated element is within the specified % decision space else set it to the appropriate extrema. if child_1(j) > u_limit(j) child_1(j) = u_limit(j); elseif child_1(j) < l_limit(j) child_1(j) = l_limit(j); end if child_2(j) > u_limit(j) child_2(j) = u_limit(j); elseif child_2(j) < l_limit(j) child_2(j) = l_limit(j); end end child_1(:,V + 1: M + V) = evaluate_objective(child_1, M, V); child_2(:,V + 1: M + V) = evaluate_objective(child_2, M, V); was_crossover = 1; was_m