基于实数编码的参数自适应遗传算法(matlab代码)

% 测试函数图像 % 测试函数图像 % 改进的自适应遗传算法： % 参考文献：[7] M. Srinivas and L. M. Patnaik, "Adaptive probabilities of crossover and mutation in genetic algorithms," % in IEEE Transactions on Systems, Man, and Cybernetics, vol. 24, no. 4, pp. 656-667, April 1994. % doi: 10.1109/21.286385 clc; clear all; mode = 'Schaffer'; % mode = 'self_define'; if strcmp(mode, 'Schaffer') figure(1) x = -4:0.1:4; y = -4:0.1:4; [X,Y] = meshgrid(x,y); % Z = 3*cos(X.*Y)+X+Y.^2; Z = 0.5-((sin(sqrt(X.^2+Y.^2)).^2)-0.5)./(1+0.001.*(X.^2+Y.^2)).^2; surf(X,Y,Z); title('Schaffer Function'); xlabel('X-轴'); ylabel('Y-轴'); zlabel('Z-轴'); figure(2); contour(X, Y, Z, 8); title('Schaffer函数等高线'); xlabel('X-轴'); ylabel('Y-轴'); end if strcmp(mode, 'self_define') figure(1); x = -4:0.1:4; y = -4:0.1:4; [X,Y] = meshgrid(x,y); % Z = 100.*(Y-X.^2).^2+(1-X).^2; Z = (cos(X.^2+Y.^2)-0.1)./(1+0.3*(X.^2+Y.^2).^2)+3; surf(X,Y,Z); %title('Rosen Brock valley Function'); title('Self define Function'); xlabel('X-轴'); ylabel('Y-轴'); zlabel('Z-轴'); end clc; clearvars -except mode; r = 0.2; b = 3; NP=400; % Pc=0.65; % 将Pc,Pm参数改进为自适应参数 % Pm=0.20; G=520; % 记得改 D=2; % 变量个数 k1 = 1; k3 = 1; k2 = 0.5; k4 = 0.5; X_min=-4; X_max=4; Y_min=-4; Y_max=4; % optimization_trace = []; % 三维数组, 行，列，叶 for count_1=1:NP % 产生初始解 temp1 = X_min+rand()*(X_max-X_min); temp2 = Y_min+rand()*(Y_max-Y_min); x(count_1,:) = [temp1,temp2]; end save_pic_cnt = 1; A = figure(3); for gen=1:G %pause(0.2); if rem(gen, 100)==1 scatter(x(:,1), x(:, 2)); axis([-4, 4, -4, 4]); title(['第', num2str(gen), '次迭代']); xlabel('变量X'); ylabel('变量Y'); base_path = 'C:\Users\18811\Desktop\graph\'; cnt = num2str(save_pic_cnt); tail_path = '.jpg'; frame = getframe(A); im=frame2im(frame); path_img = [base_path, cnt, tail_path]; % imwrite(im, path_img); % save_x(:, :, save_pic_cnt) = x; save_pic_cnt = save_pic_cnt + 1; end % scatter(0, 0, 'o', 'r'); for count_2=1:NP fitness(count_2)=func(x(count_2,:), mode); end %[fitness_min,index0] = min(fitness); %fitness_max = max(fitness); [fitness_max,index0] = max(fitness); fitness_average = sum(fitness)/(length(fitness)); % 种群的平均值 collect_fit_average(gen) = fitness_average; % 保存适应度的平均值 collect_fitmax_subtract_fit_average(gen) = fitness_max - fitness_average; % 保存f_max-f_average ; fitness_min = min(fitness); best_indiv = x(index0,:); % 最优的个体 % optimization_trace(gen,: , global_count) = best_indiv; % best_solution(gen) = fitness_min; best_solution(gen) = fitness_max; % 计算归一化的适应度值 fitness = (fitness - fitness_min)/(fitness_max - fitness_min); fitness_sum = sum(fitness); fitness = fitness./fitness_sum; fitness = cumsum(fitness); % 选择算子： ms = sort(rand(NP,1)); fiti = 1; newi = 1; while newi<=NP if ms(newi)<fitness(fiti) clone_x(newi,:) = x(newi,:); newi = newi + 1; else fiti = fiti + 1; end end clone_x = clone_x(1:NP, :); % 进行交叉，变异操作 % count=0; for count=1:2:NP % 自适应计算Pc. % 选区两个交叉的个体的较大的适应度值 if fitness(count)>=fitness(count+1) fitness_selected = fitness(count); else fitness_selected = fitness(count+1); end % 计算Pc if fitness_selected >= fitness_average Pc = k1*(fitness_max-fitness_selected)/(fitness_max-fitness_average); else Pc = k3; end collect_Pc(gen, count) = Pc; % 保存Pc的值 temp_cross = rand(); if temp_cross < Pc % 交叉算子 注：这种交叉算子效果更好 temp_alpha = 0.6; cross_x(count,:) = temp_alpha*clone_x(count,:)+(1-temp_alpha)*clone_x(count+1,:); cross_x(count+1,:) = temp_alpha*clone_x(count+1,:)+(1-temp_alpha)*clone_x(count,:); % 改进的交叉算子 参考文献：管小艳. 实数编码下遗传算法的改进及其应用[D].重庆大学,2012. 注：但这种交叉算子实际的效果不理想 % temp_gama = rand(); % temp_alpha = 0.98; % cross_x(count,:) = temp_alpha*clone_x(count,:)+(1-temp_alpha)*clone_x(count+1,:)+temp_gama*(clone_x(count,:)-clone_x(count+1,:)); % cross_x(count+1,:) = temp_alpha*clone_x(count+1,:)+(1-temp_alpha)*clone_x(count,:)+temp_gama*(clone_x(count,:)-clone_x(count+1,:)); else cross_x(count,:)=clone_x(count,:); cross_x(count+1,:)=clone_x(count+1,:); end % 边界条件检查 if cross_x(count,1)>X_max || cross_x(count,1)<X_min || cross_x(count,2)>Y_max || cross_x(count,2)<Y_min temp1 = X_min+rand()*(X_max-X_min); temp2 = Y_min+rand()*(Y_max-Y_min); cross_x(count,:) = [temp1,temp2]; end end cross_x = cross_x(1:NP,:); % cross_x为完成交叉的个体； % 变异操作 for count=1:1:NP % 计算Pm if fitness(count)>=fitness_average Pm = k2*(fitness_max-fitness(count))/(fitness_max-fitness_average); else Pm = k4; end collect_Pm(gen,count) = Pm; % 保存Pm的值 temp_mutation=rand(); if temp_mutation<Pm %mutation_x(count,:) = (1+0.01).*cross_x(count,:); %这种变异算子效果不理想 % 变异算子 参考文献：管小艳. 实数编码下遗传算法的改进及其应用[D].重庆大学,2012 mutation_pos = randi(D); if mutation_pos==1 low = X_min; high = X_max; else low = Y_min; high = Y_max; end s_t(gen) = 1-r^((1-gen/G)^b); new_low = cross_x(count, mutation_pos)-s_t(gen)*(cross_x(count, mutation_pos)-low); new_high = cross_x(count, mutation_pos)+s_t(gen)*(high-cross_x(count, mutation_pos)); mutation_x(count, :) = cross_x(count, :); mutation_x(count, mutation_pos) = new_low+rand()*(new_high-new_low); if mutation_x(count,1)>X_max || mutation_x(count,1)<X_min || mutation_x(count,2)>Y_max || mutation_x(count,2)<Y_min temp1 = X_min+rand()*(X_max-X_min); temp2 = Y_min+rand()*(Y_max-Y_min); mutation_x(count,:) = [temp1,temp2]; end else mutation_x(count,:) = cross_x(count,:); end end %边界条件处理 x=mutation_x(1:NP, :); x(1,:)= best_indiv; end %% 作图 figure(4) plot(best_solution); %hold on; xlabel('进化代数'); ylabel('适应度值'); title('适应度进化曲线'); figure(5); plot(collect_fitmax_subtract_fit_average); title('f_{max}-f_{average}曲线'); xlabel('进化代数'); ylabel('f_{max}-f_{average}'); % function f=func(buf) % f=0.5-((sin(sqrt(buf(1).^2+buf(2).^2)).^2)-0.5)./(1+0.001.*(buf(1).^2+buf(2).^2)).^2; % end