# CEC-Benchmark-Functions **Repository Path**: tsingke/CEC-Benchmark-Functions ## Basic Information - **Project Name**: CEC-Benchmark-Functions - **Description**: CEC 国际进化计算会议-优化算法测试函数汇总 - **Primary Language**: Unknown - **License**: Not specified - **Default Branch**: master - **Homepage**: None - **GVP Project**: No ## Statistics - **Stars**: 15 - **Forks**: 3 - **Created**: 2021-09-25 - **Last Updated**: 2025-07-27 ## Categories & Tags **Categories**: Uncategorized **Tags**: None ## README # CEC-benchmark-functions CEC-国际进化计算会议-测试函数 其他测试标准函数： https://www.ntu.edu.sg/home/EPNSugan/ https://github.com/P-N-Suganthan ### 绘制测试函数图像 ```matlab % plot_function.m % 脚本功能：绘制所有测试函数图像 % clear;close all % 1.二维空间绘图时，生成多个自变量 for func_num =1:16 if func_num==1 x=-100:5:100;y=x; %sphere_func elseif func_num==2 x=-100:5:100; y=x;%schwefel_102 elseif func_num==3 x=-10:0.5:10; y=x;%schwefel_102_noise_func elseif func_num==4 x=-100:5:100; y=x;%schwefel_2_21 elseif func_num==5 x=-10:0.5:10; y=x;%schwefel_2_22 elseif func_num==6 x=-200:10:200;y=x; %high_cond_elliptic_func elseif func_num==7 x=-10:0.5:10; y=x; % step_func elseif func_num==8 x=-500:10:500; y=x;%Schwefel_func(multimodal) elseif func_num==9 x=-2.048:0.05:2.048; y=x;%rosenbrock_func elseif func_num==10 x=-1.28:0.05:1.28;y=x; %Quartic function elseif func_num==11 x=-600:30:600; y=x;%griewank_func elseif func_num==12 x=-32:1:32; y=x;% ackley_func elseif func_num==13 x=-5:0.1:5; y=x;% rastrigin_func elseif func_num==14 x=-5:0.1:5; y=x;% rastrigin_noncont astrigin_noncont elseif func_num==15 x=-5:0.1:5; y=x;% weierstrass elseif func_num==16 x=-10:0.2:10;y=x;% schaffer else break; end L=length(x); f=[]; %2. 由自变量生成网格点，并计算各个网格点的函数值f(x,y) for i=1:L for j=1:L f(i,j)=benchmark_func([x(i),y(j)],func_num); % 一个点对应一个数值 end end % 3. 根据网格点绘制空间图形 figure(func_num)% 生成一份图形画布 surfc(x,y,f); % 在图形画布上绘制函数图像(带有等高线)surfC（X,Y,Z） xlabel('x'); ylabel('y'); zlabel('f(x,y)'); % 4.输出并保存函数图像到指定路径下面 filename=strcat('F:\6_张庆科\2_AlgorithmDesign\TestFunctionsMap\','F',num2str(func_num)); saveas(gcf,filename,'png'); close;% 关闭当前的输出 end ``` --- ### 测试函数完整形式 benchmark_func.m ```matlab function fitnessvalue=benchmark_func(x,func_num) % Simple benchmark functions % benchmark_func.m is the main function of selected minimize problems % e.g. f=benchmark_func(x,func_num) % x is the variable, f is the function value %% Test Functions % Unimodal function if func_num==1 fhd=str2func('sphere_func'); %等价价于语句 fhd =@spher_func elseif func_num==2 fhd=str2func('schwefel_102'); % elseif func_num==3 fhd=str2func('schwefel_102_noise_func'); % elseif func_num==4 fhd= str2func('schwefel_2_21'); elseif func_num==5 fhd= str2func('schwefel_2_22'); elseif func_num==6 fhd=str2func('high_cond_elliptic_func'); % elseif func_num==7 fhd=str2func('step_func'); % Multimodal function elseif func_num==8 fhd=str2func('Schwefel_func'); % elseif func_num==9 fhd=str2func('rosenbrock_func'); % elseif func_num==10 fhd=str2func('quartic'); % elseif func_num==11 fhd=str2func('griewank_func'); % elseif func_num==12 fhd=str2func('ackley_func'); elseif func_num==13 fhd=str2func('rastrigin_func'); elseif func_num==14 fhd=str2func('rastrigin_noncont'); elseif func_num==15 fhd=str2func('weierstrass'); % Fixed dimensions function elseif func_num ==16 fhd=str2func('schaffer'); end fitnessvalue=feval(fhd,x); % 这里的x均为行向量ps行，D列，D为x的维度数值 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%% 1.Unimodal function %%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 以下均为子函数 %% 1.Sphere Function function f=sphere_func(x) % [ps,D]=size(x); f=sum(x.^2,2); %% 2.Schwefel's Problem 1.2 function f=schwefel_102(x) [ps,D]=size(x); f=0; for i=1:D f=f+sum(x(:,1:i),2).^2; end %% 3.Schwefel's Problem 1.2 with Noise function f=schwefel_102_noise_func(x) [ps,D]=size(x); f=0; for i=1:D f=f+sum(x(:,1:i),2).^2; end f=f.*(1+0.4.*abs(normrnd(0,1,ps,1))); %% 4.Schwefel's Problem 2.21 function f=schwefel_2_21(x) [ps,D]=size(x); f= max(abs(x)); %% 5.Schwefel's Problem 2.22 function f=schwefel_2_22(x) [ps,D]=size(x); f= sum(abs(x)) + prod(abs(x)); %% 6.High Conditioned Elliptic Function function f=high_cond_elliptic_func(x) [ps,D]=size(x); a=1e+6; f=0; for i=1:D f=f+a.^((i-1)/(D-1)).*x(:,i).^2; end %% 7.Step Function function f=step_func(x) % [ps,D]=size(x); f= sum(floor(x+0.5).^2); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%% 2.Multimodal多峰函数%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 8.Schwefel Function function f= Schwefel_func(x) [ps,D]=size(x); f=418.982887272433799*D -sum(x.*sin(sqrt(abs(x)))); %% 9.Rosenbrock's Function function f=rosenbrock_func(x) [ps,D]=size(x); f=sum(100.*(x(:,1:D-1).^2-x(:,2:D)).^2+(x(:,1:D-1)-1).^2,2); %% 10.Quartic函数（最小处位置很浅，很难高精确度找到） function f= quartic(x) [ps,D]=size(x); v=1:D; xq =x.^4; f = sum(v.*xq); %% 11. Griewank's Function function f=griewank_func(x) [ps,D]=size(x); f=1; for i=1:D f=f.*cos(x(:,i)./sqrt(i)); end f=sum(x.^2,2)./4000-f+1; %% 12.Ackley's Function function f=ackley_func(x) [ps,D]=size(x); f=sum(x.^2,2); f=20-20.*exp(-0.2.*sqrt(f./D))-exp(sum(cos(2.*pi.*x),2)./D)+exp(1); %% 13.Rastrign's Function function f=rastrigin_func(x) % [ps,D]=size(x); f=sum(x.^2-10.*cos(2.*pi.*x)+10,2); %% 14.Rastrign's noncontinue Function function f=rastrigin_noncont(x) % [ps,D]=size(x); x=(abs(x)<0.5).*x+(abs(x)>=0.5).*(round(x.*2)./2); f=sum(x.^2-10.*cos(2.*pi.*x)+10,2); %% 15.Weierstrass Function function f=weierstrass(x) [ps,D]=size(x); x=x+0.5; a = 0.5; b = 3; kmax = 20; c1(1:kmax+1) = a.^(0:kmax); c2(1:kmax+1) = 2*pi*b.^(0:kmax); f=0; % c=-w(0.5,c1,c2); for i=1:D f=f+w(x(:,i)',c1,c2); end f=f+c*D; function y = w(x,c1,c2) y = zeros(length(x),1); for k = 1:length(x) y(k) = sum(c1 .* cos(c2.*x(:,k))); end %-------------------------------- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%% 3.固定维度的特殊峰函数%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 16. schaffer函数(强烈震荡) function f=schaffer(x) [ps,D]=size(x); if D==2 f = 0.5 + (sin(sqrt(x(1)^2 + x(2)^2))-0.5)/(1+0.001*(x(1)^2 + x(2)^2))^2; else disp("the value of D must be 2 for schaffer funtion"); pause; end ```