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bfm.m
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bfm.m
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%% BENCHMARK TEST FUNCTIONS FOR OPTIMISATION METHODS
% -*- mode: matlab; coding: iso-8859-1; -*-
% Copyright (c) Jorge M. Cruz-Duarte. All rights reserved.
%
% Based in A Literature Survey of Benchmark Functions For Global
% Optimization Problems, Jamil & Yang (2013)
%
% - Run "bfm" at the command window to see all functions
% - Run "F = bfm(NoF)" to get the NoF-th function as a handle function
% - Run "[F,Details] = bfm(NoF)" to get more information about the
% function
% - Run "[F,Details] = bfm(NoF,'plot')" to plot the function
%
% Enjoy it! XD bfm
function [F, info] = bfm(FID,varargin)
switch nargin,
case 0,
FID = Show_List; % Show all the list
[F,lopt] = bfm(FID);
fprintf('\nQuick selection: %d. %s\n',FID,lopt.Name);
case 1,
F = eval(sprintf('@(Y) f%d(Y);',FID));
otherwise,
[F,lopt] = bfm(FID);
% lopt = Show_List;
% I = find(lopt.ID(:) == FID);
% eval(['F = @(X)',lopt.FunctionName{I},'(X);']);
switch varargin{1},
case 'plot',
if lopt.MaxDimensions <= 2,
dvsn = 200;
lims = lopt.Constraints; % por arreglar !!!!!!!!!!
if size(lims,1) == 1,
lims = [lims;lims];
end
Xlim = [lims(1,1),lims(1,2)];
Ylim = [lims(2,1),lims(2,2)];
titl = ['Function: ',lopt.Name]; view_ = 3;
fntz = 24; fntn = 'Tahoma'; cntr = 0;
nvr = length(varargin);
if nvr > 1,
if mod(nvr,2) == 0,
warning('%s option ignored: there is not value for %s',varargin{nvr});
nvr = nvr - 1;
end
% Options for plot
for k = 2 : 2 : nvr,
switch varargin{k},
case {'Points','points'},
dvsn = varargin{k + 1};
case {'xLim','xlim'},
Xlim = varargin{k + 1};
case {'yLim','ylim'},
Ylim = varargin{k + 1};
case {'Lims','lims'},
lims = varargin{k + 1};
Xlim = lims(1:2);
Ylim = lims(3:4);
case {'FontSize','fontsize'},
fntz = varargin{k + 1};
case {'FontName','fontname'},
fntn = varargin{k + 1};
case {'Contours','contours'},
cntr = varargin{k + 1};
otherwise,
warning('%s option ignored: %s',varargin{k},'not valid');
end
end
end
[X,Y] = meshgrid(...
linspace(Xlim(1),Xlim(2),dvsn),...
linspace(Ylim(1),Ylim(2),dvsn));
for i = 1 : dvsn,
for j = 1 : dvsn,
Z(i,j) = F([X(i,j),Y(i,j)]);
end
end
fprintf('\nPlot selection: %d. %s\n',...
FID,lopt.Name);
figure('Name',titl,'Color','w');
set(gcf,'Units','Normalized','Position',[.09 .08 .5 .8]);
Zlim = [min(Z(:)) max(Z(:))];
if cntr ~= 0,
surfc(X,Y,Z),
Zlim(1) = Zlim(1) - 5*diff(Zlim)/100;
else
surf(X,Y,Z),
end
grid on, shading interp, colormap jet,
axis([Xlim Ylim Zlim])
%ht = title(titl);
hx = xlabel('$x_1$','interpreter','latex','fontsize',fntz);
hy = ylabel('$x_2$','interpreter','latex','fontsize',fntz);
hz = zlabel('$f(x_1,x_2)$','interpreter','latex','fontsize',fntz);
view(view_), box on
%set(gcf,'renderer','OpenGL');
set(gca,'FontSize',fntz,...
'LineWidth',1.5,'TickLabelInterpreter','latex');%,...
%'GridAlpha',1,'Box','on');
% 'ticklabelinterpreter','latex',...
else
warning('We still working on it...');
end
end
end
[~,info] = eval(sprintf('f%d(nan(1,10));',FID));
end
% print(gcf,'Rosenbrock','-depsc','-r300')
%% Show list function
function random_id = Show_List()
% Load list
number_of_functions = 51; % changed it when a function is added
random_id = randi(number_of_functions);
% Show list
fprintf('\nID\t%30s\tDim\tf_min=f(x*)\n','Name');
fprintf('------------------------------------------------------------\n');
for i = 1 : number_of_functions,
[~,l] = eval(sprintf('f%d(nan(1,10));',i));
% Read dimensions
if l.MaxDimensions == 0, Dim = 'N';
else Dim = num2str(l.MaxDimensions); end
% Read Foptimum
if ~ischar(l.Foptimum), l.Foptimum = num2str(l.Foptimum); end
% Print list
fprintf('%2d\t%30s\t%2s\t%s\n',i,l.Name, Dim, l.Foptimum);
end
end
% -----------------------------------------------------------------
% 1. Cosine Mixture Function [ok]
function [f,details] = f1(X)
f = -0.1*sum(cos(5*pi*X)) + sum(X.^2);
details.Name = 'Cosine Mixture';
details.MaxDimensions = 0;
details.Constraints = [-1 1];
details.Xoptimum = 0;
details.Foptimum = '-N/10';
details.Comments = 'f_obj = -dim/10';
end
% 2. Bukin 2 Function [ok]
function [f,details] = f2(X)
f = 100*(X(2)^2 + 0.01*(X(1) + 10)^2 + 1) + 0.01*(X(1) + 10)^2 - 100;
details.Name = 'Bukin 2';
details.MaxDimensions = 2;
details.Constraints = [-15 -5;-3 3];
details.Xoptimum = [-10 0]';
details.Foptimum = 0;
details.Comments = 'none';
end
% 3. Keane Function [to review]
function [f,details] = f3(X)
f = -(sin(X(1) - X(2))^2)*(sin(X(1) + X(2))^2)/sqrt(X(1)^2 + X(2)^2);
details.Name = 'Keane';
details.MaxDimensions = 2;
details.Constraints = [1 10];
details.Xoptimum = [0 1.39325;1.39325 0];
details.Foptimum = -0.673668;
details.Comments = 'two global optimum';
end
% 4. Mishra 2 Function [ok]
function [f,details] = f4(X)
N = numel(X);
Xn = N - 0.5*sum(X(1:N-1) + X(2:N));
f = (1 + Xn)^Xn;
details.Name = 'Mishra 2';
details.MaxDimensions = 0;
details.Constraints = [0 1];
details.Xoptimum = 1;
details.Foptimum = 2;
details.Comments = 'none';
end
% 5. Trigonometric 1 Function [ok] (?)
function [f,details] = f5(X)
N = length(X); I = 1:N;
Xn = N - sum(cos(X));
f = sum((Xn + I(:).*(1 - cos(X(:))) - sin(X(:))).^2);
details.Name = 'Trigonometric 1';
details.MaxDimensions = 0;
details.Constraints = [0 pi];
details.Xoptimum = 0;
details.Foptimum = 0;
details.Comments = 'none';
end
% 6. Schmidt Vetters Function [to review]
function [f,details] = f6(X)
f = (1/(1 + (X(1) - X(2))^2) + sin(pi*X(2)/2 + X(3)/2) + exp(((X(1) + X(2))/X(2) - 2)^2));
details.Name = 'Schmidt Vetters';
details.MaxDimensions = 3;
details.Constraints = [0 10];
details.Xoptimum = [0.78547 0.78547 0.78547]';
details.Foptimum = 3;
details.Comments = 'It has bugs!';
end
% 7. Exponential Function [ok]
function [f,details] = f7(X)
f = -exp(-0.5*sum(X.^2));
details.Name = 'Exponential';
details.MaxDimensions = 0;
details.Constraints = [-1 1];
details.Xoptimum = 0;
details.Foptimum = -1;
details.Comments = 'none';
end
% 8. Hosaki Function [ok]
function [f,details] = f8(X)
f = (1 - 8*X(1) + 7*X(1)^2 - 7/3*X(1)^3 + 1/4*X(1)^4)*X(2)^2*...
exp(-X(2));
details.Name = 'Hosaki';
details.MaxDimensions = 2;
details.Constraints = [0 5;0 6];
details.Xoptimum = [4 2]';
details.Foptimum = -2.3458;
details.Comments = 'none';
end
% 9. Giunta Function [ok]
function [f,details] = f9(X)
f = 0.6 + sum(sin(16/15*X - 1) + (sin(16/15*X - 1)).^2 + 1/50*sin(4*(16/15*X - 1)));
details.Name = 'Giunta';
details.MaxDimensions = 0;
details.Constraints = [-1 1];
details.Xoptimum = [0.45834282 0.45834282]';
details.Foptimum = 0.060447042;
details.Comments = 'none';
end
% 10. Quadratic Function [ok]
function [f,details] = f10(X)
f = -3803.84 - 138.08*X(1) - 232.92*X(2) + 128.08*X(1)^2 + 203.64*X(2)^2 + 182.25*X(1)*X(2);
details.Name = 'Quadratic';
details.MaxDimensions = 2;
details.Constraints = [-10 10];
details.Xoptimum = [0.19388 0.48513]';
details.Foptimum = -3873.7243;
details.Comments = 'none';
end
% 11. Schwefel 2 [ok]
function [f,details] = f11(X)
f = 0;
for i = 1 : numel(X), f = f + (sum(X(1:i)))^2; end
details.Name = 'Schwefel 2';
details.MaxDimensions = 0;
details.Constraints = [-5 5];
details.Xoptimum = 0;
details.Foptimum = 0;
details.Comments = 'none';
end
% 12. Sphere Function [ok]
function [f,details] = f12(X)
f = sum(X.^2);
details.Name = 'Sphere';
details.MaxDimensions = 0;
details.Constraints = [-10 10];
details.Xoptimum = 0;
details.Foptimum = 0;
details.Comments = 'none';
end
% 13. Camel Function - Six Hump Function [ok]
function [f,details] = f13(X)
f = (4 - 2.1*X(1)^2 + X(1)^4/3)*X(1)^2 + X(1)*X(2) + ...
(4*X(2)^2 - 4)*X(2)^2;
details.Name = 'Six Hump Camel';
details.MaxDimensions = 2;
details.Constraints = [-5 5];
details.Xoptimum = [-0.08984201368301331 0.7126564032704135;0.08984201368301331 -0.7126564032704135];
details.Foptimum = -1.031628453;
details.Comments = '2 global optimum';
end
% 14. Parsopoulos Function [ok]
function [f,details] = f14(X)
f = cos(X(1))^2 + (sin(X(2)))^2;
details.Name = 'Parsopoulos';
details.MaxDimensions = 2;
details.Constraints = [-5 5];
details.Xoptimum = [pi/2 0];
details.Foptimum = 0;
details.Comments = '12 global optimum';
end
% 15. Deb 1 Function [ok]
function [f,details] = f15(X)
f = -1/numel(X)*sum((sin(5*pi*X)).^6);
details.Name = 'Deb 1';
details.MaxDimensions = 0;
details.Constraints = [-1 1];
details.Xoptimum = 0;
details.Foptimum = -1;
details.Comments = '5 global optimum per dimension';
end
% 16. Cross in Tray Function [ok]
function [f,details] = f16(X)
f = -0.0001*(abs(sin(X(1))*sin(X(2))*exp(abs(100 - ...
sqrt((X(1)^2 + X(2)^2))/pi))) + 1)^0.1;
details.Name = 'Cross in Tray';
details.MaxDimensions = 2;
details.Constraints = [-15 15];
details.Xoptimum = [1.349406685353340 1.349406608602084];
details.Foptimum = -2.06261218;
details.Comments = 'Its optimum value is irrational';
end
% 17. Colville Function [ok]
function [f,details] = f17(X)
f = 100*(X(1)^2 - X(2))^2 + ...
(X(1) - 1)^2 + ...
(X(3) - 1)^2 + ...
90*(X(3)^2 - X(4))^2 + ...
10.1*((X(2) - 1)^2 + (X(4) - 1)^2) + ...
19.8*(X(2) - 1)*(X(4) - 1);
details.Name = 'Colville';
details.MaxDimensions = 4;
details.Constraints = [-10 10];
details.Xoptimum = [1 1 1 1];
details.Foptimum = 0;
details.Comments = 'none';
end
% 18. Needle Eye Function [improve]
function [f,details] = f18(X)
centre = 0.0001; X = abs(X); D = numel(X); f = 0; fp = 0;
for i = 1 : D,
if X(i) > centre,
fp = 1;
f = f + 100 + X(i);
else
f = f + 1;
end
end
if fp == 0, f = f/D; end
details.Name = 'Needle Eye';
details.MaxDimensions = 0;
details.Constraints = [-10 10];
details.Xoptimum = -1;
details.Foptimum = 1;
details.Comments = 'none';
end
% 19. Branin 1 Function [ok]
function [f,details] = f19(X)
f = (X(2) - 1.275*(X(1)/pi)^2 + 5*X(1)/pi - 6)^2 + ...
(10 - 5/4/pi)*cos(X(1)) + 10;
details.Name = 'Branin 1';
details.MaxDimensions = 2;
details.Constraints = [-5 10; 0 15];
details.Xoptimum = [-pi 12.275];
details.Foptimum = 0.39788735772973816;
details.Comments = '3 global optimum';
end
% 20. Beale Function [ok]
function [f,details] = f20(X)
f = (1.5 - X(1) + X(1)*X(2))^2 + (2.25 - X(1) + X(1)*X(2)^2)^2 + ...
(2.625 - X(1) + X(1)*X(2)^3)^2;
details.Name = 'Beale';
details.MaxDimensions = 2;
details.Constraints = [-4.5 4.5];
details.Xoptimum = [3 0.5];
details.Foptimum = 0;
details.Comments = 'none';
end
% 21. Alpine 1 Function [ok]
function [f,details] = f21(X)
f = sum(abs(X.*sin(X) + 0.1*X));
details.Name = 'Alpine 1';
details.MaxDimensions = 0;
details.Constraints = [-10 10];
details.Xoptimum = 0;
details.Foptimum = 0;
details.Comments = 'none';
end
% 22. Rana Function [ok]
function [f,details] = f22(X)
f = 0; D = numel(X);
for i = 1 : D - 1,
t1 = sqrt(norm(X(i + 1) + X(i) + 1));
t2 = sqrt(norm(X(i + 1) - X(i) + 1));
f = f + (X(i + 1) + 1)*cos(t2)*sin(t1) + X(i)*cos(t1)*sin(t2);
end
details.Name = 'Rana';
details.MaxDimensions = 0;
details.Constraints = [-500.000001 500.000001];
details.Xoptimum = [-500 -500];
details.Foptimum = -928.5478;
details.Comments = 'none';
end
% 23. Bird Function [ok]
function [f,details] = f23(X)
f = sin(X(1))*exp((1 - cos(X(2)))^2) + ...
cos(X(2))*exp((1 - sin(X(1)))^2) + (X(1) - X(2))^2;
details.Name = 'Bird';
details.MaxDimensions = 2;
details.Constraints = [-2*pi 2*pi];
details.Xoptimum = [4.701055751981055 3.152946019601391; -1.58214217055011,-3.130246799635430];
details.Foptimum = -106.7645367198034;
details.Comments = '2 global optimum';
end
% 24. Step Function [ok]
function [f,details] = f24(X)
f = sum((floor(X + 0.5)).^2);
details.Name = 'Step';
details.MaxDimensions = 0;
details.Constraints = [-100 100];
details.Xoptimum = 0;
details.Foptimum = 0;
details.Comments = 'none';
end
% 25. Wayburn Seader 1 Function [ok]
function [f,details] = f25(X)
f = (X(1)^6 + X(2)^4 - 17)^2 + (2*X(1) + X(2) - 4)^2;
details.Name = 'Wayburn Seader 1';
details.MaxDimensions = 2;
details.Constraints = [-5 5];
details.Xoptimum = [1 2; 1.597 0.806];
details.Foptimum = 0;
details.Comments = 'none';
end
% 26. Box Betts Quadratic Sum Function
function [f,details] = f26(X)
i = 1:10;
g = exp(-0.1*(i + 1)*X(1)) - exp(-0.1*(i + 1)*X(2)) - ...
exp(((-0.1*(i + 1)) - exp(-i - 1))*X(3));
f = sum(g.^2);
details.Name = 'Box Betts Quadratic Sum';
details.MaxDimensions = 3;
details.Constraints = [0.9 1.2; 9 11.2; 0.9 1.2];
details.Xoptimum = [1 10 1];
details.Foptimum = 0;
details.Comments = 'none';
end
% 27. Bartels Conn Function
function [f,details] = f27(X)
f = abs(X(1)^2 + X(2)^2 + X(1)*X(2)) + abs(sin(X(1))) + abs(cos(X(2)));
details.Name = 'Bartels Conn';
details.MaxDimensions = 2;
details.Constraints = [-500 500];
details.Xoptimum = 0;
details.Foptimum = 1;
details.Comments = 'none';
end
% 28. Cube Function [ok]
function [f,details] = f28(X)
f = 100*(X(2) - X(1)^3)^2 + (1 - X(1))^2;
details.Name = 'Cube';
details.MaxDimensions = 2;
details.Constraints = [-10 10];
details.Xoptimum = [1 1];
details.Foptimum = 0;
details.Comments = 'none';
end
% 29. Ackley 1 Function [ok]
function [f,details] = f29(X)
D = numel(X);
f = -20*exp(-0.02*sqrt(sum(X.^2)/D)) - exp(sum(cos(2*pi*X))/D) + 20 + exp(1);
details.Name = 'Ackley 1';
details.MaxDimensions = 0;
details.Constraints = [-35 35];
details.Xoptimum = 0;
details.Foptimum = 0;
details.Comments = 'none';
end
% 30. Rosenbrock Function [ok]
function [f,details] = f30(X)
f = sum(100*(X(2:end) - X(1:end-1).^2).^2 + (X(1:end-1) - 1).^2);
details.Name = 'Rosenbrock';
details.MaxDimensions = 0;
details.Constraints = [-30 30];
details.Xoptimum = 1;
details.Foptimum = 0;
details.Comments = 'none';
end
% 31. Trid 6 Function [ok]
function [f,details] = f31(X)
f = sum((X - 1).^2) - sum(X(2:end).*X(1:end-1));
details.Name = 'Trid 6';
details.MaxDimensions = 6;
details.Constraints = [-20 20];
details.Xoptimum = [6 10 12 12 10 6];
details.Foptimum = -50;
details.Comments = 'none';
end
% 32. Hansen Function
function [f,details] = f32(X)
i = 0:4;
f = sum((i + 1).*cos(i*X(1) + i + 1))*...
sum((i + 1).*cos((i + 2)*X(2) + i + 1));
details.Name = 'Hansen';
details.MaxDimensions = 2;
details.Constraints = [-10 10];
details.Xoptimum = [-7.589893 -7.708314];
details.Foptimum = -2.3458;
details.Comments = 'none';
end
% 33. Xor Function
function [f,details]= f33(X)
f1 = (1 + exp(-X(7)/(1 + exp(-X(1) - X(2) - X(5))) - ...
X(8)/(1 + exp(-X(3) - X(4) - X(6))) - X(9)))^(-2);
f2 = (1 + exp(-X(7)/(1 + exp(-X(5))) - X(8)/(1 + exp(-X(6))) - ...
X(9)))^(-2);
f3 = (1 - (1 + exp(-X(7)/(1 + exp(-X(1) - X(5))) - ...
X(8)/(1 + exp(-X(6))) - X(9)))^(-1))^2;
f4 = (1 - (1 + exp(-X(7)/(1 + exp(-X(2) - X(5))) - ...
X(8)/(1 + exp(-X(4) - X(6))) - X(9)))^(-1))^2;
f = f1 + f2 + f3 + f4;
details.Name = 'Xor';
details.MaxDimensions = 9;
details.Constraints = [-1 1];
details.Xoptimum = [1 -1 1 -1 -1 1 1 -1 0.421134];
details.Foptimum = 0.9597588 ;
details.Comments = 'none';
end
% 34. Ursem Waves Function
function [f,details] = f34(X)
f = -0.9*X(1)^2 + (X(2)^2 - 4.5*X(2)^2)*X(1)*X(2) + ...
4.7*cos(3*X(1) - X(2)^2*(2 + X(1)))*sin(2.5*pi*X(1));
details.Name = 'Ursem Waves';
details.MaxDimensions = 2;
details.Constraints = [-0.9 1.2; -1.2 1.2];
details.Xoptimum = 1.2;
details.Foptimum = -8.5536;
details.Comments = 'none';
end
% 35. Chichinadze Function
function [f,details] = f35(X)
f = X(1)^2 - 12*X(1) + 11 + 10*cos(pi*X(1)/2) + ...
8*sin(5*pi*X(1)/2) - (1/5)^0.5*exp(-0.5*(X(2) - 0.5)^2);
details.Name = 'Chichinadze';
details.MaxDimensions = 2;
details.Constraints = [-30 30];
details.Xoptimum = [5.90133 0.5];
details.Foptimum = -43.3159;
details.Comments = 'none';
end
% 36. Rastrigin Function [ok]
function [f,details] = f36(X)
f = 10*numel(X) + sum(X.^2 - 10*cos(2*pi*X));
details.Name = 'Rastrigin';
details.MaxDimensions = 0;
details.Constraints = [-5 5];
details.Xoptimum = 0;
details.Foptimum = 0;
details.Comments = 'none';
end
% 37. Helical Valley Function [improve]
function [f,details] = f37(X)
if X(1) >= 0, th = atan(X(1)/X(2))/(2*pi);
else th = atan(X(1)/X(2) + 0.5)/(2*pi); end
f = 100*((X(2) - 10*th)^2 + (sqrt(X(1)^2 + X(2)^2) - 1)) + X(3)^2;
details.Name = 'Helical Valley';
details.MaxDimensions = 3;
details.Constraints = [-10 10];
details.Xoptimum = [1 0 0];
details.Foptimum = 0;
details.Comments = 'none';
end
% 38. Paviani Function
function [f,details] = f38(X)
f = sum((log(X - 2)).^2 + (log(10 - X)).^2) - (prod(X))^0.2;
details.Name = 'Paviani';
details.MaxDimensions = 10;
details.Constraints = [2.0001 10];
details.Xoptimum = 9.351*[1 1 1 1 1 1 1 1 1 1];
details.Foptimum = -45.778;
details.Comments = 'none';
end
% 39. Powell 4 Function
function [f,details] = f39(X)
f = (X(3) + 10*X(1))^2 + 5*(X(2) - X(4))^2 + (X(1) - 2*X(2))^4 + ...
10*(X(3) - X(4))^4;
details.Name = 'Powell 4';
details.MaxDimensions = 4;
details.Constraints = [-4 5];
details.Xoptimum = 0;
details.Foptimum = 0;
details.Comments = 'none';
end
% 40. Weierstrass Function
function [f,details] = f40(X)
k = 0:20; a = 0.5; b = 3; n = numel(X); f = 0;
for i = 1 : n,
f = f + sum(a.^k.*cos(2*pi*b.^k*(X(i) + 0.5))) - ...
n*sum(a.^k.*cos(pi*b.^k));
end
details.Name = 'Weierstrass';
details.MaxDimensions = 0;
details.Constraints = [-0.5 0.5];
details.Xoptimum = 0;
details.Foptimum = 0;
details.Comments = 'none';
end
% 41. Watson Function [ok]
function [f,details] = f41(X)
if size(X,1) ~= 1, X = X'; end
f = X(1)^2; j1 = 0:4; j2 = 0:5;
for i = 0 : 29,
a = i/29;
f = f + (sum((j1 - 1).*a.^(j1).*X(j1 + 1)) - ...
(sum(a.^(j2).*X(j2 + 1)))^2 - 1)^2;
end
details.Name = 'Watson';
details.MaxDimensions = 6;
details.Constraints = [-5 5];
details.Xoptimum = [-0.0158 1.012 1.260 -1.513 0.9928];
details.Foptimum = 0.002288;
details.Comments = 'none';
end
% 42. Drop Wave Function [ok]
function [f,details] = f42(X)
f1 = sum(X.^2);
f = -(1 + cos(12*sqrt(f1)))/(2 + 0.5*f1);
details.Name = 'Drop Wave';
details.MaxDimensions = 0;
details.Constraints = [-5.12 5.12];
details.Xoptimum = 0;
details.Foptimum = -1;
details.Comments = 'none';
end
% 43. deVilliers Glasser 1 Function
function [f,details] = f43(X)
i = 1 : 24;
ti = 0.1*(i - 1);
yi = 60.137*1.371.^ti.*sin(3.112*ti + 1.761);
f = sum((X(1)*X(2).^ti.*sin(X(3)*ti + X(4)) - yi).^2);
details.Name = 'deVilliers Glasser 1';
details.MaxDimensions = 4;
details.Constraints = [1 100];
details.Xoptimum = [60.137 1.371 3.112 1.761];
details.Foptimum = 0;
details.Comments = 'none';
end
% 44. Stochastic Function [ok]
function [f,details] = f44(X)
n = numel(X); i = ones(size(X)); i(:) = (1 : n);
eps_ = rand(size(X));
f = sum(eps_.*abs(X - 1./i));
details.Name = 'Stochastic';
details.MaxDimensions = 0;
details.Constraints = [-5 5];
details.Xoptimum = 0.5;
details.Foptimum = 0;
details.Comments = 'none';
end
% 45. Gulf Research Problem function
function [f,details] = f45(X)
i = 1 : 99;
ui = 25 + (-50*log(0.01*i)).^(1/1.5);
f = sum((exp((-(ui - X(2)).^X(3))/X(1)) - 0.01*i).^2);
details.Name = 'Gulf Research Problem';
details.MaxDimensions = 3;
details.Constraints = [0 5];
details.Xoptimum = [50 25 1.5];
details.Foptimum = 0;
details.Comments = 'none';
end
% 46. Salomon Function
function [f,details] = f46(X)
f1 = sqrt(sum(X.^2));
f = 1 - cos(2*pi*f1) + 0.1*f1;
details.Name = 'Salomon';
details.MaxDimensions = 0;
details.Constraints = [-100 100];
details.Xoptimum = 0;
details.Foptimum = 0;
details.Comments = 'none';
end
% 47. Griewank Function
function [f,details] = f47(X)
i = 1 : numel(X);
f = sum(X.^2)/4000 - prod(cos(X./sqrt(i))) + 1;
details.Name = 'Griewank';
details.MaxDimensions = 0;
details.Constraints = [-50 50];
details.Xoptimum = 0;
details.Foptimum = 0;
details.Comments = 'none';
end
% 48. Whitley Function
function [f,details] = f48(X)
f = 0; D = numel(X);
for i = 1 : D,
f = f + sum((100*(X(i)^2 - X).^2 + (1 - X).^2).^2/4000 - ...
cos(100*(X(i)^2 - X).^2 + (1 - X).^2 + 1));
end
details.Name = 'Whitley';
details.MaxDimensions = 0;
details.Constraints = [-10.24 10.24];
details.Xoptimum = 1;
details.Foptimum = 0;
details.Comments = 'none';
end
% 49. Damavandi Function
function [f,details] = f49(X)
f = (1 - abs((sin(pi*(X(1) - 2))*sin(pi*(X(2) - 2)))...
/(pi^2*(X(1) - 2)*(X(2) - 2)))^5)*(2 + (X(1) - 7)^2 + 2*(X(2) - 7)^2);
details.Name = 'Damavandi';
details.MaxDimensions = 2;
details.Constraints = [0 14];
details.Xoptimum = 2;
details.Foptimum = 0;
details.Comments = 'none';
end
% 50. deVilliers Glasser 2 Function
function [f,details] = f50(X)
i = (1 : 24); ti = 0.1*(i - 1);
yi = 53.81*(1.27.^ti).*tanh(3.012*ti + sin(2.13*ti)).*...
cos(exp(0.507).*ti);
f = sum((X(1)*(X(2).^ti).*tanh(X(3).*ti + sin(X(4).*ti)).*...
cos(ti.*exp(X(5))) - yi).^2);
details.Name = 'deVilliers Glasser 2';
details.MaxDimensions = 5;
details.Constraints = [1 6];
details.Xoptimum = [53.81 1.27 3.012 2.13 0.507];
details.Foptimum = 0;
details.Comments = 'none';
end
% 51. 2n minima
function [f,details] = f51(X)
f = sum(X.^4 - 16*X.^2 + 5*X);
details.Name = 'Second minima';
details.MaxDimensions = 0;
details.Constraints = [-5 5];
details.Xoptimum = -2.9;
details.Foptimum = 0;
details.Comments = 'none';
end
% If you add a function, you must the constant: change number_of_functions at Line 144.