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high_fidelity_evaluation.m
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% Copyright [2016] [Proteek Chandan Roy]
%
% Licensed under the Apache License, Version 2.0 (the "License");
% you may not use this file except in compliance with the License.
% You may obtain a copy of the License at
%
% http://www.apache.org/licenses/LICENSE-2.0
%
% Unless required by applicable law or agreed to in writing, software
% distributed under the License is distributed on an "AS IS" BASIS,
% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
% See the License for the specific language governing permissions and
% limitations under the License.
%
% Proteek Chandan Roy, 2016
% Contact: [email protected], [email protected]
function [f,g] = high_fidelity_evaluation(opt,x)
opt.funcEval = opt.funcEval + 1;
problem = lower(opt.objfunction);
g = [];
switch(problem)
case 'zdt1'
n=size(x,2);
a(1)=x(1);
b=9/(n-1);
y=0;
for i=2:n
y=y+x(i);
end
b=b*y;
a(2)=1+b;
a(3)=1- sqrt(a(1)/a(2));
f(1)=a(1);
f(2)=a(2)*a(3);
case 'zdt2'
n=size(x,2);
a(1)=x(1);
b=9/(n-1);
y=0;
for i=2:n
y=y+x(i);
end
b=b*y;
a(2)=1+b;
a(3)=1- power(a(1)/a(2),2);
f(1)=a(1);
f(2)=a(2)*a(3);
case 'zdt3'
n=size(x,2);
a(1)=x(1);
b=9/(n-1);
y=0;
for i=2:n
y=y+x(i);
end
b=b*y;
a(2)=1+b;
a(3)=1- sqrt(a(1)/a(2)) - (a(1)/a(2))*sin(10*pi*a(1));
f(1)=a(1);
f(2)=a(2)*a(3);
case 'zdt4'
n=size(x,2);
a(1)=x(1);
y=0;
for i=2:n
y=y+power(x(i),2)-10*cos(4*pi*x(i));
end
a(2)=1+10*(n-1)+y;
a(3)=1- sqrt(a(1)/a(2));
f(1)=a(1);
f(2)=a(2)*a(3);
case 'zdt6'
n=size(x,2);
a(1)=1- exp(-4*x(1))*power(sin(6*pi*x(1)),6);
y=0;
for i=2:n
y=y+x(i)/9;
end
b=9*power(y,0.25);
a(2)=1+b;
a(3)=1- power(a(1)/a(2),2);
f(1)=a(1);
f(2)=a(2)*a(3);
case 'dtlz1'
n=size(x,2);
g = 0;
nfunc = opt.M;
k = n - nfunc + 1;
for i = nfunc:n
g = g + power(( x(i)-0.5),2) - cos(20 * 3.141592654 * ( x(i)-0.5));
end
g = 100 * (k + g);
for i = 1:nfunc
fit = 0.5 * (1 + g);
for j = nfunc - i:-1:1
fit = fit * x(j);
end
if i > 1
fit = fit * (1 - x(nfunc - i + 1));
end
f(i) = fit;
end
case 'c1dtlz1'
n=size(x,2);
g = 0;
nfunc = opt.M;
k = n - nfunc + 1;
for i = nfunc:n
g = g + power(( x(i)-0.5),2) - cos(20 * 3.141592654 * ( x(i)-0.5));
end
g = 100 * (k + g);
for i = 1:nfunc
fit = 0.5 * (1 + g);
for j = nfunc - i:-1:1
fit = fit * x(j);
end
if i > 1
fit = fit * (1 - x(nfunc - i + 1));
end
f(i) = fit;
end
%now calculate constraints
c = 1.0 - f(nfunc) / 0.6;
for i = 1: nfunc-1
c = c - f(i) / 0.5;
end
g = [];
if(c>=0)
g(1) = 0;
else
g(1) = c;
end
g(1) = -g(1);
case 'dtlz2'
n=size(x,2);
nfunc = opt.M;
k = n - nfunc + 1;
g = 0;
for i = nfunc:n
g = g + power( x(i)-0.5,2);
end
f = zeros(1,nfunc);
for i = 1:nfunc
h = 1 + g;
for j=1:nfunc - i
h =h * cos( x(j) * 3.141592654 / 2);
end
if (i > 1)
h = h*sin( x((nfunc - i + 1)) * 3.141592654 / 2);
end
f(i) = h;
end
case 'c2dtlz2'
n=size(x,2);
nfunc = opt.M;
k = n - nfunc + 1;
g = 0;
for i = nfunc:n
g = g + power( x(i)-0.5,2);
end
f = zeros(1,nfunc);
for i = 1:nfunc
h = 1 + g;
for j=1:nfunc - i
h =h * cos( x(j) * 3.141592654 / 2);
end
if (i > 1)
h = h*sin( x((nfunc - i + 1)) * 3.141592654 / 2);
end
f(i) = h;
end
%now calculate constraints
if(nfunc>3)
r = 0.5;
else
r = 0.4;
end
v1 = realmax;
v2 = 0.0;
for i = 1: nfunc
sum1 = power(f(i)-1.0, 2.0);
for j = 1: nfunc
if i ~= j
sum1 = sum1 + power(f(j), 2.0);
end
end
v1 = min(v1, sum1 - power(r, 2.0));
v2 = v2 + power(f(i) - (1.0 / sqrt(nfunc)), 2.0);
end
c = min(v1, v2 - power(r, 2.0));
g = [];
if(c<=0)
g(1) = c;
else
g(1) = c;
end
case 'c3dtlz2'
n = length(x);
xg=x(3:n);
gx=sum((xg-0.5).^2);
f(1)=(1+gx)*cos(x(1)*0.5*pi)*cos(x(2)*0.5*pi);
f(2)=(1+gx)*cos(x(1)*0.5*pi)*sin(x(2)*0.5*pi);
f(3)=(1+gx)*sin(x(1)*0.5*pi);
g(1) = f(1)^2/4 + f(2)^2 + f(3)^2 - 1;
g(2) = f(2)^2/4 + f(1)^2 + f(3)^2 - 1;
g(3) = f(3)^2/4 + f(1)^2 + f(2)^2 - 1;
case 'dtlz3'
n=size(x,2);
nfunc = opt.M;
k = n - nfunc + 1;
g = 0;
for i = nfunc:n
g = g + power(( x(i)-0.5),2) - cos(20 * 3.141592654 * ( x(i)-0.5));
end
g = 100 * (k + g);
f = zeros(1,nfunc);
for i = 1:nfunc
h = 1 + g;
for j=1:nfunc - i
h =h * cos( x(j) * 3.141592654 / 2);
end
if (i > 1)
h = h*sin( x((nfunc - i + 1)) * 3.141592654 / 2);
end
f(i) = h;
end
case 'dtlz4'
n=size(x,2);
nfunc = opt.M;
k = n - nfunc + 1;
g = 0;
alpha = 100;
for i = nfunc:n
g = g + power( x(i)-0.5,2);
end
f = zeros(1,nfunc);
for i = 1:nfunc
h = 1 + g;
for j=1:nfunc - i
h = h * cos(power( x(j),alpha) * 3.141592654 / 2);
end
if (i > 1)
h = h*sin(power( x((nfunc - i + 1)),alpha) * 3.141592654 / 2);
end
f(i) = h;
end
case 'dtlz5'
n=size(x,2);
nfunc = opt.M;
g = 0;
k = n - nfunc + 1;
for i = nfunc:n
g = g + power( x(i)-0.5,2);
end
t = 3.141592654 / (4 * (1 + g));
theta=[];
theta(1) = x(1) * 3.141592654 / 2;
for i = 2: nfunc - 1
theta(i) = t * (1 + 2 * g * x(i));
end
f = [];
for i = 1:nfunc
h = 1 + g;
for j=1:nfunc - i
h =h * cos(theta(j));
end
if (i > 1)
h = h*sin(theta((nfunc - i + 1)));
end
f(i) = h;
end
case 'dtlz7'
n=size(x,2);
nfunc = opt.M;
k = n - nfunc + 1;
g = sum(x(nfunc:n));
g = 1 + 9 * g / k;
for i = 1:nfunc-1
f(i)=x(i);
end
h2=0;
for j = 1:nfunc-1
h2 =h2 + x(j) / (1 + g) * (1 + sin(3 * 3.141592654 * x(j)));
end
h2 = nfunc - h2;
f(nfunc) = (1 + g) * h2;
case 'bnh'
f(1) = 4*x(1)^2+4*x(2)^2;
f(2) = (x(1)-5)^2+(x(2)-5)^2;
%g(1) = (1/25)*((x(1)-5)^2 + x(2)^2-25);
%g(2) = -(1/65.3)*((x(1)-8)^2 + (x(2)+3)^2-7.7);%1/7.7*((x(1)-8)^2 + (x(2)+3)^2-7.7);
g(1) = (1/25)*((x(1)-5)^2 + x(2)^2-25);
g(2) = -1/7.7*((x(1)-8)^2 + (x(2)+3)^2-7.7);
case 'osy'
f(1) = -(25*(x(1)-2)^2+(x(2)-2)^2+(x(3)-1)^2+(x(4)-4)^2+(x(5)-1)^2);
f(2) = x(1)^2+x(2)^2+x(3)^2+x(4)^2+x(5)^2+x(6)^2;
g(1) = (-1/2)*(x(1)+x(2)-2);
g(2) = (-1/6)*(6-x(1)-x(2));
g(3) = (-1/2)*(2-x(2)+x(1));
g(4) = (-1/2)*(2-x(1)+3*x(2));
g(5) = (-1/4)*(4-(x(3)-3)^2 -x(4));
g(6) = (-1/4)*((x(5)-3)^2+x(6)-4);
% g(1) = (-1/8)*(x(1)+x(2)-2);
% g(2) = (-1/6)*(6-x(1)-x(2));
% g(3) = (-1/12)*(2-x(2)+x(1));
% g(4) = (-1/32)*(2-x(1)+3*x(2));
% g(5) = (-1/8)*(4-(x(3)-3)^2 -x(4));
% g(6) = (-1/10)*((x(5)-3)^2+x(6)-4);
case 'srn'
f(1) = 2.0+(x(1)-2.0)^2+(x(2)-1.0)^2;
f(2) = 9.0*x(1)-(x(2)-1)^2;
g(1) = (1/225)*(x(1)^2+x(2)^2-225.0);
g(2) = 0.1*(x(1)-3.0*x(2)+10.0);
%g(1) = (1/575)*(x(1)^2+x(2)^2-225.0);
%g(2) = (1/30)*(x(1)-3.0*x(2)+10.0);
case 'tnk'
f(1) = x(1);
f(2) = x(2);
g(1) = (-1)*(x(1)^2+x(2)^2-1.0-0.1*cos(16*atan(x(1)/x(2))));
g(2) = (1/0.5)*((x(1)-0.5)^2+(x(2)-0.5)^2-0.5);
%g(1) = (-1/(2*(pi^2)-2))*(x(1)^2+x(2)^2-1.0-0.1*cos(16*atan(x(1)/x(2))));
%g(2) = (1/(2*(pi^2)-2*pi))*((x(1)-0.5)^2+(x(2)-0.5)^2-0.5);
case 'water'
f(1) = (106780.37 * (x(2) + x(3)) + 61704.67)/(8 * power(10, 4));
f(2) = (3000.0 * x(1))/1500;
f(3) = ((305700 * 2289*x(2))/power(0.06 * 2289.0,0.65))/(3 * power(10, 6));
f(4) = (250.0 * 2289.0 * exp(-39.75*x(2) + 9.9*x(3) + 2.74))/(6*power(10, 6));
f(5) = (25.0*((1.39/(x(1)*x(2))) + 4940.0*x(3) - 80.0))/8000;
g(1) = (0.00139/(x(1)*x(2)) + 4.94*x(3) - 0.08 - 1)/13.314;
g(2) = (0.000306/(x(1)*x(2)) + 1.082*x(3) - 0.0986 - 1)/2.0696;
g(3) = (12.307/(x(1)*x(2)) + 49408.24*x(3) + 4051.02 - 50000)/82061.844;
g(4) = (2.098/(x(1)*x(2)) + 8046.33*x(3) - 696.71 - 16000)/5087.923;
g(5) = (2.138/(x(1)*x(2)) + 7883.39*x(3) - 705.04 - 10000)/11463.299;
g(6) = (0.417*(x(1)*x(2)) + 1721.26*x(3) - 136.54 - 2000)/1.0; %this is always feasible
g(7) = (0.164/(x(1)*x(2)) + 631.13*x(3) - 54.48 - 550)/1098.633;
case 'carside'
%{
f(1) = 1.98 + 4.9*x(1) + 6.67*x(2) + 6.98*x(3) + 4.01*x(4) + 1.78*x(5) + 0.00001*x(6) + 2.73*x(7);
g(1) = (1/0.16)*(1.16 - 0.3717*x(2)*x(4) - 0.0092928*x(3) - 1);
g(2) = (1/.059)*(0.261 - 0.0159*x(1)*x(2) - 0.06486*x(1) - 0.019*x(2)*x(7) + 0.0144*x(3)*x(5) + 0.0154464*x(6) - 0.32);
g(3) = (1/0.106)*(0.214 + 0.00817*x(5) - 0.045195*x(1) - 0.0135168*x(1) + 0.03099*x(2)*x(6) - 0.018*x(2)*x(7) + 0.007176*x(3)+ 0.023232*x(3) - 0.00364*x(5)*x(6) - 0.018*x(2)*x(2)- 0.32);
g(4) = (1/0.42)*(0.74 - 0.61*x(2) - 0.031296*x(3) - 0.031872*x(7) + 0.227*x(2)*x(2)- 0.32);
g(5) = (1/3.02)*(28.98 + 3.818*x(3) - 4.2*x(1)*x(2) + 1.27296*x(6) - 2.68065*x(7) - 32);
g(6) = (1/1.86)*(33.86 + 2.95*x(3) - 5.057*x(1)*x(2) - 3.795*x(2) - 3.4431*x(7)+ 1.45728 - 32);
g(7) = (1/14.36)*(46.36 - 9.9*x(2) - 4.4505*x(1) - 32);
g(8) = (1/0.72)*(4.72 - 0.5*x(4) - 0.19*x(2)*x(3) - 4);
g(9) = (10.58 - 0.674*x(1)*x(2) - 0.67275*x(2) - 9.9);
g(10) = (16.45 - 0.489*x(3)*x(7) - 0.843*x(5)*x(6) - 15.7);
f(2) = g(8);
f(3) = 0.5*(g(9)+g(10)+ 9.9+ 15.7);
g(9) = (1/0.68)*g(9);
g(10) = (1/0.75)*g(10);
%}
g(1) = 1.16 - 0.3717 *x(2)*x(4)- 0.0092928 *x(3);
g(2) = 0.261 - 0.0159 * x(1) *x(2)- 0.188 *x(1)* 0.345 - 0.019 *x(2)*x(7) + 0.0144*x(3)*x(5)+ 0.08045 *x(6)* 0.192;
g(3) = 0.214 + 0.00817 *x(5)- 0.131 * x(1) * 0.345 - 0.0704 * x(1) * 0.192 + 0.03099*x(2)*x(6)- 0.018 *x(2)*x(7)+ 0.0208 *x(3)* 0.345 + 0.121 *x(3)* 0.192 - 0.00364*x(5)*x(6)- 0.018 *x(2)^2;
g(4) = 0.74 - 0.61 *x(2) - 0.031296 *x(3)- 0.166 *x(7)* 0.192 + 0.227 *x(2)^2;
g(5) = 28.98 + 3.818 *x(3)- 4.2 * x(1)*x(2)+ 6.63 *x(6)* 0.192 - 7.77 *x(7)* 0.345;
g(6) = 33.86 + 2.95 *x(3)- 5.057 * x(1) *x(2)- 11 *x(2)* 0.345 - 9.98 *x(7)* 0.345 +22 * 0.345 * 0.192;
g(7) = 46.36 - 9.9 *x(2)- 12.9 * x(1) * 0.345;
g(8) = 4.72 - 0.5 *x(4)- 0.19 *x(2)*x(3);
g(9) = 10.58 - 0.674 * x(1)*x(2)- 1.95 *x(2)* 0.345;
g(10) = 16.45 - 0.489 *x(3)*x(7)- 0.843 *x(5)*x(6);
f(1) = 1.98 + 4.9 *x(1)+ 6.67 *x(2)+ 6.98 *x(3)+ 4.01 *x(4) + 1.78 *x(5)+ 0.00001*x(6)+ 2.73 *x(7);
f(2) = g(8);
f(3) = (g(9) + g(10)) / 2.0;
g(1)=- 1 + g(1) / 1.0;
g(2)= -1 + g(2) / 0.32;
g(3)= -1 + g(3) / 0.32;
g(4)= -1 + g(4) / 0.32;
g(5)= -1 + g(5) / 32.0;
g(6)= -1 +g(6)/ 32.0;
g(7)= -1 + g(7)/ 32.0;
g(8)= -1 + g(8)/ 4.0;
g(9)= -1 + g(9)/ 9.9;
g(10)= -1 + g(10)/ 15.7;
case 'welded'
f(1) = 1.10471*x(1)^2*x(2)+0.04811*x(3)*x(4)*(14.0+x(2));
f(2) = 2.1952/(x(4)*x(3)^3);
P = 6000; L = 14; t_max = 13600; s_max = 30000;
R = sqrt(0.25*(x(2)^2+(x(1)+x(3))^2));
M = P*(L+x(2)/2);
J = 2*sqrt(0.5)*x(1)*x(2)*(x(2)^2/12 +0.25*(x(1)+x(3))^2);
t1 = P/(sqrt(2)*x(1)*x(2));
t2 = M*R/J;
t = sqrt(t1^2+t2^2+t1*t2*x(2)/R);
s = 6*P*L/(x(4)*x(3)^2);
P_c = 64746.022*(1-0.0282346*x(3))* x(3)*x(4)^3;
% Constraints
g(1) = (1/t_max)*(t - t_max);
g(2) = (1/s_max)*(s - s_max);
g(3) = (1/(5-0.125))*(x(1)-x(4));
g(4) = (1/P)*(P-P_c);
case 'do2dk2'
javaaddpath(pwd);
method = KneeProblem;
method.evaluate_DO2DK2(x)
f = method.objective;
f = f';
case 'deb2dk'
javaaddpath(pwd);
method = KneeProblem;
method.evaluate_DEB2DK(x)
f = method.objective;
f = f';
case 'deb3dk'
javaaddpath(pwd);
method = KneeProblem;
method.evaluate_DEB3DK(x)
f = method.objective;
f = f';
case 'toy'
a = 0.1;
b = 40;
c = a*(-cos(2*pi*b*x));
if x<0
f(1) = x + c +a; % x<0.5
f(2) = 1 - x + c + a;
else
f(1) = x;
f(2) = 1 - x;
end
case 'uf1'
f = UF1(x')';
case 'uf2'
f = UF2(x')';
case 'uf3'
f = UF3(x')';
case 'uf4'
f = UF4(x')';
case 'uf5'
f = UF5(x')';
case 'uf6'
f = UF6(x')';
case 'uf7'
f = UF7(x')';
case 'uf8'
f = UF8(x')';
case 'uf9'
f = UF9(x')';
otherwise
input('Function defition is not found inside high fidelity evaluation');
end
if opt.C==0
g = [];
end
end