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cec09.cpp
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// cec09.cpp
#ifndef __CEC09_CPP_
#define __CEC09_CPP_
//#include "cec09.h"
//#include "global.h"
#include "common.h"
#include <math.h>
//------------------------------DTLZ-------------------------------//
void DTLZ1(vector<double> x_var, vector<double> &y_obj, int nvar, int nobj)
{
double g = 0;
for(int n=nobj-1; n<nvar;n++)
g = g + pow(x_var[n]-0.5,2) - cos(20*PI*(x_var[n] - 0.5));
g = 100*(nvar + 1 - nobj + g);
int i,j, aux;
for (i = 0; i < nobj; i++) y_obj[i] = (1.0 + g) * 0.5;
for (i = 0; i < nobj; i++)
{
for (j = 0; j < nobj - (i + 1); j++) y_obj[i] *= x_var[j];
if (i != 0) {
aux = nobj - (i + 1);
y_obj[i] *= 1 - x_var[aux];
} //if
}//for
return;
}
void DTLZ2(vector<double> x_var, vector<double> &y_obj, int nvar, int nobj)
{
int i,j, aux;
double g = 0.0;
for (i = nobj - 1; i < nvar; i++) g += (x_var[i] - 0.5) * (x_var[i] - 0.5);
for (i = 0; i < nobj; i++) y_obj[i] = 1.0 + g;
for (i = 0; i < nobj; i++)
{
for (j = 0; j < nobj - (i + 1); j++)
y_obj[i] *= cos(x_var[j] * 0.5 * PI);
if (i != 0) {
aux = nobj - (i + 1);
y_obj[i] *= sin(x_var[aux] * 0.5 * PI);
} // if
} // for
return;
}
void DTLZ3(vector<double> x_var, vector<double> &y_obj, int nvar, int nobj)
{
double g = 0;
for(int n=nobj-1; n<nvar;n++)
g = g + pow(x_var[n]-0.5,2) - cos(20*PI*(x_var[n] - 0.5));
g = 100*(nvar + 1 - nobj + g);
int i,j, aux;
for (i = 0; i < nobj; i++) y_obj[i] = 1.0 + g;
for (i = 0; i < nobj; i++)
{
for (j = 0; j < nobj - (i + 1); j++)
y_obj[i] *= cos(x_var[j] * 0.5 * PI);
if (i != 0) {
aux = nobj - (i + 1);
y_obj[i] *= sin(x_var[aux] * 0.5 * PI);
} //if
} // for
return;
}
void DTLZ4(vector<double> x_var, vector<double> &y_obj, int nvar, int nobj)
{
int i,j, aux;
double alpha = 100;
double g = 0.0;
for (i = nobj-1; i < nvar; i++) g += (x_var[i] - 0.5) * (x_var[i] - 0.5);
for (i = 0; i < nobj; i++) y_obj[i] = 1.0 + g;
for (i = 0; i < nobj; i++)
{
for (j = 0; j < nobj - (i + 1); j++)
y_obj[i] *= cos( pow(x_var[j], alpha) * 0.5 * PI);
if (i != 0) {
aux = nobj - (i + 1);
y_obj[i] *= sin( pow(x_var[aux], alpha) * 0.5 * PI);
} //if
} // for
return;
}
void DTLZ7(vector<double> x_var, vector<double> &y_obj, int nvar, int nobj)
{
int i;
double g = 0.0, h = 0.0;
for (i = nobj - 1; i < nvar; i++) g += x_var[i];
g = 1 + (9.0 * g) / (nvar + 1 - nobj);
for (i = 0; i < nobj - 1; i++) y_obj[i] = x_var[i];
for (i = 0; i < nobj - 1; i++) h += (y_obj[i] / (1.0 + g)) * (1 + sin(3.0 * PI * y_obj[i]));
h = nobj - h;
y_obj[nobj - 1] = (1 + g) * h;
return;
}
//------------------------------DTLZ-------------------------------//
//------------------------------WFG-------------------------------//
void WFG1(vector<double> x_var, vector<double> &y_obj, int nvar, int nobj)
{
vector<double> y = WFG_normalise_z( x_var );
int k = position_parameters;
y = WFG1_t1(y, k);
y = WFG1_t2(y, k);
//y = WFG1_t3(y);
y = WFG1_t4(y, k);
y_obj = WFG1_shape(y);
return;
}
void WFG2(vector<double> x_var, vector<double> &y_obj, int nvar, int nobj)
{
vector< double > y = WFG_normalise_z( x_var );
int k = position_parameters;
y = WFG1_t1( y, k);
y = WFG2_t2( y, k);
y = WFG2_t3( y, k);
y_obj = WFG2_shape( y );
return;
}
void WFG3(vector<double> x_var, vector<double> &y_obj, int nvar, int nobj)
{
vector< double > y = WFG_normalise_z( x_var );
int k = position_parameters;
y = WFG1_t1( y, k);
y = WFG2_t2( y, k);
y = WFG2_t3( y, k);
y_obj = WFG3_shape( y );
return;
}
void WFG4(vector<double> x_var, vector<double> &y_obj, int nvar, int nobj)
{
vector< double > y = WFG_normalise_z( x_var );
int k = position_parameters;
y = WFG4_t1( y);
y = WFG2_t3( y, k);
y_obj = WFG4_shape( y );
return;
}
void WFG5(vector<double> x_var, vector<double> &y_obj, int nvar, int nobj)
{
vector< double > y = WFG_normalise_z( x_var );
int k = position_parameters;
y = WFG5_t1( y );
y = WFG2_t3( y, k);
y_obj = WFG4_shape( y );
return;
}
void WFG6(vector<double> x_var, vector<double> &y_obj, int nvar, int nobj)
{
vector< double > y = WFG_normalise_z( x_var );
int k = position_parameters;
y = WFG1_t1( y, k);
y = WFG6_t2( y, k);
y_obj = WFG4_shape( y );
return;
}
void WFG7(vector<double> x_var, vector<double> &y_obj, int nvar, int nobj)
{
vector< double > y = WFG_normalise_z( x_var );
int k = position_parameters;
y = WFG7_t1( y, k );
y = WFG1_t1( y, k);
y = WFG2_t3( y, k);
y_obj = WFG4_shape( y );
return;
}
void WFG8(vector<double> x_var, vector<double> &y_obj, int nvar, int nobj)
{
vector< double > y = WFG_normalise_z( x_var );
int k = position_parameters;
y = WFG8_t1( y, k );
y = WFG1_t1( y, k);
y = WFG2_t3( y, k);
y_obj = WFG4_shape( y );
return;
}
void WFG9(vector<double> x_var, vector<double> &y_obj, int nvar, int nobj)
{
vector< double > y = WFG_normalise_z( x_var );
int k = position_parameters;
y = WFG9_t1( y);
y = WFG9_t2( y, k);
y = WFG6_t2( y, k);
y_obj = WFG4_shape( y );
return;
}
//------------------------------WFG-------------------------------//
//---MOPs for Visually Examining Diversity Maintenance Behavior in a Decision Space---//
void PStar(vector<double> x_var, vector<double> &y_obj, int nvar, int nobj)
{
int i;
double Radius = 20.0, theta = 0.0, MidPointX = 50, MidPointY = 50;
vector<double> temp_object;
//1. generate nobj vertexes (in decision space) evenly distributed on the circle.
for (i = 0; i < nobj; i++)
{
theta = 2.0 * PI * i / nobj;
temp_object.push_back(Radius * cos(theta) + MidPointX);
temp_object.push_back(Radius * sin(theta) + MidPointY);
y_obj[i] = dist_vector(temp_object, x_var);
temp_object.clear();
}
return;
}
void LPMS(vector<double> x_var, vector<double> &y_obj, int nvar, int nobj)
{
y_obj[0] = InformationLoss(x_var);
vector<double> xx = vector<double>(nvar, 0.0);
xx[0] = x_var[0] - 1.2; xx[1] = x_var[1] - 1.5;
y_obj[1] = InformationLoss(xx);
xx[0] = x_var[0] + 0.3; xx[1] = x_var[1] - 3.0;
y_obj[2] = InformationLoss(xx);
xx[0] = x_var[0] - 1; xx[1] = x_var[1] + 0.5;
y_obj[3] = InformationLoss(xx);
xx[0] = x_var[0] -0.5; xx[1] = x_var[1]-1.7;
y_obj[4] = InformationLoss(xx);
xx.clear();
return;
}
//---MOPs for Visually Examining Diversity Maintenance Behavior in a Decision Space---//
//--------------MOPs with a low-dimensional Pareto-optimal front--------------//
void DTLZ5_3(vector<double> x_var, vector<double> &y_obj, int nvar, int nobj)
{
int i,j, aux;
double g = 0.0;
for (i = nobj - 1; i < nvar; i++) g += (x_var[i] - 0.5) * (x_var[i] - 0.5);
for (i = 0; i < nobj; i++) y_obj[i] = 1.0 + g;
int I = 3;
for (i = 0; i < nobj; i++)
{
for (j = 0; j < nobj - (i + 1); j++) {
if (j < I - 1) {
y_obj[i] *= cos(PI * (1 + 2 * g * x_var[j]) * 0.25 / (1 + g)); }
else {
y_obj[i] *= cos(x_var[j] * 0.5 * PI); }
}
if (i != 0) {
aux = nobj - (i + 1);
if (aux < I - 1) {
y_obj[i] *= sin(PI * (1 + 2 * g * x_var[aux]) * 0.25 / (1 + g)); }
else {
y_obj[i] *= sin(x_var[aux] * 0.5 * PI); }
} //if
} // for
return;
}
//--------------MOPs with a low-dimensional Pareto-optimal front--------------//
namespace CEC09
{
#define PI 3.1415926535897932384626433832795
#define MYSIGN(x) ((x)>0?1.0:-1.0)
/*
void UF1(vector<double> x, vector<double> &f, const unsigned int nx)
{
unsigned int j, count1, count2;
double sum1, sum2, yj;
sum1 = sum2 = 0.0;
count1 = count2 = 0;
for(j = 2; j <= nx; j++)
{
yj = x[j-1] - sin(6.0*PI*x[0] + j*PI/nx);
yj = yj * yj;
if(j % 2 == 0)
{
sum2 += yj;
count2++;
}
else
{
sum1 += yj;
count1++;
}
}
f[0] = x[0] + 2.0 * sum1 / (double)count1;
f[1] = 1.0 - sqrt(x[0]) + 2.0 * sum2 / (double)count2;
}
void UF2(vector<double> x, vector<double> &f, const unsigned int nx)
{
unsigned int j, count1, count2;
double sum1, sum2, yj;
sum1 = sum2 = 0.0;
count1 = count2 = 0;
for(j = 2; j <= nx; j++)
{
if(j % 2 == 0)
{
yj = x[j-1]-0.3*x[0]*(x[0]*cos(4.0*(6.0*PI*x[0]+j*PI/nx))+2.0)*cos(6.0*PI*x[0]+j*PI/nx);
sum2 += yj*yj;
count2++;
}
else
{
yj = x[j-1]-0.3*x[0]*(x[0]*cos(4.0*(6.0*PI*x[0]+j*PI/nx))+2.0)*sin(6.0*PI*x[0]+j*PI/nx);
sum1 += yj*yj;
count1++;
}
}
f[0] = x[0] + 2.0 * sum1 / (double)count1;
f[1] = 1.0 - sqrt(x[0]) + 2.0 * sum2 / (double)count2;
}
void UF3(vector<double> x, vector<double> &f, const unsigned int nx)
{
unsigned int j, count1, count2;
double sum1, sum2, prod1, prod2, yj, pj;
sum1 = sum2 = 0.0;
count1 = count2 = 0;
prod1 = prod2 = 1.0;
for(j = 2; j <= nx; j++)
{
yj = x[j-1]-pow(x[0],0.5*(1.0+3.0*(j-2.0)/(nx-2.0)));
pj = cos(20.0*yj*PI/sqrt(j+0.0));
if (j % 2 == 0)
{
sum2 += yj*yj;
prod2 *= pj;
count2++;
}
else
{
sum1 += yj*yj;
prod1 *= pj;
count1++;
}
}
f[0] = x[0] + 2.0*(4.0*sum1 - 2.0*prod1 + 2.0) / (double)count1;
f[1] = 1.0 - sqrt(x[0]) + 2.0*(4.0*sum2 - 2.0*prod2 + 2.0) / (double)count2;
}
void UF4(vector<double> x, vector<double> &f, const unsigned int nx)
{
unsigned int j, count1, count2;
double sum1, sum2, yj, hj;
sum1 = sum2 = 0.0;
count1 = count2 = 0;
for(j = 2; j <= nx; j++)
{
yj = x[j-1]-sin(6.0*PI*x[0]+j*PI/nx);
hj = fabs(yj)/(1.0+exp(2.0*fabs(yj)));
if (j % 2 == 0)
{
sum2 += hj;
count2++;
}
else
{
sum1 += hj;
count1++;
}
}
f[0] = x[0] + 2.0*sum1 / (double)count1;
f[1] = 1.0 - x[0]*x[0] + 2.0*sum2 / (double)count2;
}
void UF5(vector<double> x, vector<double> &f, const unsigned int nx)
{
unsigned int j, count1, count2;
double sum1, sum2, yj, hj, N, E;
sum1 = sum2 = 0.0;
count1 = count2 = 0;
N = 10.0; E = 0.1;
for(j = 2; j <= nx; j++)
{
yj = x[j-1] - sin(6.0*PI*x[0]);
hj = 2.0*yj*yj - cos(4.0*PI*yj) + 1.0;
if (j % 2 == 0)
{
sum2 += hj;
count2++;
}
else
{
sum1 += hj;
count1++;
}
}
hj = 0.5*(0.5/N + E)*fabs(sin(2.0*N*PI*x[0]));
f[0] = x[0] + hj + 2.0*sum1 / (double)count1;
f[1] = 1.0 - x[0] + hj + 2.0*sum2 / (double)count2;
}
void UF6(vector<double> x, vector<double> &f, const unsigned int nx)
{
unsigned int j, count1, count2;
double sum1, sum2, yj, hj, N, E;
sum1 = sum2 = 0.0;
count1 = count2 = 0;
N = 2.0; E = 0.1;
for(j = 2; j <= nx; j++)
{
yj = x[j-1] - sin(6.0*PI*x[0]+j*PI/nx);
if (j % 2 == 0)
{
sum2 += yj*yj;
count2++;
}
else
{
sum1 += yj*yj;
count1++;
}
}
hj = 0.5*(0.5/N + E)*sin(2.0*N*PI*x[0]);
if(hj<0.0) hj = 0.0;
f[0] = x[0] + hj + 2.0*sum1 / (double)count1;
f[1] = 1.0 - x[0] + hj + 2.0*sum2 / (double)count2;
}
void UF7(vector<double> x, vector<double> &f, const unsigned int nx)
{
unsigned int j, count1, count2;
double sum1, sum2, yj;
sum1 = sum2 = 0.0;
count1 = count2 = 0;
for(j = 2; j <= nx; j++)
{
yj = x[j-1] - sin(6.0*PI*x[0]+j*PI/nx);
if (j % 2 == 0)
{
sum2 += yj*yj;
count2++;
}
else
{
sum1 += yj*yj;
count1++;
}
}
yj = pow(x[0],0.2);
f[0] = yj + 2.0*sum1 / (double)count1;
f[1] = 1.0 - yj + 2.0*sum2 / (double)count2;
}
void UF8(vector<double> x, vector<double> &f, const unsigned int nx)
{
unsigned int j, count1, count2, count3;
double sum1, sum2, sum3, yj;
sum1 = sum2 = sum3 = 0.0;
count1 = count2 = count3 = 0;
for(j = 3; j <= nx; j++)
{
yj = x[j-1] - 2.0*x[1]*sin(2.0*PI*x[0]+j*PI/nx);
if(j % 3 == 1)
{
sum1 += yj*yj;
count1++;
}
else if(j % 3 == 2)
{
sum2 += yj*yj;
count2++;
}
else
{
sum3 += yj*yj;
count3++;
}
}
f[0] = cos(0.5*PI*x[0])*cos(0.5*PI*x[1]) + 2.0*sum1 / (double)count1;
f[1] = cos(0.5*PI*x[0])*sin(0.5*PI*x[1]) + 2.0*sum2 / (double)count2;
f[2] = sin(0.5*PI*x[0]) + 2.0*sum3 / (double)count3;
}
void UF9(vector<double> x, vector<double> &f, const unsigned int nx)
{
unsigned int j, count1, count2, count3;
double sum1, sum2, sum3, yj, E;
E = 0.1;
sum1 = sum2 = sum3 = 0.0;
count1 = count2 = count3 = 0;
for(j = 3; j <= nx; j++)
{
yj = x[j-1] - 2.0*x[1]*sin(2.0*PI*x[0]+j*PI/nx);
if(j % 3 == 1)
{
sum1 += yj*yj;
count1++;
}
else if(j % 3 == 2)
{
sum2 += yj*yj;
count2++;
}
else
{
sum3 += yj*yj;
count3++;
}
}
yj = (0.5+E)*(1.0-4.0*(2.0*x[0]-1.0)*(2.0*x[0]-1.0));
if(yj<0.0) yj = 0.0;
f[0] = 0.5*(yj + 2*x[0])*x[1] + 2.0*sum1 / (double)count1;
f[1] = 0.5*(yj - 2*x[0] + 2.0)*x[1] + 2.0*sum2 / (double)count2;
f[2] = 1.0 - x[1] + 2.0*sum3 / (double)count3;
}
void UF10(vector<double> x, vector<double> &f, const unsigned int nx)
{
unsigned int j, count1, count2, count3;
double sum1, sum2, sum3, yj, hj;
sum1 = sum2 = sum3 = 0.0;
count1 = count2 = count3 = 0;
for(j = 3; j <= nx; j++)
{
yj = x[j-1] - 2.0*x[1]*sin(2.0*PI*x[0]+j*PI/nx);
hj = 4.0*yj*yj - cos(8.0*PI*yj) + 1.0;
if(j % 3 == 1)
{
sum1 += hj;
count1++;
}
else if(j % 3 == 2)
{
sum2 += hj;
count2++;
}
else
{
sum3 += hj;
count3++;
}
}
f[0] = cos(0.5*PI*x[0])*cos(0.5*PI*x[1]) + 2.0*sum1 / (double)count1;
f[1] = cos(0.5*PI*x[0])*sin(0.5*PI*x[1]) + 2.0*sum2 / (double)count2;
f[2] = sin(0.5*PI*x[0]) + 2.0*sum3 / (double)count3;
}
*/
/****************************************************************************/
// 5-objctive test instances
/****************************************************************************/
/*
#define a 1
#define b 10
#define c 8
#define c1 (a+c/2)
#define c2 (c+2*a)
#define b1 (b/2)
void R2_DTLZ2_M5(vector<double> x, vector<double> &f, const unsigned int nx, const unsigned int n_obj)
{
int i=0,j=0;
int k = nx - n_obj + 1;
double g = 0;
double sum = 0;
//double z[nx],zz[nx],p[nx],psum[n_obj],M[nx][nx],lamda_l[nx];
double *z, *zz, *p, *psum, **M, *lamda_l;
double M_10D[10][10]={{0.0346, -0.7523, 0.3561, -0.2958, 0.4675,0,0,0,0,0},{0.8159, -0.0423, 0.4063, 0.3455, -0.2192,0,0,0,0,0},{-0.3499, 0.3421, 0.8227, -0.2190, -0.1889,0,0,0,0,0},{-0.0963, -0.4747, -0.0998, -0.2429, -0.8345,0,0,0,0,0},{-0.4487, -0.2998, 0.1460, 0.8283, -0.0363,0,0,0,0,0},{0,0,0,0,0,1,0,0,0,0},{0,0,0,0,0,0,1,0,0,0},{0,0,0,0,0,0,0,1,0,0},{0,0,0,0,0,0,0,0,1,0},{0,0,0,0,0,0,0,0,0,1}};
double lamda_l_10D[10]={0.313,0.312,0.321,0.316,0.456,1,1,1,1,1};
double M_30D[30][30]={{0.0128,0.2165,0.4374,-0.0800,0.0886,-0.2015,0.1071,0.2886,0.2354,0.2785,-0.1748,0.2147,0.1649,-0.3043,0.5316,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{0.4813, 0.2420, -0.3663, -0.0420, -0.0088, -0.4945, -0.3073, 0.1990, 0.0441, -0.0627, 0.0191, 0.3880, -0.0618, -0.0319, -0.1833,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{0.4816, -0.2254, 0.0663, 0.4801, 0.2009, -0.0008, -0.1501, 0.0269, -0.2037,0.4334, -0.2157, -0.3175, -0.0923, 0.1451, 0.1118,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{-0.0876, -0.2667, -0.0063, 0.2114, 0.4506, 0.0823, -0.0125, 0.2313, 0.0840,-0.2376, 0.1938, -0.0030, 0.3391, 0.0863, 0.1231,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{-0.1025, 0.4011, -0.0117, 0.2076, 0.2585, 0.1124, -0.0288, 0.3095, -0.6146,-0.2376, 0.1938, -0.0030, 0.3391, 0.0863, 0.1231,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{0.4543, -0.2761, -0.2985, -0.2837, 0.0634, 0.1070, 0.2996, -0.2690, -0.1634,-0.1452, 0.1799, -0.0014, 0.2394, -0.2745, 0.3969,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{-0.1422, -0.4364, 0.0751, -0.2235, 0.3966, -0.0252, 0.0908, 0.0477, -0.2254,0.1801, -0.0552, 0.5770, -0.0396, 0.3765, -0.0522,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{0.3542, -0.2245, 0.3497, -0.1609, -0.1107, 0.0079, 0.2241, 0.4517, 0.1309,-0.3355, -0.1123, -0.1831, 0.3000, 0.2045, -0.3191,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{0.0005, 0.0377, -0.2808, -0.0641, 0.1316, 0.2191, 0.0207, 0.3308, 0.4117,0.3839, 0.5775, -0.1219, 0.1192, 0.2435, 0.0414,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{-0.1177, -0.0001, -0.1992, -0.4533, 0.4234, -0.0191, -0.3740, 0.1325, 0.0972,-0.2042, -0.3493, -0.4018, -0.1087, 0.0918, 0.2217,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{0.1818, 0.3022, -0.1388, -0.2380, -0.0773, 0.6463, 0.0450, 0.1030, -0.0958,0.2837, -0.3969, 0.1779, -0.0251, -0.1543, -0.2452,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{-0.1889, -0.4397, -0.2206, 0.0981, -0.5203, 0.1325, -0.3427, 0.4242, -0.1271,-0.0291, -0.0795, 0.1213, 0.0565, -0.1092, 0.2720,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{-0.1808, -0.0624, -0.2689, 0.2289, 0.1128, -0.0844, -0.0549, -0.2202, 0.2450,0.0825, -0.3319, 0.0513, 0.7523, 0.0043, -0.1472,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{-0.0983, 0.0611, -0.4145, 0.3017, 0.0410, -0.0703, 0.6250, 0.2449, 0.1307,-0.1714, -0.3045, 0.0218, -0.2837, 0.1408, 0.1633,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{0.2026, 0.0324, 0.1496, 0.3129, 0.1437, 0.4331, -0.2629, -0.1498, 0.3746,-0.4366, 0.0163, 0.3316, -0.0697, 0.1833, 0.2412,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}};
double lamda_l_30D[30]={0.113,0.105,0.117,0.119,0.108,0.110,0.101,0.107,0.111,0.109,0.120,0.108,0.101,0.105,0.116,1.000,1.000,1.000,1.000,1.000,1.000,1.000,1.000,1.000,1.000,1.000,1.000,1.000,1.000,1.000};
z = new double[nx];
zz = new double[nx];
p = new double[nx];
psum = new double[n_obj];
M = new double*[nx]; for(i=0; i<nx; i++) M[i] = new double[nx];
lamda_l = new double[nx];
if (nx==10)
{
for (i=0;i<nx;i++)
{
for (j=0;j<nx;j++)
{
M[i][j]=M_10D[i][j];
}
lamda_l[i]=lamda_l_10D[i];
}
}
else
{
for (i=0;i<nx;i++)
{
for (j=0;j<nx;j++)
{
M[i][j]=M_30D[i][j];
}
lamda_l[i]=lamda_l_30D[i];
}
}
for (i=0;i<nx;i++)
{
z[i]=0;
for (j=0;j<nx;j++)
{
z[i]+=M[i][j]*x[j];
}
if (z[i]>=0 && z[i]<=1)
{
zz[i]=z[i];
p[i]=0;
}
else if (z[i]<0)
{
zz[i]=-lamda_l[i] * z[i];
p[i]=-z[i];
}
else
{
zz[i]=1-lamda_l[i]*(z[i]-1);
p[i]=z[i]-1;
}
}
for(j=0;j<n_obj;j++)
{
psum[j] = 0;
}
for (i = nx - k + 1; i <= nx; i++)
{
g += pow(zz[i-1]-0.5,2);
for(j=0;j<n_obj;j++)
{
psum[j]= sqrt( pow(psum[j],2) + pow(p[i-1],2) );
}
}
for (i = 1; i <= n_obj; i++)
{
double ff = (1 + g);
for (j = n_obj - i; j >= 1; j--)
{
ff *= cos(zz[j-1] * PI / 2.0);
psum[i-1] = sqrt( pow(psum[i-1],2) + pow(p[j-1],2) );
}
if (i > 1)
{
ff *= sin(zz[(n_obj - i + 1) - 1] * PI / 2.0);
psum[i-1] = sqrt( pow(psum[i-1],2) + pow(p[(n_obj - i + 1) - 1],2) );
}
f[i-1] = 2.0/(1+exp(-psum[i-1])) * (ff+1);
}
delete []z; delete []zz; delete []p;delete []psum; delete []lamda_l;
for(i=0; i<nx; i++) delete []M[i]; delete []M;
}
void R2_DTLZ3_M5(vector<double> x, vector<double> &f, const unsigned int nx, const unsigned int n_obj)
{
int i=0,j=0;
int k = nx - n_obj + 1;
double g = 0;
double sum = 0;
//double z[nx],zz[nx],p[nx],psum[n_obj],M[nx][nx],lamda_l[nx];
double *z, *zz, *p, *psum, **M, *lamda_l;
double M_10D[10][10]={{-0.2861, 0.2796, -0.8507, 0.2837, 0.1893,0,0,0,0,0},{0.2837, 0.8861, 0.1219, -0.3157, 0.1407,0,0,0,0,0},{0.6028, 0.1119, -0.0810, 0.5963, -0.5119,0,0,0,0,0},{-0.6450, 0.3465, 0.4447, 0.4753, -0.2005,0,0,0,0,0},{0.2414, -0.0635, 0.2391, 0.4883, 0.8013,0,0,0,0,0},{0,0,0,0,0,1,0,0,0,0},{0,0,0,0,0,0,1,0,0,0},{0,0,0,0,0,0,0,1,0,0},{0,0,0,0,0,0,0,0,1,0},{0,0,0,0,0,0,0,0,0,1}};
double lamda_l_10D[10]={0.313,0.312,0.321,0.316,0.456,1,1,1,1,1};
double M_30D[30][30]={{-0.1565, -0.2418, 0.5427, -0.2191, 0.2522, -0.0563, 0.1991, 0.1166, 0.2140,-0.0973, -0.0755, 0.4073, 0.4279, -0.1876, -0.0968,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{0.1477, -0.2396, -0.0022, 0.4180, 0.2675, -0.1365, -0.0729, 0.4761, -0.0685,0.2105, 0.1388, 0.1465, -0.0256, 0.0292, 0.5767,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{0.0322, 0.3727, -0.0467, 0.1651, -0.0672, 0.0638, -0.1168, 0.4055, 0.6714,-0.1948, -0.1451, 0.1734, -0.2788, -0.0769, -0.1433,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{-0.3688, 0.1935, 0.3691, 0.4298, 0.2340, 0.2593, -0.3081, -0.2013, -0.2779,-0.0932, 0.0003, 0.0149, -0.2303, -0.3261, -0.0517,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{0.0580, -0.0609, 0.0004, -0.1831, 0.0003, 0.4742, -0.2530, -0.0750, 0.0839,0.1606, 0.6020, 0.4103, -0.0857, 0.2954, -0.0819,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{-0.2145, -0.0056, -0.0251, 0.2288, -0.4870, -0.5486, 0.1253, -0.1512, -0.0390,0.0722, 0.3074, 0.4160, -0.1304, -0.1610, -0.0848,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{0.2557, -0.1087, 0.0679, -0.3120, 0.3567, -0.4644, -0.3535, 0.1060, -0.2158,-0.1330, -0.0154, 0.0911, -0.4154, 0.0356, -0.3085,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{0.2303, 0.4996, 0.1883, 0.1870, 0.1850, -0.0216, 0.4409, -0.0573, -0.2396,0.1471, -0.1540, 0.2731, -0.0398, 0.4505, -0.1131,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{-0.1576, -0.0023, 0.2588, 0.2105, 0.2250, -0.2978, 0.0175, -0.1157, 0.3717,0.0562, 0.4068, -0.5081, 0.0718, 0.3443, -0.1488,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{0.1047, -0.0568, -0.2771, 0.3803, 0.0046, 0.0188, -0.1500, 0.2053, -0.2290,-0.4582, 0.1191, 0.0639, 0.4946, 0.1121, -0.4018,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{0.3943, -0.0374, 0.3004, 0.1472, -0.2988, 0.0443, -0.2483, 0.1350, -0.0160,0.5834, -0.1095, -0.1398, 0.1711, -0.1867, -0.3518,0,0,0,0,0,0,0,0,0,0,0,0,0,0.000,0.000},
{0.1244, -0.6134, 0.1823, 0.3012, -0.1968, 0.1616, 0.1025, -0.1972, 0.1162,-0.2079, -0.3062, 0.0585, -0.3286, 0.3187, -0.0812,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{0.1832, -0.1559, -0.4327, 0.2059, 0.4677, 0.0317, 0.2233, -0.3589, 0.2393,0.2468, 0.0148, 0.1193, -0.0279, -0.3600, -0.2261,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{0.5027, 0.1935, 0.1571, 0.0503, -0.0503, -0.1443, -0.3080, -0.4939, 0.1847,-0.2762, 0.0042, 0.0960, 0.2239, -0.0579, 0.3840,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{0.3948, -0.0002, 0.2172, -0.0293, -0.0835, 0.1614, 0.4559, 0.1626, -0.1155,-0.3087, 0.4331, -0.2223, -0.2213, -0.3658, -0.0188,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}};
double lamda_l_30D[30]={0.113,0.105,0.117,0.119,0.108,0.110,0.101,0.107,0.111,0.109,0.120,0.108,0.101,0.105,0.116,1.000,1.000,1.000,1.000,1.000,1.000,1.000,1.000,1.000,1.000,1.000,1.000,1.000,1.000,1.000};
z = new double[nx];
zz = new double[nx];
p = new double[nx];
psum = new double[n_obj];
M = new double*[nx]; for(i=0; i<nx; i++) M[i] = new double[nx];
lamda_l = new double[nx];
if (nx==10)
{
for (i=0;i<nx;i++)
{
for (j=0;j<nx;j++)
{
M[i][j]=M_10D[i][j];
}
lamda_l[i]=lamda_l_10D[i];
}
}
else
{
for (i=0;i<nx;i++)
{
for (j=0;j<nx;j++)
{
M[i][j]=M_30D[i][j];
}
lamda_l[i]=lamda_l_30D[i];
}
}
for (i=0;i<nx;i++)
{
z[i]=0;
for (j=0;j<nx;j++)
{
z[i]+=M[i][j]*x[j];
}
if (z[i]>=0 && z[i]<=1)
{
zz[i]=z[i];
p[i]=0;
}
else if (z[i]<0)
{
zz[i]=-lamda_l[i] * z[i];
p[i]=-z[i];
}
else
{
zz[i]=1-lamda_l[i]*(z[i]-1);
p[i]=z[i]-1;
}
}
for(j=0;j<n_obj;j++)
{
psum[j] = 0;
}
for (i = nx - k + 1; i <= nx; i++)
{
g += pow(zz[i-1]-0.5,2) - cos(20 * PI * (zz[i-1]-0.5));
for(j=0;j<n_obj;j++)
{
psum[j]= sqrt( pow(psum[j],2) + pow(p[i-1],2) );
}
}
g = 100 * (k + g);
for (i = 1; i <= n_obj; i++)
{
double ff = (1 + g);
for (j = n_obj - i; j >= 1; j--)
{
ff *= cos(zz[j-1] * PI / 2.0);
psum[i-1] = sqrt( pow(psum[i-1],2) + pow(p[j-1],2) );
}
if (i > 1)
{
ff *= sin(zz[(n_obj - i + 1) - 1] * PI / 2.0);
psum[i-1] = sqrt( pow(psum[i-1],2) + pow(p[(n_obj - i + 1) - 1],2) );
}
f[i-1] = 2.0/(1+exp(-psum[i-1])) * (ff+1);
}
delete []z; delete []zz; delete []p;delete []psum; delete []lamda_l;
for(i=0; i<nx; i++) delete []M[i]; delete []M;
}
*/
/*
//// Implemented constants. /////////////////////////////////////////////////
#define EPSILON (1.0e-10)
double correct_to_01(double aa, double epsilon)
{
double min = 0.0, max = 1.0;
double min_epsilon = min - epsilon;
double max_epsilon = max + epsilon;
if ( aa <= min && aa >= min_epsilon )
{
return min;
}
else if ( aa >= max && aa <= max_epsilon )
{
return max;
}
else
{
return aa;
}
}
int vector_in_01( const double *x, int nx )
{
int i;
for( i = 0; i < nx; i++ )
{
if( x[i] < 0.0 || x[i] > 1.0 )
{
return 0;
}
}
return 1;
}
//// Local functions/values. ////////////////////////////////////////////////
double linear( const double *x, const int m,int M )
{
int i;
double result = 1.0;
for( i=1; i <= M-m; i++ )
{
result *= x[i-1];
}
if( m != 1 )
{
result *= 1 - x[M-m];
}
return correct_to_01( result, EPSILON );
}
double convex( const double *x, const int m,int M )
{
int i;
double result = 1.0;
for( i=1; i <= M-m; i++ )
{
result *= 1.0 - cos( x[i-1]*PI/2.0 );
}
if( m != 1 )
{
result *= 1.0 - sin( x[M-m]*PI/2.0 );
}
return correct_to_01( result, EPSILON );
}
double concave( const double *x, const int m,int M )
{
int i;
double result = 1.0;
for( i=1; i <= M-m; i++ )
{
result *= sin( x[i-1]*PI/2.0 );
}
if( m != 1 )
{
result *= cos( x[M-m]*PI/2.0 );
}
return correct_to_01( result, EPSILON );
}
double mixed( const double *x, const int A, const double alpha )
{
const double tmp = 2.0*A*PI;
return correct_to_01( pow( 1.0-x[0]-cos( tmp*x[0] + PI/2.0 )/tmp, alpha ), EPSILON );
}
double disc( const double *x, const int A, const double alpha, const double beta )
{
const double tmp1 = A*pow( x[0], beta )*PI;
return correct_to_01( 1.0 - pow( x[0], alpha )*pow( cos( tmp1 ), 2.0 ), EPSILON );
}
//** Calculate the minimum of two doubles. **********************************
static double min_double( const double aa, const double bb )
{
return aa < bb ? aa : bb;
}
//// Implemented functions. /////////////////////////////////////////////////
double b_poly( const double y, const double alpha )
{
return correct_to_01( pow( y, alpha ), EPSILON );
}
double b_flat
(
const double y,
const double A,
const double B,
const double C
)
{
const double tmp1 = min_double( 0.0, floor( y-B ) ) * A*( B-y )/B;
const double tmp2 = min_double( 0.0, floor( C-y ) ) * ( 1.0-A )*( y-C )/( 1.0-C );
return correct_to_01( A+tmp1-tmp2, EPSILON );
}
double b_param
(
const double y,
const double u,
const double A,