TwoDoubles f4(double* x) {
/* skew Rastrigin-Bueche, condition 10, skew-"condition" 100*/
int i, rseed; /*Loop over dim*/
static unsigned int funcId = 4;
static double condition = 10.;
static double alpha = 100.;
double tmp, tmp2, Fadd, Fval, Fpen = 0., Ftrue = 0.;
TwoDoubles res;
if (!isInitDone)
{
rseed = 3 + 10000 * trialid; /* Not the same as before.*/
/*INITIALIZATION*/
Fopt = computeFopt(funcId, trialid);
computeXopt(rseed, DIM);
for (i = 0; i < DIM; i += 2)
Xopt[i] = fabs(Xopt[i]); /*Skew*/
isInitDone = 1;
}
Fadd = Fopt;
for (i = 0; i < DIM; i++) {
tmp = fabs(x[i]) - 5.;
if (tmp > 0.)
Fpen += tmp * tmp;
}
Fpen *= 1e2;
Fadd += Fpen;
for (i = 0; i < DIM; i++)
{
tmx[i] = x[i] - Xopt[i];
}
monotoneTFosc(tmx);
for (i = 0; i < DIM; i++)
{
if (i % 2 == 0 && tmx[i] > 0)
tmx[i] = sqrt(alpha) * tmx[i];
tmx[i] = pow(sqrt(condition), ((double)i)/((double)(DIM-1))) * tmx[i];
}
/* COMPUTATION core*/
tmp = 0.;
tmp2 = 0.;
for (i = 0; i < DIM; i++)
{
tmp += cos(2*M_PI*tmx[i]);
tmp2 += tmx[i]*tmx[i];
}
Ftrue = 10 * (DIM - tmp) + tmp2;
Ftrue += Fadd;
Fval = Ftrue; /* without noise*/
res.Fval = Fval;
res.Ftrue = Ftrue;
return res;
}
TwoDoubles f118(double* x) {
/* ellipsoid with Cauchy noise, monotone x-transformation, condition 1e4*/
int i, j, rseed; /*Loop over dim*/
static int funcId = 118;
static int rrseed = 10;
static double condition = 1e4;
double Fadd, Fval, tmp, Fpen = 0., Ftrue = 0.;
TwoDoubles res;
if (!isInitDone)
{
rseed = rrseed + 10000 * trialid;
/*INITIALIZATION*/
Fopt = computeFopt(funcId, trialid);
computeXopt(rseed, DIM);
computeRotation(rotation, rseed + 1000000, DIM);
isInitDone = 1;
}
Fadd = Fopt;
/* BOUNDARY HANDLING*/
for (i = 0; i < DIM; i++)
{
tmp = fabs(x[i]) - 5.;
if (tmp > 0.)
{
Fpen += tmp * tmp;
}
}
Fadd += 100. * Fpen;
/* TRANSFORMATION IN SEARCH SPACE*/
for (i = 0; i < DIM; i++)
{
tmx[i] = 0.;
for (j = 0; j < DIM; j++) {
tmx[i] += rotation[i][j] * (x[j] - Xopt[j]);
}
}
monotoneTFosc(tmx);
/* COMPUTATION core*/
for (i = 0; i < DIM; i++)
{
Ftrue += pow(condition, ((double)i)/((double)(DIM-1))) * tmx[i] * tmx[i];
}
Fval = FCauchy(Ftrue, 1., 0.2);
Ftrue += Fadd;
Fval += Fadd;
res.Fval = Fval;
res.Ftrue = Ftrue;
return res;
}
TwoDoubles f3(double* x) {
/* Rastrigin with monotone transformation separable "condition" 10*/
int i, rseed; /*Loop over dim*/
static unsigned int funcId = 3;
static double condition = 10.;
static double beta = 0.2;
double tmp, tmp2, Fadd, Fval, Ftrue = 0.;
TwoDoubles res;
if (!isInitDone)
{
rseed = funcId + 10000 * trialid;
/*INITIALIZATION*/
Fopt = computeFopt(funcId, trialid);
computeXopt(rseed, DIM);
isInitDone = 1;
}
Fadd = Fopt;
for (i = 0; i < DIM; i++)
{
tmx[i] = x[i] - Xopt[i];
}
monotoneTFosc(tmx);
for (i = 0; i < DIM; i++)
{
tmp = ((double)i)/((double)(DIM-1));
if (tmx[i] > 0)
tmx[i] = pow(tmx[i], 1 + beta * tmp * sqrt(tmx[i]));
tmx[i] = pow(sqrt(condition), tmp) * tmx[i];
}
/* COMPUTATION core*/
tmp = 0.;
tmp2 = 0.;
for (i = 0; i < DIM; i++)
{
tmp += cos(2*M_PI*tmx[i]);
tmp2 += tmx[i]*tmx[i];
}
Ftrue = 10 * (DIM - tmp) + tmp2;
Ftrue += Fadd;
Fval = Ftrue; /* without noise*/
res.Fval = Fval;
res.Ftrue = Ftrue;
return res;
}
TwoDoubles f11(double* x) {
/* discus (tablet) with monotone transformation, condition 1e6*/
int i, j, rseed; /*Loop over dim*/
static unsigned int funcId = 11;
static double condition = 1e6;
double Fadd, Fval, Ftrue;
TwoDoubles res;
if (!isInitDone)
{
rseed = funcId + 10000 * trialid;
/*INITIALIZATION*/
Fopt = computeFopt(funcId, trialid);
computeXopt(rseed, DIM);
computeRotation(rotation, rseed + 1000000, DIM);
isInitDone = 1;
}
Fadd = Fopt;
/* BOUNDARY HANDLING*/
/* TRANSFORMATION IN SEARCH SPACE*/
for (i = 0; i < DIM; i++)
{
tmx[i] = 0.;
for (j = 0; j < DIM; j++) {
tmx[i] += rotation[i][j] * (x[j] - Xopt[j]);
}
}
monotoneTFosc(tmx);
/* COMPUTATION core*/
Ftrue = condition * tmx[0] * tmx[0];
for (i = 1; i < DIM; i++)
{
Ftrue += tmx[i] * tmx[i];
}
Ftrue += Fadd;
Fval = Ftrue; /* without noise*/
res.Fval = Fval;
res.Ftrue = Ftrue;
return res;
}
TwoDoubles f2(double* x) {
/* separable ellipsoid with monotone transformation, condition 1e6*/
int i, rseed; /*Loop over dim*/
static double condition = 1e6;
static unsigned int funcId = 2;
double Fadd, Fval, Ftrue = 0.;
TwoDoubles res;
if (!isInitDone)
{
rseed = funcId + 10000 * trialid;
/*INITIALIZATION*/
Fopt = computeFopt(funcId, trialid);
computeXopt(rseed, DIM);
isInitDone = 1;
}
Fadd = Fopt;
for (i = 0; i < DIM; i++)
{
tmx[i] = x[i] - Xopt[i];
}
monotoneTFosc(tmx);
/* COMPUTATION core*/
for (i = 0; i < DIM; i++)
{
Ftrue += pow(condition, ((double)i)/((double)(DIM-1))) * tmx[i] * tmx[i];
}
Ftrue += Fadd;
Fval = Ftrue; /* without noise*/
res.Fval = Fval;
res.Ftrue = Ftrue;
return res;
}
TwoDoubles f16(double* x) {
/* Weierstrass, condition 100*/
int i, j, k, rseed; /*Loop over dim*/
static unsigned int funcId = 16;
static double condition = 100.;
static double aK[12];
static double bK[12];
static double F0;
double tmp, Fadd, Fval, Fpen = 0., Ftrue = 0.;
TwoDoubles res;
if (!isInitDone)
{
rseed = funcId + 10000 * trialid;
/*INITIALIZATION*/
Fopt = computeFopt(funcId, trialid);
computeXopt(rseed, DIM);
computeRotation(rotation, rseed + 1000000, DIM);
computeRotation(rot2, rseed, DIM);
for (i = 0; i < DIM; i++)
{
for (j = 0; j < DIM; j++)
{
linearTF[i][j] = 0.;
for (k = 0; k < DIM; k++) {
linearTF[i][j] += rotation[i][k] * pow(1./sqrt(condition), ((double)k)/((double)(DIM-1))) * rot2[k][j];
}
}
}
F0 = 0.;
for (i = 0; i < 12; i ++) /* number of summands, 20 in CEC2005, 10/12 saves 30% of time*/
{
aK[i] = pow(0.5, (double)i);
bK[i] = pow(3., (double)i);
F0 += aK[i] * cos(2 * M_PI * bK[i] * 0.5);
}
isInitDone = 1;
}
Fadd = Fopt;
/* BOUNDARY HANDLING*/
for (i = 0; i < DIM; i++)
{
tmp = fabs(x[i]) - 5.;
if (tmp > 0.)
{
Fpen += tmp * tmp;
}
}
Fadd += 10./(double)DIM * Fpen;
/* TRANSFORMATION IN SEARCH SPACE*/
for (i = 0; i < DIM; i++)
{
tmpvect[i] = 0.;
for (j = 0; j < DIM; j++)
{
tmpvect[i] += rotation[i][j] * (x[j] - Xopt[j]);
}
}
monotoneTFosc(tmpvect);
for (i = 0; i < DIM; i++)
{
tmx[i] = 0.;
for (j = 0; j < DIM; j++)
{
tmx[i] += linearTF[i][j] * tmpvect[j];
}
}
/* COMPUTATION core*/
for (i = 0; i < DIM; i++)
{
tmp = 0.;
for (j = 0; j < 12; j++)
{
tmp += cos(2 * M_PI * (tmx[i] + 0.5) * bK[j]) * aK[j];
}
Ftrue += tmp;
}
Ftrue = 10. * pow(Ftrue/(double)DIM - F0, 3.);
Ftrue += Fadd;
Fval = Ftrue; /* without noise*/
res.Fval = Fval;
res.Ftrue = Ftrue;
return res;
}
TwoDoubles f15(double* x) {
/* Rastrigin with asymmetric non-linear distortion, "condition" 10*/
int i, j, k, rseed; /*Loop over dim*/
static unsigned int funcId = 15;
static double condition = 10.;
static double beta = 0.2;
double tmp = 0., tmp2 = 0., Fadd, Fval, Ftrue;
TwoDoubles res;
if (!isInitDone)
{
rseed = funcId + 10000 * trialid;
/*INITIALIZATION*/
Fopt = computeFopt(funcId, trialid);
computeXopt(rseed, DIM);
computeRotation(rotation, rseed + 1000000, DIM);
computeRotation(rot2, rseed, DIM);
for (i = 0; i < DIM; i++)
{
for (j = 0; j < DIM; j++)
{
linearTF[i][j] = 0.;
for (k = 0; k < DIM; k++) {
linearTF[i][j] += rotation[i][k] * pow(sqrt(condition), ((double)k)/((double)(DIM-1))) * rot2[k][j];
}
}
}
isInitDone = 1;
}
Fadd = Fopt;
/* BOUNDARY HANDLING*/
/* TRANSFORMATION IN SEARCH SPACE*/
for (i = 0; i < DIM; i++)
{
tmpvect[i] = 0.;
for (j = 0; j < DIM; j++)
{
tmpvect[i] += rotation[i][j] * (x[j] - Xopt[j]);
}
}
monotoneTFosc(tmpvect);
for (i = 0; i < DIM; i++)
{
if (tmpvect[i] > 0)
tmpvect[i] = pow(tmpvect[i], 1 + beta * ((double)i)/((double)(DIM-1)) * sqrt(tmpvect[i]));
}
for (i = 0; i < DIM; i++)
{
tmx[i] = 0.;
for (j = 0; j < DIM; j++)
{
tmx[i] += linearTF[i][j] * tmpvect[j];
}
}
/* COMPUTATION core*/
for (i = 0; i < DIM; i++)
{
tmp += cos(2. * M_PI * tmx[i]);
tmp2 += tmx[i] * tmx[i];
}
Ftrue = 10. * ((double)DIM - tmp) + tmp2;
Ftrue += Fadd;
Fval = Ftrue; /* without noise*/
res.Fval = Fval;
res.Ftrue = Ftrue;
return res;
}
