TwoDoubles f1(double* x) {
/*Sphere function*/
int i, rseed; /*Loop over dim*/
static unsigned int funcId = 1;
double Fadd, r, Fval, Ftrue = 0.;
TwoDoubles res;
if (!isInitDone)
{
rseed = funcId + 10000 * trialid;
/*INITIALIZATION*/
Fopt = computeFopt(funcId, trialid);
computeXopt(rseed, DIM);
isInitDone = 1;
}
Fadd = Fopt;
/* COMPUTATION core*/
for (i = 0; i < DIM; i++)
{
r = x[i] - Xopt[i];
Ftrue += r * r;
}
Ftrue += Fadd;
Fval = Ftrue; /* without noise*/
res.Ftrue = Ftrue;
res.Fval = Fval;
return res;
}
TwoDoubles f5(double* x) {
/* linear slope*/
int i, rseed; /*Loop over dim*/
static unsigned int funcId = 5;
static double alpha = 100.;
static double Fadd; /*Treatment is different from other functions.*/
double tmp, Fval, Ftrue = 0.;
TwoDoubles res;
if (!isInitDone)
{
rseed = funcId + 10000 * trialid;
/*INITIALIZATION*/
Fopt = computeFopt(funcId, trialid);
Fadd = Fopt;
computeXopt(rseed, DIM);
for (i = 0; i < DIM; i ++)
{
tmp = pow(sqrt(alpha), ((double)i)/((double)(DIM-1)));
if (Xopt[i] > 0)
{
Xopt[i] = 5.;
}
else if (Xopt[i] < 0)
{
Xopt[i] = -5.;
}
Fadd += 5. * tmp;
}
isInitDone = 1;
}
/* BOUNDARY HANDLING*/
/* move "too" good coordinates back into domain*/
for (i = 0; i < DIM; i++) {
if ((Xopt[i] == 5.) && (x[i] > 5))
tmx[i] = 5.;
else if ((Xopt[i] == -5.) && (x[i] < -5))
tmx[i] = -5.;
else
tmx[i] = x[i];
}
/* COMPUTATION core*/
for (i = 0; i < DIM; i++)
{
if (Xopt[i] > 0) {
Ftrue -= pow(sqrt(alpha), ((double)i)/((double)(DIM-1))) * tmx[i];
} else {
Ftrue += pow(sqrt(alpha), ((double)i)/((double)(DIM-1))) * tmx[i];
}
}
Ftrue += Fadd;
Fval = Ftrue; /* without noise*/
res.Fval = Fval;
res.Ftrue = Ftrue;
return res;
}
TwoDoubles f104(double* x) {
/* Rosenbrock non-rotated with moderate Gauss noise*/
int i, rseed; /*Loop over dim*/
static int funcId = 104;
static int rrseed = 8;
static double scales;
double Fadd, Fval, tmp, Fpen = 0., Ftrue = 0.;
TwoDoubles res;
if (!isInitDone)
{
rseed = rrseed + 10000 * trialid;
/*INITIALIZATION*/
Fopt = computeFopt(funcId, trialid);
computeXopt(rseed, DIM);
scales = fmax(1., sqrt((double)DIM) / 8.);
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] = scales * (x[i] - 0.75 * Xopt[i]) + 1;
}
/* COMPUTATION core*/
Ftrue = 0.;
for (i = 0; i < DIM - 1; i++)
{
tmp = (tmx[i] * tmx[i] - tmx[i+1]);
Ftrue += tmp * tmp;
}
Ftrue *= 1e2;
for (i = 0; i < DIM - 1; i ++)
{
tmp = (tmx[i] - 1);
Ftrue += tmp * tmp;
}
Fval = FGauss(Ftrue, 0.01);
Ftrue += Fadd;
Fval += Fadd;
res.Fval = Fval;
res.Ftrue = Ftrue;
return res;
}
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 f13(double* x) {
/* sharp ridge*/
int i, j, k, rseed; /*Loop over dim*/
static unsigned int funcId = 13;
static double condition = 10.;
static double alpha = 100.;
double Fadd, Fval, 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(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++)
{
tmx[i] = 0.;
for (j = 0; j < DIM; j++) {
tmx[i] += linearTF[i][j] * (x[j] - Xopt[j]);
}
}
/* COMPUTATION core*/
for (i = 1; i < DIM; i++)
{
Ftrue += tmx[i] * tmx[i];
}
Ftrue = alpha * sqrt(Ftrue);
Ftrue += tmx[0] * tmx[0];
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 f121(double* x) {
/* sum of different powers with seldom Cauchy Noise, between x^2 and x^6*/
int i, j, rseed; /*Loop over dim*/
static int funcId = 121;
static int rrseed = 14;
static double alpha = 4.;
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]);
}
}
/* COMPUTATION core*/
for (i = 0; i < DIM; i++)
{
Ftrue += pow(fabs(tmx[i]), 2 + alpha * ((double)i)/((double)(DIM-1)));
}
Ftrue = sqrt(Ftrue);
Fval = FCauchy(Ftrue, 1., 0.2);
Ftrue += Fadd;
Fval += Fadd;
res.Fval = Fval;
res.Ftrue = Ftrue;
return res;
}
TwoDoubles f12(double* x) {
/* bent cigar with asymmetric space distortion, condition 1e6*/
int i, j, rseed; /*Loop over dim*/
static unsigned int funcId = 12;
static double condition = 1e6;
static double beta = 0.5;
double Fadd, Fval, Ftrue;
TwoDoubles res;
if (!isInitDone)
{
rseed = funcId + 10000 * trialid;
/*INITIALIZATION*/
Fopt = computeFopt(funcId, trialid);
computeXopt(rseed + 1000000, DIM);
computeRotation(rotation, rseed + 1000000, DIM);
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]);
}
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] += rotation[i][j] * tmpvect[j];
}
}
/* COMPUTATION core*/
Ftrue = tmx[0] * tmx[0];
for (i = 1; i < DIM; i++)
{
Ftrue += condition * tmx[i] * tmx[i];
}
Ftrue += Fadd;
Fval = Ftrue; /* without noise*/
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 f8(double* x) {
/* Rosenbrock, non-rotated*/
static unsigned int funcId = 8;
int i, rseed; /*Loop over dim*/
static double scales;
double tmp, Fadd, Fval, Ftrue = 0.;
TwoDoubles res;
if (!isInitDone)
{
rseed = funcId + 10000 * trialid;
scales = fmax(1., sqrt(DIM) / 8.);
/*INITIALIZATION*/
Fopt = computeFopt(funcId, trialid);
computeXopt(rseed, DIM);
for (i = 0; i < DIM; i ++)
Xopt[i] *= 0.75;
isInitDone = 1;
}
Fadd = Fopt;
/* BOUNDARY HANDLING*/
/* TRANSFORMATION IN SEARCH SPACE*/
for (i = 0; i < DIM; i++) {
tmx[i] = scales * (x[i] - Xopt[i]) + 1;
}
/* COMPUTATION core*/
for (i = 0; i < DIM - 1; i++)
{
tmp = (tmx[i] * tmx[i] - tmx[i+1]);
Ftrue += tmp * tmp;
}
Ftrue *= 1e2;
for (i = 0; i < DIM - 1; i ++)
{
tmp = (tmx[i] - 1.);
Ftrue += tmp * tmp;
}
Ftrue += Fadd;
Fval = Ftrue; /* without noise*/
res.Fval = Fval;
res.Ftrue = Ftrue;
return res;
}
TwoDoubles f101(double* x) {
/*sphere with moderate Gauss noise*/
int i, rseed; /*Loop over dim*/
static unsigned int funcId = 101;
static unsigned int rrseed = 1;
double Fadd, Fval, tmp, Fpen = 0., Ftrue = 0.;
TwoDoubles res;
if (!isInitDone)
{
rseed = rrseed + 10000 * trialid;
Fopt = computeFopt(funcId, trialid);
computeXopt(rseed, 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;
/* COMPUTATION core*/
for (i = 0; i < DIM; i++)
{
tmp = (x[i] - Xopt[i]);
Ftrue += tmp * tmp;
}
Fval = FGauss(Ftrue, 0.01);
Ftrue += Fadd;
Fval += Fadd;
res.Fval = Fval;
res.Ftrue = Ftrue;
return res;
}
TwoDoubles f14(double* x) {
/* sum of different powers, between x^2 and x^6*/
int i, j, rseed;
static unsigned int funcId = 14;
static double alpha = 4.;
double Fadd, Fval, Ftrue = 0.;
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]);
}
}
/* COMPUTATION core*/
for (i = 0; i < DIM; i++)
{
Ftrue += pow(fabs(tmx[i]), 2. + alpha * ((double)i)/((double)(DIM-1)));
}
Ftrue = sqrt(Ftrue);
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 f115(double* x) {
/* step-ellipsoid with Cauchy noise, condition 100*/
int i, j, rseed; /*Loop over dim*/
static int funcId = 115;
static int rrseed = 7;
static double condition = 100.;
static double alpha = 10.;
double x1, 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);
computeRotation(rot2, rseed, 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++) {
tmpvect[i] = 0.;
tmp = sqrt(pow(condition/10., ((double)i)/((double)(DIM-1))));
for (j = 0; j < DIM; j++) {
tmpvect[i] += tmp * rot2[i][j] * (x[j] - Xopt[j]);
}
}
x1 = tmpvect[0];
for (i = 0; i < DIM; i++) {
if (fabs(tmpvect[i]) > 0.5)
{
tmpvect[i] = round(tmpvect[i]);
}
else
{
tmpvect[i] = round(alpha * tmpvect[i])/alpha;
}
}
for (i = 0; i < DIM; i++) {
tmx[i] = 0.;
for (j = 0; j < DIM; j++) {
tmx[i] += rotation[i][j] * tmpvect[j];
}
}
/* COMPUTATION core*/
for (i = 0; i < DIM; i++)
{
Ftrue += pow(condition, ((double)i)/((double)(DIM-1))) * tmx[i] * tmx[i];
}
Ftrue = 0.1 * fmax(1e-4 * fabs(x1), Ftrue);
Fval = FCauchy(Ftrue, 1., 0.2);
Ftrue += Fadd;
Fval += Fadd;
res.Fval = Fval;
res.Ftrue = Ftrue;
return res;
}
TwoDoubles f6(double* x) {
/* attractive sector function*/
int i, j, k, rseed; /*Loop over dim*/
static unsigned int funcId = 6;
static double alpha = 100.;
double Fadd, Fval, Ftrue = 0.;
TwoDoubles res;
if (!isInitDone)
{
static double condition = 10.;
rseed = funcId + 10000 * trialid;
/*INITIALIZATION*/
Fopt = computeFopt(funcId, trialid);
computeXopt(rseed, DIM);
computeRotation(rotation, rseed + 1000000, DIM);
computeRotation(rot2, rseed, DIM);
/* decouple scaling from function definition*/
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++) {
tmx[i] = 0.;
for (j = 0; j < DIM; j++) {
tmx[i] += linearTF[i][j] * (x[j] - Xopt[j]);
}
}
/* COMPUTATION core*/
for (i = 0; i < DIM; i++)
{
if (tmx[i] * Xopt[i] > 0)
tmx[i] *= alpha;
Ftrue += tmx[i] * tmx[i];
}
/*MonotoneTFosc...*/
if (Ftrue > 0)
{
Ftrue = pow(exp(log(Ftrue)/0.1 + 0.49*(sin(log(Ftrue)/0.1) + sin(0.79*log(Ftrue)/0.1))), 0.1);
}
else if (Ftrue < 0)
{
Ftrue = -pow(exp(log(-Ftrue)/0.1 + 0.49*(sin(0.55 * log(-Ftrue)/0.1) + sin(0.31*log(-Ftrue)/0.1))), 0.1);
}
Ftrue = pow(Ftrue, 0.9);
Ftrue += Fadd;
Fval = Ftrue; /* without noise*/
res.Fval = Fval;
res.Ftrue = Ftrue;
return res;
}
TwoDoubles f124(double* x) {
/* Schaffers F7 with seldom Cauchy noise, with asymmetric non-linear transformation, condition 10*/
int i, j, rseed; /*Loop over dim*/
static int funcId = 124;
static int rrseed = 17;
static double condition = 10.;
static double beta = 0.5;
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);
computeRotation(rot2, rseed, 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++)
{
tmpvect[i] = 0.;
for (j = 0; j < DIM; j++)
{
tmpvect[i] += rotation[i][j] * (x[j] - Xopt[j]);
}
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.;
tmp = pow(sqrt(condition), ((double)i)/((double)(DIM-1)));
for (j = 0; j < DIM; j++)
{
tmx[i] += tmp * rot2[i][j] * tmpvect[j];
}
}
/* COMPUTATION core*/
for (i = 0; i < DIM - 1; i++)
{
tmp = tmx[i] * tmx[i] + tmx[i+1] * tmx[i+1];
Ftrue += pow(tmp, 0.25) * (pow(sin(50. * pow(tmp, 0.1)), 2.) + 1.);
}
Ftrue = pow(Ftrue/(double)(DIM - 1), 2.);
Fval = FCauchy(Ftrue, 1., 0.2);
Ftrue += Fadd;
Fval += Fadd;
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;
}
TwoDoubles f23(double* x) {
/* Katsuura function*/
int i, j, k, rseed; /*Loop over dim*/
static unsigned int funcId = 23;
static double condition = 100.;
double Fadd = 0., Fpen = 0., tmp, Ftrue = 0., arr, prod = 1., tmp2, Fval;
double *ptmx, *plinTF, *ptmp;
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*/
for (i = 0; i < DIM; i++)
{
tmp = fabs(x[i]) - 5.;
if (tmp > 0.)
{
Fpen += tmp * tmp;
}
}
Fadd += Fpen;
/* TRANSFORMATION IN SEARCH SPACE*/
/* write rotated difference vector into tmx*/
for (j = 0; j < DIM; j++) /* store difference vector*/
tmpvect[j] = x[j] - Xopt[j];
for (i = 0; i < DIM; i++) {
tmx[i] = 0.;
ptmx = &tmx[i];
plinTF = linearTF[i];
ptmp = tmpvect;
for (j = 0; j < DIM; j++) {
*ptmx += *plinTF++ * *ptmp++;
}
}
/* for (i = 0; i < DIM; i++) {
tmx[i] = 0.;
for (j = 0; j < DIM; j++) {
tmx[i] += linearTF[i][j] * (x[j] - Xopt[j]);
}
}*/
/* COMPUTATION core*/
for (i = 0; i < DIM; i++)
{
tmp = 0.;
for (j = 1; j < 33; j++)
{
tmp2 = pow(2., (double)j);
arr = tmx[i] * tmp2;
tmp += fabs(arr - round(arr)) / tmp2;
}
tmp = 1. + tmp * (double)(i + 1);
prod *= tmp;
}
Ftrue = 10./(double)DIM/(double)DIM * (-1. + pow(prod, 10./pow((double)DIM, 1.2)));
Ftrue += Fadd;
Fval = Ftrue; /* without noise*/
res.Fval = Fval;
res.Ftrue = Ftrue;
return res;
}