cec17_test_func.cpp

/*
  CEC17 Test Function Suite for Single Objective Optimization
  Noor Awad (email: noor0029@ntu.edu.sg)
  Dec. 20th 2013
*/


/* #include <WINDOWS.H>    Janez   */
#include "cec17_test_func.hpp"

#include <stdio.h>
#include <cmath>

#define INF 1.0e99
#define EPS 1.0e-14
#define E  2.7182818284590452353602874713526625
#define PI 3.1415926535897932384626433832795029

void shiftfunc (double *x, double *xshift, int nx,double *Os);
void rotatefunc (double *x, double *xrot, int nx,double *Mr);
void oszfunc (double *x, double *xosz, int nx);
void asyfunc (double *x, double *xasy, int nx, double beta);

int result;

CEC17::CEC17(const CEC17& o) : BoundedObjectiveFunction(o) {}

CEC17::~CEC17() {
	if (M != nullptr) {
		delete[] M;
		M = nullptr;
	}
	if (OShift != nullptr) {
		delete[] OShift;
		OShift = nullptr;
	}
	if (SS != nullptr) {
		delete[] SS;
		SS = nullptr;
	}
}

CEC17::CEC17(int nx, int func_num): BoundedObjectiveFunction(nx) {
	int cf_num = 10, i, j;
	FILE *fpt;
	char FileName[256];
	if (func_num < 20) {
		M = new double[nx * nx];
		OShift = new double[nx];
	} else {
		M = new double[cf_num * nx * nx];
		OShift = new double[cf_num * nx];
	}
	if (func_num >= 11 && func_num <= 20)    {
		SS = new int[nx];
	} else if (func_num == 29 || func_num == 30) {
		SS = new int[cf_num * nx];
	}
	if (!(nx == 2 || nx==10 || nx == 20 || nx == 30 || nx == 50 || nx == 100)) {
		throw "Error: Test functions are only defined for D=2,10,20,30,50,100.";
	}
	if (nx==2&&((func_num>=17&&func_num<=22)||(func_num>=29&&func_num<=30))) {
		throw "Error: hf01,hf02,hf03,hf04,hf05,hf06,cf07&cf08 are NOT defined for D=2.";
	}
	/* Set bounds */
	for (i = 0; i < nx; i++) {
		_x_bound_min[i] = -100.0;
		_x_bound_max[i] = 100.0;
	}
	/* Load Matrix M*/
	sprintf(FileName, "input_data/M_%d_D%d.txt", func_num,nx);
	fpt = fopen(FileName, "r");
	if (fpt == nullptr) throw "Error: Cannot open input file for reading.";
	if (func_num < 20) {
		if (M == nullptr) throw "Error: there is insufficient memory available!";
		for (i = 0; i < nx * nx; i++) result = fscanf(fpt,"%lf",&M[i]);
	} else {
		if (M == nullptr) throw "Error: there is insufficient memory available!";
		for (i = 0; i < cf_num * nx * nx; i++) result = fscanf(fpt,"%lf",&M[i]);
	}
	fclose(fpt);
	/* Load shift_data */
	sprintf(FileName, "input_data/shift_data_%d.txt", func_num);
	fpt = fopen(FileName, "r");
	if (fpt == nullptr) throw "Error: Cannot open input file for reading.";
	if (func_num < 20) {
		if (OShift == nullptr) throw "Error: there is insufficient memory available!";
		for(i = 0; i < nx; i++) result = fscanf(fpt,"%lf",&OShift[i]);
	} else {
		if (OShift == nullptr) throw "Error: there is insufficient memory available!";
		for(i = 0; i < cf_num - 1; i++) {
			for (j = 0; j < nx; j++) result = fscanf(fpt,"%lf",&OShift[i*nx+j]);
			result=fscanf(fpt,"%*[^\n]%*c");
		}
		for (j=0;j<nx;j++) result = fscanf(fpt,"%lf",&OShift[(cf_num-1)*nx+j]);
	}
	fclose(fpt);
	/* Load Shuffle_data */
	if (func_num >= 11 && func_num <= 20)    {
		sprintf(FileName, "input_data/shuffle_data_%d_D%d.txt", func_num, nx);
		fpt = fopen(FileName,"r");
		if (fpt == nullptr) throw "Error: Cannot open input file for reading.";
		if (SS == nullptr) throw "Error: there is insufficient memory available!";
		for(i = 0; i < nx; i++) result = fscanf(fpt,"%d",&SS[i]);
		fclose(fpt);
	} else if (func_num == 29 || func_num == 30) {
		sprintf(FileName, "input_data/shuffle_data_%d_D%d.txt", func_num, nx);
		fpt = fopen(FileName,"r");
		if (fpt == nullptr) throw "Error: Cannot open input file for reading.";
		if (SS == nullptr) throw "Error: there is insufficient memory available!";
		for(i = 0;i < nx * cf_num; i++) result = fscanf(fpt,"%d",&SS[i]);
		fclose(fpt);
	}
	n_flag = nx;
	func_flag = func_num;
}

double CEC17::func(double *x, size_t dim) {
	int i;
	double f;
	switch(func_flag) {
		case 1:
			bent_cigar_func(&x[i*n_flag],&f,n_flag,OShift,M,1,1);
			return f + 100.0;
		case 2:
			sum_diff_pow_func(&x[i*n_flag],&f,n_flag,OShift,M,1,1);
			return f + 200.0;
		case 3:
			zakharov_func(&x[i*n_flag],&f,n_flag,OShift,M,1,1);
			return f + 300.0;
		case 4:
			rosenbrock_func(&x[i*n_flag],&f,n_flag,OShift,M,1,1);
			return f + 400.0;
		case 5:
			rastrigin_func(&x[i*n_flag],&f,n_flag,OShift,M,1,1);
			return f + 500.0;
		case 6:
			schaffer_F7_func(&x[i*n_flag],&f,n_flag,OShift,M,1,1);
			return f + 600.0;
		case 7:
			bi_rastrigin_func(&x[i*n_flag],&f,n_flag,OShift,M,1,1);
			return f + 700.0;
		case 8:
			step_rastrigin_func(&x[i*n_flag],&f,n_flag,OShift,M,1,1);
			return f + 800.0;
		case 9:
			levy_func(&x[i*n_flag],&f,n_flag,OShift,M,1,1);
			return f + 900.0;
		case 10:
			schwefel_func(&x[i*n_flag],&f,n_flag,OShift,M,1,1);
			return f + 1000.0;
		case 11:
			hf01(&x[i*n_flag],&f,n_flag,OShift,M,SS,1,1);
			return f + 1100.0;
		case 12:
			hf02(&x[i*n_flag],&f,n_flag,OShift,M,SS,1,1);
			return f + 1200.0;
		case 13:
			hf03(&x[i*n_flag],&f,n_flag,OShift,M,SS,1,1);
			return f + 1300.0;
		case 14:
			hf04(&x[i*n_flag],&f,n_flag,OShift,M,SS,1,1);
			return f + 1400.0;
		case 15:
			hf05(&x[i*n_flag],&f,n_flag,OShift,M,SS,1,1);
			return f + 1500.0;
		case 16:
			hf06(&x[i*n_flag],&f,n_flag,OShift,M,SS,1,1);
			return f + 1600.0;
		case 17:
			hf07(&x[i*n_flag],&f,n_flag,OShift,M,SS,1,1);
			return f + 1700.0;
		case 18:
			hf08(&x[i*n_flag],&f,n_flag,OShift,M,SS,1,1);
			return f + 1800.0;
		case 19:
			hf09(&x[i*n_flag],&f,n_flag,OShift,M,SS,1,1);
			return f + 1900.0;
		case 20:
			hf10(&x[i*n_flag],&f,n_flag,OShift,M,SS,1,1);
			return f + 2000.0;
		case 21:
			cf01(&x[i*n_flag],&f,n_flag,OShift,M,1);
			return f + 2100.0;
		case 22:
			cf02(&x[i*n_flag],&f,n_flag,OShift,M,1);
			return f + 2200.0;
		case 23:
			cf03(&x[i*n_flag],&f,n_flag,OShift,M,1);
			return f + 2300.0;
		case 24:
			cf04(&x[i*n_flag],&f,n_flag,OShift,M,1);
			return f + 2400.0;
		case 25:
			cf05(&x[i*n_flag],&f,n_flag,OShift,M,1);
			return f + 2500.0;
		case 26:
			cf06(&x[i*n_flag],&f,n_flag,OShift,M,1);
			return f + 2600.0;
		case 27:
			cf07(&x[i*n_flag],&f,n_flag,OShift,M,1);
			return f + 2700.0;
		case 28:
			cf08(&x[i*n_flag],&f,n_flag,OShift,M,1);
			return f + 2800.0;
		case 29:
			cf09(&x[i*n_flag],&f,n_flag,OShift,M,SS,1);
			return f + 2900.0;
		case 30:
			cf10(&x[i*n_flag],&f,n_flag,OShift,M,SS,1);
			return f + 3000.0;
		default:
			throw "Error: There are only 30 test functions in this test suite!";
	}
	return f;
}

void CEC17::sphere_func (double *x, double *f, int nx, double *Os, double *Mr, int s_flag, int r_flag) /* Sphere */ {
	int i;
	f[0] = 0.0;
	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); /* shift and rotate */
	for (i=0; i<nx; i++)  f[0] += z[i]*z[i];
}

void CEC17::ellips_func (double *x, double *f, int nx, double *Os,double *Mr, int s_flag, int r_flag) /* Ellipsoidal */ {
	int i;
	f[0] = 0.0;
	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr,1.0, s_flag, r_flag); /* shift and rotate */
	for (i=0; i<nx; i++) f[0] += pow(10.0,6.0*i/(nx-1))*z[i]*z[i];
}

void CEC17::sum_diff_pow_func (double *x, double *f, int nx, double *Os,double *Mr, int s_flag, int r_flag) /* sum of different power */ {
	int i;
	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr,1.0, s_flag, r_flag); // shift and rotate
	f[0] = 0.0;
	double sum = 0.0;
	for (i=0; i<nx; i++) {
		double xi = z[i];
		double newv = pow((fabs(xi)),(i+1));   // JANEZ 16.12.2016   abs --> fabs
		sum = sum + newv;
	}
	f[0] = sum;
}

void CEC17::zakharov_func (double *x, double *f, int nx, double *Os,double *Mr, int s_flag, int r_flag) /* zakharov */ {
	int i;
	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); // shift and rotate
	f[0] = 0.0;
	double sum1 = 0.0;
	double sum2 = 0.0;
	for (i=0; i<nx; i++) {
		double xi = z[i];
		sum1 = sum1 + pow(xi,2);
		sum2 = sum2 + 0.5*(i+1)*xi;
	}
	f[0] = sum1 + pow(sum2,2) + pow(sum2,4);
}

/* Levy function */
void CEC17::levy_func (double *x, double *f, int nx, double *Os,double *Mr, int s_flag, int r_flag) /* Levy */ {
	int i;
	f[0] = 0.0;
	std::vector<double> z(_dim), y(_dim), w(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); /* shift and rotate */
	double sum1= 0.0;
	for (i=0; i<nx; i++) w[i] = 1.0 + (z[i] - 1.0)/4.0;
	double term1 = pow((sin(PI*w[0])),2);
	double term3 = pow((w[nx-1]-1),2) * (1+pow((sin(2*PI*w[nx-1])),2));
	double sum = 0.0;
	for (i=0; i<nx-1; i++) {
		double wi = w[i];
		double newv = pow((wi-1),2) * (1+10*pow((sin(PI*wi+1)),2));
		sum = sum + newv;
	}
	f[0] = term1 + sum + term3;
}

/* Dixon and Price */
void CEC17::dixon_price_func (double *x, double *f, int nx, double *Os,double *Mr, int s_flag, int r_flag) /* Dixon and Price */ {
	int i;
	int j;
	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); // shift and rotate
	f[0] = 0;
	double x1 = z[0];;
	double term1 = pow((x1-1),2);
	double sum = 0;
	for (i=1; i<nx; i++) {
		double xi = z[i];
		double xold = z[i-1];
		double newv = i * pow((pow(2*xi,2) - xold),2);
		sum = sum + newv;
	}
	f[0] = term1 + sum;
}

void CEC17::bent_cigar_func (double *x, double *f, int nx, double *Os,double *Mr, int s_flag, int r_flag) /* Bent_Cigar */ {
	int i;
	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); /* shift and rotate */
	f[0] = z[0]*z[0];
	for (i=1; i<nx; i++) f[0] += pow(10.0,6.0)*z[i]*z[i];
}

void CEC17::discus_func (double *x, double *f, int nx, double *Os,double *Mr, int s_flag, int r_flag) /* Discus */ {
	int i;
	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); /* shift and rotate */
	f[0] = pow(10.0,6.0)*z[0]*z[0];
	for (i=1; i<nx; i++) f[0] += z[i]*z[i];
}

void CEC17::dif_powers_func (double *x, double *f, int nx, double *Os,double *Mr,int s_flag, int r_flag) /* Different Powers */ {
	int i;
	f[0] = 0.0;
	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); /* shift and rotate */
	for (i=0; i<nx; i++) f[0] += pow(fabs(z[i]),2+4*i/(nx-1));
	f[0]=pow(f[0],0.5);
}

void CEC17::rosenbrock_func (double *x, double *f, int nx, double *Os,double *Mr,int s_flag, int r_flag) /* Rosenbrock's */ {
	int i;
	double tmp1,tmp2;
	std::vector<double> z(_dim), y(_dim);
	f[0] = 0.0;
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 2.048/100.0, s_flag, r_flag); /* shift and rotate */
	z[0] += 1.0;//shift to orgin
	for (i=0; i<nx-1; i++) {
		z[i+1] += 1.0;//shift to orgin
		tmp1=z[i]*z[i]-z[i+1];
		tmp2=z[i]-1.0;
		f[0] += 100.0*tmp1*tmp1 +tmp2*tmp2;
	}
}

void CEC17::schaffer_F7_func (double *x, double *f, int nx, double *Os,double *Mr,int s_flag, int r_flag) /* Schwefel's 1.2  */ {
	int i;
	double tmp;
	std::vector<double> z(_dim), y(_dim);
	f[0] = 0.0;
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); /* shift and rotate */
	for (i=0; i<nx-1; i++) {
		z[i]=pow(y[i]*y[i]+y[i+1]*y[i+1],0.5);
		tmp=sin(50.0*pow(z[i],0.2));
		f[0] += pow(z[i],0.5)+pow(z[i],0.5)*tmp*tmp ;
	}
	f[0] = f[0]*f[0]/(nx-1)/(nx-1);
}

void CEC17::ackley_func (double *x, double *f, int nx, double *Os,double *Mr,int s_flag, int r_flag) /* Ackley's  */ {
	int i;
	double sum1, sum2;
	sum1 = 0.0;
	sum2 = 0.0;
	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); /* shift and rotate */
	for (i=0; i<nx; i++) {
		sum1 += z[i]*z[i];
		sum2 += cos(2.0*PI*z[i]);
	}
	sum1 = -0.2*sqrt(sum1/nx);
	sum2 /= nx;
	f[0] =  E - 20.0*exp(sum1) - exp(sum2) +20.0;
}

void CEC17::weierstrass_func (double *x, double *f, int nx, double *Os,double *Mr,int s_flag, int r_flag) /* Weierstrass's  */ {
	int i,j,k_max;
	double sum,sum2, a, b;
	std::vector<double> z(_dim), y(_dim);
	a = 0.5;
	b = 3.0;
	k_max = 20;
	f[0] = 0.0;

	sr_func (x, z.data(), y.data(), nx, Os, Mr, 0.5/100.0, s_flag, r_flag); /* shift and rotate */

	for (i=0; i<nx; i++) {
		sum = 0.0;
		sum2 = 0.0;
		for (j=0; j<=k_max; j++) {
			sum += pow(a,j)*cos(2.0*PI*pow(b,j)*(z[i]+0.5));
			sum2 += pow(a,j)*cos(2.0*PI*pow(b,j)*0.5);
		}
		f[0] += sum;
	}
	f[0] -= nx*sum2;
}

void CEC17::griewank_func (double *x, double *f, int nx, double *Os,double *Mr,int s_flag, int r_flag) /* Griewank's  */ {
	int i;
	double s, p;
	s = 0.0;
	p = 1.0;
	std::vector<double> z(_dim), y(_dim);

	sr_func (x, z.data(), y.data(), nx, Os, Mr, 600.0/100.0, s_flag, r_flag); /* shift and rotate */

	for (i=0; i<nx; i++) {
		s += z[i]*z[i];
		p *= cos(z[i]/sqrt(1.0+i));
	}
	f[0] = 1.0 + s/4000.0 - p;
}

void CEC17::rastrigin_func (double *x, double *f, int nx, double *Os,double *Mr,int s_flag, int r_flag) /* Rastrigin's  */ {
	int i;
	f[0] = 0.0;
	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 5.12/100.0, s_flag, r_flag); /* shift and rotate */
	for (i=0; i<nx; i++) f[0] += (z[i]*z[i] - 10.0*cos(2.0*PI*z[i]) + 10.0);
}

void CEC17::step_rastrigin_func (double *x, double *f, int nx, double *Os,double *Mr,int s_flag, int r_flag) /* Noncontinuous Rastrigin's  */ {
	int i;
	std::vector<double> y(_dim), z(_dim);
	f[0]=0.0;
	for (i=0; i<nx; i++) 	{
		if (fabs(y[i]-Os[i])>0.5) y[i]=Os[i]+floor(2*(y[i]-Os[i])+0.5)/2;
	}
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 5.12/100.0, s_flag, r_flag); /* shift and rotate */
	for (i=0; i<nx; i++) f[0] += (z[i]*z[i] - 10.0*cos(2.0*PI*z[i]) + 10.0);
}

void CEC17::schwefel_func (double *x, double *f, int nx, double *Os,double *Mr,int s_flag, int r_flag) /* Schwefel's  */ {
	int i;
	double tmp;
	f[0]=0.0;
	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1000.0/100.0, s_flag, r_flag); /* shift and rotate */
	for (i=0; i<nx; i++) {
		z[i] += 4.209687462275036e+002;
		if (z[i]>500) {
			f[0]-=(500.0-fmod(z[i],500))*sin(pow(500.0-fmod(z[i],500),0.5));
			tmp=(z[i]-500.0)/100;
			f[0]+= tmp*tmp/nx;
		} else if (z[i]<-500) {
			f[0]-=(-500.0+fmod(fabs(z[i]),500))*sin(pow(500.0-fmod(fabs(z[i]),500),0.5));
			tmp=(z[i]+500.0)/100;
			f[0]+= tmp*tmp/nx;
		} else {
			f[0]-=z[i]*sin(pow(fabs(z[i]),0.5));
		}
	}
	f[0] +=4.189828872724338e+002*nx;
}

void CEC17::katsuura_func (double *x, double *f, int nx, double *Os,double *Mr,int s_flag, int r_flag) /* Katsuura  */ {
	int i,j;
	double temp,tmp1,tmp2,tmp3;
	std::vector<double> z(_dim), y(_dim);
	f[0]=1.0;
	tmp3=pow(1.0*nx,1.2);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 5.0/100.0, s_flag, r_flag); /* shift and rotate */
	for (i=0; i<nx; i++) {
		temp=0.0;
		for (j=1; j<=32; j++) {
			tmp1=pow(2.0,j);
			tmp2=tmp1*z[i];
			temp += fabs(tmp2-floor(tmp2+0.5))/tmp1;
		}
		f[0] *= pow(1.0+(i+1)*temp,10.0/tmp3);
	}
	tmp1=10.0/nx/nx;
	f[0]=f[0]*tmp1-tmp1;

}

void CEC17::bi_rastrigin_func (double *x, double *f, int nx, double *Os,double *Mr,int s_flag, int r_flag) /* Lunacek Bi_rastrigin Function */ {
	int i;
	double mu0=2.5,d=1.0,s,mu1,tmp,tmp1,tmp2;
	std::vector<double> y(_dim), z(_dim), tmpx(_dim);
	s=1.0-1.0/(2.0*pow(nx+20.0,0.5)-8.2);
	mu1=-pow((mu0*mu0-d)/s,0.5);
	if (s_flag==1)
		shiftfunc(x, y.data(), nx, Os);
	else {
		for (i=0; i<nx; i++)/* shrink to the orginal search range */ {
			y[i] = x[i];
		}
	}
	for (i=0; i<nx; i++)/* shrink to the orginal search range */ {
		y[i] *= 10.0/100.0;
	}

	for (i = 0; i < nx; i++) {
		tmpx[i]=2*y[i];
		if (Os[i] < 0.0) tmpx[i] *= -1.;
	}
	for (i=0; i<nx; i++) {
		z[i]=tmpx[i];
		tmpx[i] += mu0;
	}
	tmp1=0.0;tmp2=0.0;
	for (i=0; i<nx; i++) {
		tmp = tmpx[i]-mu0;
		tmp1 += tmp*tmp;
		tmp = tmpx[i]-mu1;
		tmp2 += tmp*tmp;
	}
	tmp2 *= s;
	tmp2 += d*nx;
	tmp=0.0;

	if (r_flag==1) {
		rotatefunc(z.data(), y.data(), nx, Mr);
		for (i=0; i<nx; i++) tmp+=cos(2.0*PI*y[i]);
		if(tmp1<tmp2) f[0] = tmp1;
		else f[0] = tmp2;
		f[0] += 10.0*(nx-tmp);
	} else {
		for (i=0; i<nx; i++) tmp+=cos(2.0*PI*z[i]);
		if(tmp1<tmp2) f[0] = tmp1;
		else f[0] = tmp2;
		f[0] += 10.0*(nx-tmp);
	}
}

void CEC17::grie_rosen_func (double *x, double *f, int nx, double *Os,double *Mr,int s_flag, int r_flag) /* Griewank-Rosenbrock  */ {
	int i;
	double temp,tmp1,tmp2;
	f[0]=0.0;
	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 5.0/100.0, s_flag, r_flag); /* shift and rotate */
	z[0] += 1.0;//shift to orgin
	for (i=0; i<nx-1; i++) {
		z[i+1] += 1.0;//shift to orgin
		tmp1 = z[i]*z[i]-z[i+1];
		tmp2 = z[i]-1.0;
		temp = 100.0*tmp1*tmp1 + tmp2*tmp2;
		f[0] += (temp*temp)/4000.0 - cos(temp) + 1.0;
	}
	tmp1 = z[nx-1]*z[nx-1]-z[0];
	tmp2 = z[nx-1]-1.0;
	temp = 100.0*tmp1*tmp1 + tmp2*tmp2;
	f[0] += (temp*temp)/4000.0 - cos(temp) + 1.0 ;
}


void CEC17::escaffer6_func (double *x, double *f, int nx, double *Os,double *Mr,int s_flag, int r_flag) /* Expanded Scaffer??s F6  */ {
	int i;
	double temp1, temp2;
	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); /* shift and rotate */
	f[0] = 0.0;
	for (i=0; i<nx-1; i++) {
		temp1 = sin(sqrt(z[i]*z[i]+z[i+1]*z[i+1]));
		temp1 =temp1*temp1;
		temp2 = 1.0 + 0.001*(z[i]*z[i]+z[i+1]*z[i+1]);
		f[0] += 0.5 + (temp1-0.5)/(temp2*temp2);
	}
	temp1 = sin(sqrt(z[nx-1]*z[nx-1]+z[0]*z[0]));
	temp1 =temp1*temp1;
	temp2 = 1.0 + 0.001*(z[nx-1]*z[nx-1]+z[0]*z[0]);
	f[0] += 0.5 + (temp1-0.5)/(temp2*temp2);
}

void CEC17::happycat_func (double *x, double *f, int nx, double *Os,double *Mr,int s_flag, int r_flag) /* HappyCat, provdided by Hans-Georg Beyer (HGB) */
/* original global optimum: [-1,-1,...,-1] */ {
	int i;
	double alpha,r2,sum_z;
	alpha=1.0/8.0;

	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 5.0/100.0, s_flag, r_flag); /* shift and rotate */

	r2 = 0.0;
	sum_z=0.0;
	for (i=0; i<nx; i++) {
		z[i]=z[i]-1.0;//shift to orgin
		r2 += z[i]*z[i];
		sum_z += z[i];
	}
	f[0]=pow(fabs(r2-nx),2*alpha) + (0.5*r2 + sum_z)/nx + 0.5;
}

void CEC17::hgbat_func (double *x, double *f, int nx, double *Os,double *Mr,int s_flag, int r_flag) /* HGBat, provdided by Hans-Georg Beyer (HGB)*/
/* original global optimum: [-1,-1,...,-1] */ {
	int i;
	double alpha,r2,sum_z;
	alpha=1.0/4.0;

	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 5.0/100.0, s_flag, r_flag); /* shift and rotate */

	r2 = 0.0;
	sum_z=0.0;
	for (i=0; i<nx; i++) {
		z[i]=z[i]-1.0;//shift to orgin
		r2 += z[i]*z[i];
		sum_z += z[i];
	}
	f[0]=pow(fabs(pow(r2,2.0)-pow(sum_z,2.0)),2*alpha) + (0.5*r2 + sum_z)/nx + 0.5;
}

void CEC17::hf01 (double *x, double *f, int nx, double *Os,double *Mr,int *S,int s_flag,int r_flag) /* Hybrid Function 1 */
{
	int i,tmp,cf_num=3;
	double fit[3];
	int G[3],G_nx[3];
	double Gp[3]={0.2,0.4,0.4};

	tmp=0;
	for (i=0; i<cf_num-1; i++)
	{
		G_nx[i] = ceil(Gp[i]*nx);
		tmp += G_nx[i];
	}
	G_nx[cf_num-1]=nx-tmp;
	G[0]=0;
	for (i=1; i<cf_num; i++)
	{
		G[i] = G[i-1]+G_nx[i-1];
	}

	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); /* shift and rotate */

	for (i = 0; i < nx; i++) y[i] = z[S[i] - 1];
	i=0;
	zakharov_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=1;
	rosenbrock_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=2;
	rastrigin_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	f[0]=0.0;
	for(i=0;i<cf_num;i++) f[0] += fit[i];
}

void CEC17::hf02 (double *x, double *f, int nx, double *Os,double *Mr,int *S,int s_flag,int r_flag) /* Hybrid Function 2 */ {
	int i,tmp,cf_num=3;
	double fit[3];
	int G[3],G_nx[3];
	double Gp[3]={0.3,0.3,0.4};

	tmp=0;
	for (i=0; i<cf_num-1; i++) {
		G_nx[i] = ceil(Gp[i]*nx);
		tmp += G_nx[i];
	}
	G_nx[cf_num-1]=nx-tmp;

	G[0]=0;
	for (i=1; i<cf_num; i++) G[i] = G[i-1]+G_nx[i-1];
	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); /* shift and rotate */

	for (i=0; i<nx; i++) y[i]=z[S[i]-1];
	i=0;
	ellips_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=1;
	schwefel_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=2;
	bent_cigar_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);

	f[0]=0.0;
	for(i=0;i<cf_num;i++) f[0] += fit[i];
}

void CEC17::hf03 (double *x, double *f, int nx, double *Os,double *Mr,int *S,int s_flag,int r_flag) /* Hybrid Function 2 */ {
	int i,tmp,cf_num=3;
	double fit[3];
	int G[3],G_nx[3];
	double Gp[3]={0.3,0.3,0.4};

	tmp=0;
	for (i=0; i<cf_num-1; i++)
	{
		G_nx[i] = ceil(Gp[i]*nx);
		tmp += G_nx[i];
	}
	G_nx[cf_num-1]=nx-tmp;

	G[0]=0;
	for (i=1; i<cf_num; i++)
	{
		G[i] = G[i-1]+G_nx[i-1];
	}

	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); /* shift and rotate */

	for (i=0; i<nx; i++)
	{
		y[i]=z[S[i]-1];
	}

	i=0;
	bent_cigar_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=1;
	rosenbrock_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=2;
	bi_rastrigin_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);

	f[0]=0.0;
	for(i=0;i<cf_num;i++)
	{
		f[0] += fit[i];
	}

}

void CEC17::hf04 (double *x, double *f, int nx, double *Os,double *Mr,int *S,int s_flag,int r_flag) /* Hybrid Function 3 */ {
	int i,tmp,cf_num=4;
	double fit[4];
	int G[4],G_nx[4];
	double Gp[4]={0.2,0.2,0.2,0.4};

	tmp=0;
	for (i=0; i<cf_num-1; i++) {
		G_nx[i] = ceil(Gp[i]*nx);
		tmp += G_nx[i];
	}
	G_nx[cf_num-1]=nx-tmp;

	G[0]=0;
	for (i=1; i<cf_num; i++) G[i] = G[i-1]+G_nx[i-1];

	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); /* shift and rotate */

	for (i=0; i<nx; i++) y[i]=z[S[i]-1];
	i=0;
	ellips_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=1;
	ackley_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=2;
	schaffer_F7_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=3;
	rastrigin_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);

	f[0]=0.0;
	for(i=0;i<cf_num;i++) f[0] += fit[i];
}

void CEC17::hf05 (double *x, double *f, int nx, double *Os,double *Mr,int *S,int s_flag,int r_flag) /* Hybrid Function 4 */ {
	int i,tmp,cf_num=4;
	double fit[4];
	int G[4],G_nx[4];
	double Gp[4]={0.2,0.2,0.3,0.3};

	tmp=0;
	for (i=0; i<cf_num-1; i++) {
		G_nx[i] = ceil(Gp[i]*nx);
		tmp += G_nx[i];
	}
	G_nx[cf_num-1]=nx-tmp;

	G[0]=0;
	for (i=1; i<cf_num; i++) G[i] = G[i-1]+G_nx[i-1];

	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); /* shift and rotate */

	for (i=0; i<nx; i++) y[i]=z[S[i]-1];
	i=0;

	bent_cigar_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=1;
	hgbat_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=2;
	rastrigin_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=3;
	rosenbrock_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);

	f[0]=0.0;
	for(i=0;i<cf_num;i++) f[0] += fit[i];
}

void CEC17::hf06 (double *x, double *f, int nx, double *Os,double *Mr,int *S,int s_flag,int r_flag) /* Hybrid Function 5 */
{
	int i,tmp,cf_num=4;
	double fit[4];
	int G[4],G_nx[4];
	double Gp[4]={0.2,0.2,0.3,0.3};

	tmp=0;
	for (i=0; i<cf_num-1; i++)
	{
		G_nx[i] = ceil(Gp[i]*nx);
		tmp += G_nx[i];
	}
	G_nx[cf_num-1]=nx-tmp;

	G[0]=0;
	for (i=1; i<cf_num; i++)
	{
		G[i] = G[i-1]+G_nx[i-1];
	}

	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); /* shift and rotate */

	for (i=0; i<nx; i++)
	{
		y[i]=z[S[i]-1];
	}
	i=0;
	escaffer6_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=1;
	hgbat_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=2;
	rosenbrock_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=3;
	schwefel_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);

	f[0]=0.0;
	for(i=0;i<cf_num;i++)
	{
		f[0] += fit[i];
	}
}

void CEC17::hf07 (double *x, double *f, int nx, double *Os,double *Mr,int *S,int s_flag,int r_flag) /* Hybrid Function 6 */ {
	int i,tmp,cf_num=5;
	double fit[5];
	int G[5],G_nx[5];
	double Gp[5]={0.1,0.2,0.2,0.2,0.3};

	tmp=0;
	for (i=0; i<cf_num-1; i++) {
		G_nx[i] = ceil(Gp[i]*nx);
		tmp += G_nx[i];
	}
	G_nx[cf_num-1]=nx-tmp;

	G[0]=0;
	for (i=1; i<cf_num; i++) G[i] = G[i-1]+G_nx[i-1];

	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); /* shift and rotate */

	for (i=0; i<nx; i++) y[i]=z[S[i]-1];
	i=0;
	katsuura_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=1;
	ackley_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=2;
	grie_rosen_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=3;
	schwefel_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=4;
	rastrigin_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);

	f[0]=0.0;
	for(i=0;i<cf_num;i++) f[0] += fit[i];
}

void CEC17::hf08 (double *x, double *f, int nx, double *Os,double *Mr,int *S,int s_flag,int r_flag) /* Hybrid Function 6 */ {
	int i,tmp,cf_num=5;
	double fit[5];
	int G[5],G_nx[5];
	double Gp[5]={0.2,0.2,0.2,0.2,0.2};

	tmp=0;
	for (i=0; i<cf_num-1; i++) {
		G_nx[i] = ceil(Gp[i]*nx);
		tmp += G_nx[i];
	}
	G_nx[cf_num-1]=nx-tmp;

	G[0]=0;
	for (i=1; i<cf_num; i++) G[i] = G[i-1]+G_nx[i-1];

	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); /* shift and rotate */

	for (i=0; i<nx; i++) y[i]=z[S[i]-1];

	i=0;
	ellips_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=1;
	ackley_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=2;
	rastrigin_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=3;
	hgbat_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=4;
	discus_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);

	f[0]=0.0;
	for(i=0;i<cf_num;i++) f[0] += fit[i];
}

void CEC17::hf09 (double *x, double *f, int nx, double *Os,double *Mr,int *S,int s_flag,int r_flag) /* Hybrid Function 6 */ {
	int i,tmp,cf_num=5;
	double fit[5];
	int G[5],G_nx[5];
	double Gp[5]={0.2,0.2,0.2,0.2,0.2};

	tmp=0;
	for (i=0; i<cf_num-1; i++) {
		G_nx[i] = ceil(Gp[i]*nx);
		tmp += G_nx[i];
	}
	G_nx[cf_num-1]=nx-tmp;

	G[0]=0;
	for (i=1; i<cf_num; i++) G[i] = G[i-1]+G_nx[i-1];

	std::vector<double> z(_dim), y(_dim);
	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); /* shift and rotate */

	for (i=0; i<nx; i++) y[i]=z[S[i]-1];

	i=0;
	bent_cigar_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=1;
	rastrigin_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=2;
	grie_rosen_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=3;
	weierstrass_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=4;
	escaffer6_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);

	f[0]=0.0;
	for(i=0;i<cf_num;i++) f[0] += fit[i];
}

void CEC17::hf10 (double *x, double *f, int nx, double *Os,double *Mr,int *S,int s_flag,int r_flag) /* Hybrid Function 6 */ {
	int i,tmp,cf_num=6;
	double fit[6];
	int G[6],G_nx[6];
	double Gp[6]={0.1,0.1,0.2,0.2,0.2,0.2};

	tmp=0;
	for (i=0; i<cf_num-1; i++) {
		G_nx[i] = ceil(Gp[i]*nx);
		tmp += G_nx[i];
	}
	G_nx[cf_num-1]=nx-tmp;

	G[0]=0;
	for (i=1; i<cf_num; i++) G[i] = G[i-1]+G_nx[i-1];
	std::vector<double> z(_dim), y(_dim);

	sr_func (x, z.data(), y.data(), nx, Os, Mr, 1.0, s_flag, r_flag); /* shift and rotate */

	for (i=0; i<nx; i++) y[i]=z[S[i]-1];

	i=0;
	hgbat_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=1;
	katsuura_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=2;
	ackley_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=3;
	rastrigin_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=4;
	schwefel_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);
	i=5;
	schaffer_F7_func(&y[G[i]],&fit[i],G_nx[i],Os,Mr,0,0);

	f[0]=0.0;
	for(i=0;i<cf_num;i++)
	{
		f[0] += fit[i];
	}
}

void CEC17::cf01 (double *x, double *f, int nx, double *Os,double *Mr,int r_flag) /* Composition Function 1 */ {
	int i,cf_num=3;
	double fit[3];
	double delta[3] = {10, 20, 30};
	double bias[3] = {0, 100, 200};

	i=0;
	rosenbrock_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	i=1;
	ellips_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=10000*fit[i]/1e+10;
	i=2;
	rastrigin_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	std::vector<double> y(_dim);
	cf_cal(x, f, y.data(), nx, Os, delta,bias,fit,cf_num);
}

void CEC17::cf02 (double *x, double *f, int nx, double *Os,double *Mr,int r_flag) /* Composition Function 2 */ {
	int i,cf_num=3;
	double fit[3];
	double delta[3] = {10,20,30};
	double bias[3] = {0, 100, 200};

	i=0;
	rastrigin_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	i=1;
	griewank_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=1000*fit[i]/100;
	i=2;
	schwefel_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	std::vector<double> y(_dim);
	cf_cal(x, f, y.data(), nx, Os, delta,bias,fit,cf_num);
}

void CEC17::cf03 (double *x, double *f, int nx, double *Os,double *Mr,int r_flag) /* Composition Function 3 */ {
	int i,cf_num=4;
	double fit[4];
	double delta[4] = {10,20,30,40};
	double bias[4] = {0, 100, 200, 300};
	i=0;
	rosenbrock_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	i=1;
	ackley_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=1000*fit[i]/100;
	i=2;
	schwefel_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	i=3;
	rastrigin_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	std::vector<double> y(_dim);
	cf_cal(x, f, y.data(), nx, Os, delta,bias,fit,cf_num);
}

void CEC17::cf04 (double *x, double *f, int nx, double *Os,double *Mr,int r_flag) /* Composition Function 3 */ {
	int i,cf_num=4;
	double fit[4];
	double delta[4] = {10,20,30,40};
	double bias[4] = {0, 100, 200, 300};

	i=0;
	ackley_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=1000*fit[i]/100;
	i=1;
	ellips_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=10000*fit[i]/1e+10;
	i=2;
	griewank_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=1000*fit[i]/100;
	i=3;
	rastrigin_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	std::vector<double> y(_dim);
	cf_cal(x, f, y.data(), nx, Os, delta,bias,fit,cf_num);
}

void CEC17::cf05 (double *x, double *f, int nx, double *Os,double *Mr,int r_flag) /* Composition Function 4 */ {
	int i,cf_num=5;
	double fit[5];
	double delta[5] = {10,20,30,40,50};
	double bias[5] = {0, 100, 200, 300, 400};
	i=0;
	rastrigin_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=10000*fit[i]/1e+3;
	i=1;
	happycat_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=1000*fit[i]/1e+3;
	i=2;
	ackley_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=1000*fit[i]/100;
	i=3;
	discus_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=10000*fit[i]/1e+10;
	i=4;
	rosenbrock_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	std::vector<double> y(_dim);
	cf_cal(x, f, y.data(), nx, Os, delta,bias,fit,cf_num);
}		

void CEC17::cf06 (double *x, double *f, int nx, double *Os,double *Mr,int r_flag) /* Composition Function 4 */ {
	int i,cf_num=5;
	double fit[5];
	double delta[5] = {10,20,20,30,40};
	double bias[5] = {0, 100, 200, 300, 400};
	i=0;
	escaffer6_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=10000*fit[i]/2e+7;
	i=1;
	schwefel_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	i=2;
	griewank_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=1000*fit[i]/100;
	i=3;
	rosenbrock_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	i=4;
	rastrigin_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=10000*fit[i]/1e+3;
	std::vector<double> y(_dim);
	cf_cal(x, f, y.data(), nx, Os, delta,bias,fit,cf_num);
}

void CEC17::cf07 (double *x, double *f, int nx, double *Os,double *Mr,int r_flag) /* Composition Function 4 */ {
	int i,cf_num=6;
	double fit[6];
	double delta[6] = {10,20,30,40,50,60};
	double bias[6] = {0, 100, 200, 300, 400, 500};
	i=0;
	hgbat_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=10000*fit[i]/1000;
	i=1;
	rastrigin_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=10000*fit[i]/1e+3;
	i=2;
	schwefel_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=10000*fit[i]/4e+3;
	i=3;
	bent_cigar_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=10000*fit[i]/1e+30;
	i=4;
	ellips_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=10000*fit[i]/1e+10;
	i=5;
	escaffer6_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=10000*fit[i]/2e+7;
	std::vector<double> y(_dim);
	cf_cal(x, f, y.data(), nx, Os, delta,bias,fit,cf_num);
}

void CEC17::cf08 (double *x, double *f, int nx, double *Os,double *Mr,int r_flag) /* Composition Function 4 */ {
	int i,cf_num=6;
	double fit[6];
	double delta[6] = {10,20,30,40,50,60};
	double bias[6] = {0, 100, 200, 300, 400, 500};
	i=0;
	ackley_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=1000*fit[i]/100;
	i=1;
	griewank_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=1000*fit[i]/100;
	i=2;
	discus_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=10000*fit[i]/1e+10;
	i=3;
	rosenbrock_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	i=4;
	happycat_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=1000*fit[i]/1e+3;
	i=5;
	escaffer6_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],1,r_flag);
	fit[i]=10000*fit[i]/2e+7;
	std::vector<double> y(_dim);
	cf_cal(x, f, y.data(), nx, Os, delta,bias,fit,cf_num);
}

void CEC17::cf09 (double *x, double *f, int nx, double *Os,double *Mr,int *SS,int r_flag) {

	int i,cf_num=3;
	double fit[3];
	double delta[3] = {10,30,50};
	double bias[3] = {0, 100, 200};
	i=0;
	hf05(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],&SS[i*nx],1,r_flag);
	i=1;
	hf06(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],&SS[i*nx],1,r_flag);
	i=2;
	hf07(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],&SS[i*nx],1,r_flag);
	std::vector<double> y(_dim);
	cf_cal(x, f, y.data(), nx, Os, delta,bias,fit,cf_num);

}

void CEC17::cf10 (double *x, double *f, int nx, double *Os,double *Mr,int *SS,int r_flag) {
	int i,cf_num=3;
	double fit[3];
	double delta[3] = {10,30,50};
	double bias[3] = {0, 100, 200};
	i=0;
	hf05(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],&SS[i*nx],1,r_flag);
	i=1;
	hf08(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],&SS[i*nx],1,r_flag);
	i=2;
	hf09(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],&SS[i*nx],1,r_flag);
	std::vector<double> y(_dim);
	cf_cal(x, f, y.data(), nx, Os, delta,bias,fit,cf_num);
}

void shiftfunc (double *x, double *xshift, int nx,double *Os) {
	int i;
	for (i=0; i<nx; i++) xshift[i]=x[i]-Os[i];
}

void rotatefunc (double *x, double *xrot, int nx,double *Mr) {
	int i,j;
	for (i=0; i<nx; i++) {
		xrot[i]=0;
		for (j=0; j<nx; j++) xrot[i]=xrot[i]+x[j]*Mr[i*nx+j];
	}
}

void CEC17::sr_func (double *x, double *sr_x, double *y, int nx, double *Os,double *Mr, double sh_rate, int s_flag,int r_flag) /* shift and rotate */ {
	int i;
	if (s_flag == 1) {
		if (r_flag == 1) {
			shiftfunc(x, y, nx, Os);
			for (i=0; i<nx; i++)//shrink to the original search range
			{
				y[i]=y[i]*sh_rate;
			}
			rotatefunc(y, sr_x, nx, Mr);
		} else {
			shiftfunc(x, sr_x, nx, Os);
			for (i=0; i<nx; i++)//shrink to the original search range
			{
				sr_x[i]=sr_x[i]*sh_rate;
			}
		}
	} else {
		if (r_flag==1) {
			for (i=0; i<nx; i++)//shrink to the original search range
			{
				y[i]=x[i]*sh_rate;
			}
			rotatefunc(y, sr_x, nx, Mr);
		}
		else
			for (i=0; i<nx; i++)//shrink to the original search range
			{
				sr_x[i]=x[i]*sh_rate;
			}
	}
}

void asyfunc (double *x, double *xasy, int nx, double beta) {
	int i;
	for (i=0; i<nx; i++) {
		if (x[i]>0) xasy[i] = pow(x[i],1.0+beta*i/(nx-1)*pow(x[i],0.5));
	}
}

void oszfunc (double *x, double *xosz, int nx) {
	int i,sx;
	double c1,c2,xx;
	for (i=0; i<nx; i++) {
		if (i==0||i==nx-1) {
			if (x[i]!=0) xx=log(fabs(x[i]));
			if (x[i]>0) {
				c1=10;
				c2=7.9;
			} else {
				c1=5.5;
				c2=3.1;
			}
			if (x[i]>0) sx=1;
			else if (x[i]==0) sx=0;
			else sx=-1;
			xosz[i]=sx*exp(xx+0.049*(sin(c1*xx)+sin(c2*xx)));
		} else {
			xosz[i]=x[i];
		}
	}
}


void CEC17::cf_cal(double *x, double *f, double *w, int nx, double *Os,double * delta,double * bias,double * fit, int cf_num) {
	int i,j;
	double w_max=0,w_sum=0;
	for (i=0; i<cf_num; i++) {
		fit[i]+=bias[i];
		w[i]=0;
		for (j=0; j<nx; j++) w[i]+=pow(x[j]-Os[i*nx+j],2.0);
		if (w[i]!=0) w[i]=pow(1.0/w[i],0.5)*exp(-w[i]/2.0/nx/pow(delta[i],2.0));
		else w[i]=INF;
		if (w[i]>w_max) w_max=w[i];
	}
	for (i=0; i<cf_num; i++) w_sum=w_sum+w[i];
	if(w_max==0) {
		for (i=0; i<cf_num; i++) w[i]=1;
		w_sum=cf_num;
	}
	f[0] = 0.0;
	for (i=0; i<cf_num; i++) f[0]=f[0]+w[i]/w_sum*fit[i];
}