/*

CEC17 Test Function Suite for Single Objective Optimization- Bound constraints

Noor Awad (email: noor0029@e.ntu.edu.sg)

Sep. 10th 2016

Last update on 26_5_2017

1. Run the following command in Matlab window:

mex cec17_func.cpp -DWINDOWS

2. Then you can use the test functions as the following example:

f = cec17_func(x,func_num);

Here x is a D*pop_size matrix.

*/

// #include <WINDOWS.H>

#include <stdio.h>

#include <math.h>

#include <malloc.h>

#include <mex.h>

double *OShift,*M,*y,*z,*x_bound;

int ini_flag=0,n_flag,func_flag,*SS;

// #include <WINDOWS.H>

// #include <stdio.h>

// #include <math.h>

// #include <malloc.h>

#define INF 1.0e99

#define EPS 1.0e-14

#define E 2.7182818284590452353602874713526625

#define PI 3.1415926535897932384626433832795029

void sphere_func (double *, double *, int , double *,double *, int, int); /* Sphere */

void ellips_func(double *, double *, int , double *,double *, int, int); /* Ellipsoidal */

void bent_cigar_func(double *, double *, int , double *,double *, int, int); /* Discus */

void discus_func(double *, double *, int , double *,double *, int, int); /* Bent_Cigar */

void dif_powers_func(double *, double *, int , double *,double *, int, int); /* Different Powers */

void rosenbrock_func (double *, double *, int , double *,double *, int, int); /* Rosenbrock's */

void schaffer_F7_func (double *, double *, int , double *,double *, int, int); /* Schwefel's F7 */

void ackley_func (double *, double *, int , double *,double *, int, int); /* Ackley's */

void rastrigin_func (double *, double *, int , double *,double *, int, int); /* Rastrigin's */

void weierstrass_func (double *, double *, int , double *,double *, int, int); /* Weierstrass's */

void griewank_func (double *, double *, int , double *,double *, int, int); /* Griewank's */

void schwefel_func (double *, double *, int , double *,double *, int, int); /* Schwefel's */

void katsuura_func (double *, double *, int , double *,double *, int, int); /* Katsuura */

void bi_rastrigin_func (double *, double *, int , double *,double *, int, int); /* Lunacek Bi_rastrigin */

void grie_rosen_func (double *, double *, int , double *,double *, int, int); /* Griewank-Rosenbrock */

void escaffer6_func (double *, double *, int , double *,double *, int, int); /* Expanded Scaffer¡¯s F6 */

void step_rastrigin_func (double *, double *, int , double *,double *, int, int); /* Noncontinuous Rastrigin's */

void happycat_func (double *, double *, int , double *,double *, int, int); /* HappyCat */

void hgbat_func (double *, double *, int , double *,double *, int, int); /* HGBat */

/* New functions Noor Changes */

void sum_diff_pow_func(double *, double *, int , double *,double *, int, int); /* Sum of different power */

void zakharov_func(double *, double *, int , double *,double *, int, int); /* ZAKHAROV */

void levy_func(double *, double *, int , double *,double *, int, int); /* Levy */

void dixon_price_func(double *, double *, int , double *,double *, int, int); /* Dixon and Price */

void hf01 (double *, double *, int, double *,double *, int *,int, int); /* Hybrid Function 1 */

void hf02 (double *, double *, int, double *,double *, int *,int, int); /* Hybrid Function 2 */

void hf03 (double *, double *, int, double *,double *, int *,int, int); /* Hybrid Function 3 */

void hf04 (double *, double *, int, double *,double *, int *,int, int); /* Hybrid Function 4 */

void hf05 (double *, double *, int, double *,double *, int *,int, int); /* Hybrid Function 5 */

void hf06 (double *, double *, int, double *,double *, int *,int, int); /* Hybrid Function 6 */

void hf07 (double *, double *, int, double *,double *, int *,int, int); /* Hybrid Function 7 */

void hf08 (double *, double *, int, double *,double *, int *,int, int); /* Hybrid Function 8 */

void hf09 (double *, double *, int, double *,double *, int *,int, int); /* Hybrid Function 9 */

void hf10 (double *, double *, int, double *,double *, int *,int, int); /* Hybrid Function 10 */

void cf01 (double *, double *, int , double *,double *, int); /* Composition Function 1 */

void cf02 (double *, double *, int , double *,double *, int); /* Composition Function 2 */

void cf03 (double *, double *, int , double *,double *, int); /* Composition Function 3 */

void cf04 (double *, double *, int , double *,double *, int); /* Composition Function 4 */

void cf05 (double *, double *, int , double *,double *, int); /* Composition Function 5 */

void cf06 (double *, double *, int , double *,double *, int); /* Composition Function 6 */

void cf07 (double *, double *, int , double *,double *, int); /* Composition Function 7 */

void cf08 (double *, double *, int , double *,double *, int); /* Composition Function 8 */

void cf09 (double *, double *, int , double *,double *, int *, int); /* Composition Function 7 */

void cf10 (double *, double *, int , double *,double *, int *, int); /* Composition Function 8 */

void shiftfunc (double*,double*,int,double*);

void rotatefunc (double*,double*,int, double*);

void sr_func (double *, double *, int, double*, double*, double, int, int); /* shift and rotate */

void asyfunc (double *, double *x, int, double);

void oszfunc (double *, double *, int);

void cf_cal(double *, double *, int, double *,double *,double *,double *,int);

void cec17_test_func(double *, double *,int,int,int);

void mexFunction (int nlhs, mxArray * plhs[], int nrhs, const mxArray * prhs[])

{

int m, n,func_num;

double *f, *x;

if ((nrhs < 2) || (nlhs < 1))

{

mexPrintf ("usage: f = cec17_func(x, func_num);\n");

mexErrMsgTxt ("example: f= cec17_func([3.3253000e+000, -1.2835000e+000]', 1);");

}

n = mxGetM (prhs[0]);

if (!(n==2||n==10||n==30||n==50||n==100))

{

mexPrintf ("usage: f = cec17_func(x, func_num);\n");

mexErrMsgTxt ("Error: Test functions are only defined for D=2,10,30,50,100.");

}

m = mxGetN (prhs[0]);

x = mxGetPr (prhs[0]);

func_num= (int)*mxGetPr (prhs[1]);

if (func_num>30)

{

mexPrintf ("usage: f = cec17_func(x, func_num);\n");

mexErrMsgTxt ("Error: There are only 30 test functions in this test suite!");

}

plhs[0] = mxCreateDoubleMatrix (1, m, mxREAL);

f = mxGetPr (plhs[0]);

cec17_test_func(&x[0], &f[0], n,m,func_num);

}

void cec17_test_func(double *x, double *f, int nx, int mx,int func_num)

{

int cf_num=10,i,j;

if (ini_flag==1)

{

if ((n_flag!=nx)||(func_flag!=func_num))

{

ini_flag=0;

}

}

if (ini_flag==0)

{

FILE *fpt;

char FileName[256];

free(M);

free(OShift);

free(y);

free(z);

free(x_bound);

y=(double *)malloc(sizeof(double) * nx);

z=(double *)malloc(sizeof(double) * nx);

x_bound=(double *)malloc(sizeof(double) * nx);

for (i=0; i<nx; i++)

x_bound[i]=100.0;

if (!(nx==2||nx==10||nx==20||nx==30||nx==50||nx==100))

{

printf("\nError: Test functions are only defined for D=2,10,20,30,50,100.\n");

}

if (nx==2&&((func_num>=17&&func_num<=22)||(func_num>=29&&func_num<=30)))

{

printf("\nError: hf01,hf02,hf03,hf04,hf05,hf06,cf07&cf08 are NOT defined for D=2.\n");

}

/* Load Matrix M*/

sprintf(FileName, "input_data/M_%d_D%d.txt", func_num,nx);

fpt = fopen(FileName,"r");

if (fpt==NULL)

{

printf("\n Error: Cannot open input file for reading \n");

}

if (func_num<20)

{

M=(double*)malloc(nx*nx*sizeof(double));

if (M==NULL)

printf("\nError: there is insufficient memory available!\n");

for (i=0; i<nx*nx; i++)

{

fscanf(fpt,"%lf",&M[i]);

}

}

else

{

M=(double*)malloc(cf_num*nx*nx*sizeof(double));

if (M==NULL)

printf("\nError: there is insufficient memory available!\n");

for (i=0; i<cf_num*nx*nx; i++)

{

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==NULL)

{

printf("\n Error: Cannot open input file for reading \n");

}

if (func_num<20)

{

OShift=(double *)malloc(nx*sizeof(double));

if (OShift==NULL)

printf("\nError: there is insufficient memory available!\n");

for(i=0;i<nx;i++)

{

fscanf(fpt,"%lf",&OShift[i]);

}

}

else

{

OShift=(double *)malloc(nx*cf_num*sizeof(double));

if (OShift==NULL)

printf("\nError: there is insufficient memory available!\n");

for(i=0;i<cf_num-1;i++)

{

for (j=0;j<nx;j++)

{

fscanf(fpt,"%lf",&OShift[i*nx+j]);

}

fscanf(fpt,"%*[^\n]%*c");

}

for (j=0;j<nx;j++)

{

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==NULL)

{

printf("\n Error: Cannot open input file for reading \n");

}

SS=(int *)malloc(nx*sizeof(int));

if (SS==NULL)

printf("\nError: there is insufficient memory available!\n");

for(i=0;i<nx;i++)

{

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==NULL)

{

printf("\n Error: Cannot open input file for reading \n");

}

SS=(int *)malloc(nx*cf_num*sizeof(int));

if (SS==NULL)

printf("\nError: there is insufficient memory available!\n");

for(i=0;i<nx*cf_num;i++)

{

fscanf(fpt,"%d",&SS[i]);

}

fclose(fpt);

}

n_flag=nx;

func_flag=func_num;

ini_flag=1;

//printf("Function has been initialized!\n");

}

for (i = 0; i < mx; i++)

{

switch(func_num)

{

case 1:

bent_cigar_func(&x[i*nx],&f[i],nx,OShift,M,1,1);

f[i]+=100.0;

break;

case 2:

//sum_diff_pow_func(&x[i*nx],&f[i],nx,OShift,M,1,1);

//f[i]+=200.0;

printf("\nError: This function (F2) has been deleted\n");

break;

case 3:

zakharov_func(&x[i*nx],&f[i],nx,OShift,M,1,1);

f[i]+=300.0;

break;

case 4:

rosenbrock_func(&x[i*nx],&f[i],nx,OShift,M,1,1);

f[i]+=400.0;

break;

case 5:

rastrigin_func(&x[i*nx],&f[i],nx,OShift,M,1,1);

f[i]+=500.0;

break;

case 6:

schaffer_F7_func(&x[i*nx],&f[i],nx,OShift,M,1,1);

f[i]+=600.0;

break;

case 7:

bi_rastrigin_func(&x[i*nx],&f[i],nx,OShift,M,1,1);

f[i]+=700.0;

break;

case 8:

step_rastrigin_func(&x[i*nx],&f[i],nx,OShift,M,1,1);

f[i]+=800.0;

break;

case 9:

levy_func(&x[i*nx],&f[i],nx,OShift,M,1,1);

f[i]+=900.0;

break;

case 10:

schwefel_func(&x[i*nx],&f[i],nx,OShift,M,1,1);

f[i]+=1000.0;

break;

case 11:

hf01(&x[i*nx],&f[i],nx,OShift,M,SS,1,1);

f[i]+=1100.0;

break;

case 12:

hf02(&x[i*nx],&f[i],nx,OShift,M,SS,1,1);

f[i]+=1200.0;

break;

case 13:

hf03(&x[i*nx],&f[i],nx,OShift,M,SS,1,1);

f[i]+=1300.0;

break;

case 14:

hf04(&x[i*nx],&f[i],nx,OShift,M,SS,1,1);

f[i]+=1400.0;

break;

case 15:

hf05(&x[i*nx],&f[i],nx,OShift,M,SS,1,1);

f[i]+=1500.0;

break;

case 16:

hf06(&x[i*nx],&f[i],nx,OShift,M,SS,1,1);

f[i]+=1600.0;

break;

case 17:

hf07(&x[i*nx],&f[i],nx,OShift,M,SS,1,1);

f[i]+=1700.0;

break;

case 18:

hf08(&x[i*nx],&f[i],nx,OShift,M,SS,1,1);

f[i]+=1800.0;

break;

case 19:

hf09(&x[i*nx],&f[i],nx,OShift,M,SS,1,1);

f[i]+=1900.0;

break;

case 20:

hf10(&x[i*nx],&f[i],nx,OShift,M,SS,1,1);

f[i]+=2000.0;

break;

case 21:

cf01(&x[i*nx],&f[i],nx,OShift,M,1);

f[i]+=2100.0;

break;

case 22:

cf02(&x[i*nx],&f[i],nx,OShift,M,1);

f[i]+=2200.0;

break;

case 23:

cf03(&x[i*nx],&f[i],nx,OShift,M,1);

f[i]+=2300.0;

break;

case 24:

cf04(&x[i*nx],&f[i],nx,OShift,M,1);

f[i]+=2400.0;

break;

case 25:

cf05(&x[i*nx],&f[i],nx,OShift,M,1);

f[i]+=2500.0;

break;

case 26:

cf06(&x[i*nx],&f[i],nx,OShift,M,1);

f[i]+=2600.0;

break;

case 27:

cf07(&x[i*nx],&f[i],nx,OShift,M,1);

f[i]+=2700.0;

break;

case 28:

cf08(&x[i*nx],&f[i],nx,OShift,M,1);

f[i]+=2800.0;

break;

case 29:

cf09(&x[i*nx],&f[i],nx,OShift,M,SS,1);

f[i]+=2900.0;

break;

case 30:

cf10(&x[i*nx],&f[i],nx,OShift,M,SS,1);

f[i]+=3000.0;

break;

default:

printf("\nError: There are only 30 test functions in this test suite!\n");

f[i] = 0.0;

break;

}

}

}

void 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;

sr_func (x, z, 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 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;

sr_func (x, z, 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 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;

sr_func (x, z, 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((abs(xi)),(i+1));

sum = sum + newv;

}

f[0] = sum;

}

void zakharov_func (double *x, double *f, int nx, double *Os,double *Mr, int s_flag, int r_flag) /* zakharov */

{

int i;

sr_func (x, z, 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 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;

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

double *w;

w=(double *)malloc(sizeof(double) * nx);

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;

free(w); // ADD THIS LINE to free memory! Thanks for Dr. Janez

}

/* Dixon and Price */

void 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;

sr_func (x, z, 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 bent_cigar_func (double *x, double *f, int nx, double *Os,double *Mr, int s_flag, int r_flag) /* Bent_Cigar */

{

int i;

sr_func (x, z, 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 discus_func (double *x, double *f, int nx, double *Os,double *Mr, int s_flag, int r_flag) /* Discus */

{

int i;

sr_func (x, z, 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 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;

sr_func (x, z, 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 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;

f[0] = 0.0;

sr_func (x, z, 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 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;

f[0] = 0.0;

sr_func (x, z, 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 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;

sr_func (x, z, 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 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;

a = 0.5;

b = 3.0;

k_max = 20;

f[0] = 0.0;

sr_func (x, z, 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 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;

sr_func (x, z, 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 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;

sr_func (x, z, 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 step_rastrigin_func (double *x, double *f, int nx, double *Os,double *Mr,int s_flag, int r_flag) /* Noncontinuous Rastrigin's */

{

int i;

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, 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 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;

sr_func (x, z, 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 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;

f[0]=1.0;

tmp3=pow(1.0*nx,1.2);

sr_func (x, z, 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 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;

double *tmpx;

tmpx=(double *)malloc(sizeof(double) * nx);

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, 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, y, 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);

}

free(tmpx);

}

void 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;

sr_func (x, z, 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 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;

sr_func (x, z, 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 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;

sr_func (x, z, 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 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;

sr_func (x, z, 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 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];

}

sr_func (x, z, 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 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];

}

sr_func (x, z, 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 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];

}

sr_func (x, z, 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;