CEC2013 Benchmark Functions
CEC13 Func
介绍
CEC13 Test Function Suite
Jane Jing Liang (email: liangjing@zzu.edu.cn)
14th Feb. 2013
1. Run the following command in Matlab window:
mex cec13_func.cpp -DWINDOWS
2. Then you can use the test functions as the following example:
f = cec13_func(x,func_num);
Here x is a D*pop_size matrix.
代码
#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;
#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); /* Sphere */
void ellips_func(double *, double *, int , double *,double *, int); /* Ellipsoidal */
void bent_cigar_func(double *, double *, int , double *,double *, int); /* Discus */
void discus_func(double *, double *, int , double *,double *, int); /* Bent_Cigar */
void dif_powers_func(double *, double *, int , double *,double *, int); /* Different Powers */
void rosenbrock_func (double *, double *, int , double *,double *, int); /* Rosenbrock's */
void schaffer_F7_func (double *, double *, int , double *,double *, int); /* Schwefel's F7 */
void ackley_func (double *, double *, int , double *,double *, int); /* Ackley's */
void griewank_func (double *, double *, int , double *,double *, int); /* Griewank's */
void rastrigin_func (double *, double *, int , double *,double *, int); /* Rastrigin's */
void step_rastrigin_func (double *, double *, int , double *,double *, int); /* Noncontinuous Rastrigin's */
void weierstrass_func (double *, double *, int , double *,double *, int); /* Weierstrass's */
void schwefel_func (double *, double *, int , double *,double *, int); /* Schwefel's */
void katsuura_func (double *, double *, int , double *,double *, int); /* Katsuura */
void bi_rastrigin_func (double *, double *, int , double *,double *, int); /* Lunacek Bi_rastrigin Function */
void grie_rosen_func (double *, double *, int , double *,double *, int); /* Griewank-Rosenbrock */
void escaffer6_func (double *, double *, int , double *,double *, int); /* Expanded Scaffer¡¯s F6 */
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 shiftfunc (double*,double*,int,double*);
void rotatefunc (double*,double*,int, double*);
void asyfunc (double *, double *x, int, double);
void oszfunc (double *, double *, int);
void cf_cal(double *, double *, int, double *,double *,double *,double *,int);
void 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 = cec13_func(x, func_num);\n");
mexErrMsgTxt ("example: f= cec13_func([3.3253000e+000, -1.2835000e+000]', 1);");
}
n = mxGetM (prhs[0]);
if (!(n==2||n==5||n==10||n==20||n==30||n==40||n==50||n==60||n==70||n==80||n==90||n==100))
{
mexPrintf ("usage: f = cec13_func(x, func_num);\n");
mexErrMsgTxt ("Error: Test functions are only defined for D=2,5,10,20,30,40,50,60,70,80,90,100.");
}
m = mxGetN (prhs[0]);
x = mxGetPr (prhs[0]);
func_num= (int)*mxGetPr (prhs[1]);
if (func_num>28)
{
mexPrintf ("usage: f = cec13_func(x, func_num);\n");
mexErrMsgTxt ("Error: There are only 28 test functions in this test suite!");
}
plhs[0] = mxCreateDoubleMatrix (1, m, mxREAL);
f = mxGetPr (plhs[0]);
test_func(&x[0], &f[0], n,m,func_num);
}
void test_func(double *x, double *f, int nx, int mx,int func_num)
{
int cf_num=10,i;
if (ini_flag==1)
{
if ((n_flag!=nx)||(func_flag!=func_num))
{
ini_flag=0;
}
}
if (ini_flag==0)
{
FILE *fpt;
char FileName[30];
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;
sprintf(FileName, "input_data/M_D%d.txt", nx);
fpt = fopen(FileName,"r");
if (fpt==NULL)
{
printf("\n Error: Cannot open input file for reading \n");
}
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);
fpt=fopen("input_data/shift_data.txt","r");
if (fpt==NULL)
{
printf("\n Error: Cannot open input file for reading \n");
}
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*nx;i++)
{
fscanf(fpt,"%Lf",&OShift[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:
sphere_func(&x[i*nx],&f[i],nx,OShift,M,0);
f[i]+=-1400.0;
break;
case 2:
ellips_func(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=-1300.0;
break;
case 3:
bent_cigar_func(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=-1200.0;
break;
case 4:
discus_func(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=-1100.0;
break;
case 5:
dif_powers_func(&x[i*nx],&f[i],nx,OShift,M,0);
f[i]+=-1000.0;
break;
case 6:
rosenbrock_func(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=-900.0;
break;
case 7:
schaffer_F7_func(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=-800.0;
break;
case 8:
ackley_func(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=-700.0;
break;
case 9:
weierstrass_func(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=-600.0;
break;
case 10:
griewank_func(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=-500.0;
break;
case 11:
rastrigin_func(&x[i*nx],&f[i],nx,OShift,M,0);
f[i]+=-400.0;
break;
case 12:
rastrigin_func(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=-300.0;
break;
case 13:
step_rastrigin_func(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=-200.0;
break;
case 14:
schwefel_func(&x[i*nx],&f[i],nx,OShift,M,0);
f[i]+=-100.0;
break;
case 15:
schwefel_func(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=100.0;
break;
case 16:
katsuura_func(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=200.0;
break;
case 17:
bi_rastrigin_func(&x[i*nx],&f[i],nx,OShift,M,0);
f[i]+=300.0;
break;
case 18:
bi_rastrigin_func(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=400.0;
break;
case 19:
grie_rosen_func(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=500.0;
break;
case 20:
escaffer6_func(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=600.0;
break;
case 21:
cf01(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=700.0;
break;
case 22:
cf02(&x[i*nx],&f[i],nx,OShift,M,0);
f[i]+=800.0;
break;
case 23:
cf03(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=900.0;
break;
case 24:
cf04(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=1000.0;
break;
case 25:
cf05(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=1100.0;
break;
case 26:
cf06(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=1200.0;
break;
case 27:
cf07(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=1300.0;
break;
case 28:
cf08(&x[i*nx],&f[i],nx,OShift,M,1);
f[i]+=1400.0;
break;
default:
printf("\nError: There are only 28 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 r_flag) /* Sphere */
{
int i;
shiftfunc(x, y, nx, Os);
if (r_flag==1)
rotatefunc(y, z, nx, Mr);
else
for (i=0; i<nx; i++)
z[i]=y[i];
f[0] = 0.0;
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 r_flag) /* Ellipsoidal */
{
int i;
shiftfunc(x, y, nx, Os);
if (r_flag==1)
rotatefunc(y, z, nx, Mr);
else
for (i=0; i<nx; i++)
z[i]=y[i];
oszfunc (z, y, nx);
f[0] = 0.0;
for (i=0; i<nx; i++)
{
f[0] += pow(10.0,6.0*i/(nx-1))*y[i]*y[i];
}
}
void bent_cigar_func (double *x, double *f, int nx, double *Os,double *Mr,int r_flag) /* Bent_Cigar */
{
int i;
double beta=0.5;
shiftfunc(x, y, nx, Os);
if (r_flag==1)
rotatefunc(y, z, nx, Mr);
else
for (i=0; i<nx; i++)
z[i]=y[i];
asyfunc (z, y, nx,beta);
if (r_flag==1)
rotatefunc(y, z, nx, &Mr[nx*nx]);
else
for (i=0; i<nx; i++)
z[i]=y[i];
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 r_flag) /* Discus */
{
int i;
shiftfunc(x, y, nx, Os);
if (r_flag==1)
rotatefunc(y, z, nx, Mr);
else
for (i=0; i<nx; i++)
z[i]=y[i];
oszfunc (z, y, nx);
f[0] = pow(10.0,6.0)*y[0]*y[0];
for (i=1; i<nx; i++)
{
f[0] += y[i]*y[i];
}
}
void dif_powers_func (double *x, double *f, int nx, double *Os,double *Mr,int r_flag) /* Different Powers */
{
int i;
shiftfunc(x, y, nx, Os);
if (r_flag==1)
rotatefunc(y, z, nx, Mr);
else
for (i=0; i<nx; i++)
z[i]=y[i];
f[0] = 0.0;
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 r_flag) /* Rosenbrock's */
{
int i;
double tmp1,tmp2;
shiftfunc(x, y, nx, Os);//shift
for (i=0; i<nx; i++)//shrink to the orginal search range
{
y[i]=y[i]*2.048/100;
}
if (r_flag==1)
rotatefunc(y, z, nx, Mr);//rotate
else
for (i=0; i<nx; i++)
z[i]=y[i];
for (i=0; i<nx; i++)//shift to orgin
{
z[i]=z[i]+1;
}
f[0] = 0.0;
for (i=0; i<nx-1; i++)
{
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 r_flag) /* Schwefel's 1.2 */
{
int i;
double tmp;
shiftfunc(x, y, nx, Os);
if (r_flag==1)
rotatefunc(y, z, nx, Mr);
else
for (i=0; i<nx; i++)
z[i]=y[i];
asyfunc (z, y, nx, 0.5);
for (i=0; i<nx; i++)
z[i] = y[i]*pow(10.0,1.0*i/(nx-1)/2.0);
if (r_flag==1)
rotatefunc(z, y, nx, &Mr[nx*nx]);
else
for (i=0; i<nx; i++)
y[i]=z[i];
for (i=0; i<nx-1; i++)
z[i]=pow(y[i]*y[i]+y[i+1]*y[i+1],0.5);
f[0] = 0.0;
for (i=0; i<nx-1; i++)
{
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 r_flag) /* Ackley's */
{
int i;
double sum1, sum2;
shiftfunc(x, y, nx, Os);
if (r_flag==1)
rotatefunc(y, z, nx, Mr);
else
for (i=0; i<nx; i++)
z[i]=y[i];
asyfunc (z, y, nx, 0.5);
for (i=0; i<nx; i++)
z[i] = y[i]*pow(10.0,1.0*i/(nx-1)/2.0);
if (r_flag==1)
rotatefunc(z, y, nx, &Mr[nx*nx]);
else
for (i=0; i<nx; i++)
y[i]=z[i];
sum1 = 0.0;
sum2 = 0.0;
for (i=0; i<nx; i++)
{
sum1 += y[i]*y[i];
sum2 += cos(2.0*PI*y[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 r_flag) /* Weierstrass's */
{
int i,j,k_max;
double sum,sum2, a, b;
shiftfunc(x, y, nx, Os);
for (i=0; i<nx; i++)//shrink to the orginal search range
{
y[i]=y[i]*0.5/100;
}
if (r_flag==1)
rotatefunc(y, z, nx, Mr);
else
for (i=0; i<nx; i++)
z[i]=y[i];
asyfunc (z, y, nx, 0.5);
for (i=0; i<nx; i++)
z[i] = y[i]*pow(10.0,1.0*i/(nx-1)/2.0);
if (r_flag==1)
rotatefunc(z, y, nx, &Mr[nx*nx]);
else
for (i=0; i<nx; i++)
y[i]=z[i];
a = 0.5;
b = 3.0;
k_max = 20;
f[0] = 0.0;
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)*(y[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 r_flag) /* Griewank's */
{
int i;
double s, p;
shiftfunc(x, y, nx, Os);
for (i=0; i<nx; i++)//shrink to the orginal search range
{
y[i]=y[i]*600.0/100.0;
}
if (r_flag==1)
rotatefunc(y, z, nx, Mr);
else
for (i=0; i<nx; i++)
z[i]=y[i];
for (i=0; i<nx; i++)
z[i] = z[i]*pow(100.0,1.0*i/(nx-1)/2.0);
s = 0.0;
p = 1.0;
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 r_flag) /* Rastrigin's */
{
int i;
double alpha=10.0,beta=0.2;
shiftfunc(x, y, nx, Os);
for (i=0; i<nx; i++)//shrink to the orginal search range
{
y[i]=y[i]*5.12/100;
}
if (r_flag==1)
rotatefunc(y, z, nx, Mr);
else
for (i=0; i<nx; i++)
z[i]=y[i];
oszfunc (z, y, nx);
asyfunc (y, z, nx, beta);
if (r_flag==1)
rotatefunc(z, y, nx, &Mr[nx*nx]);
else
for (i=0; i<nx; i++)
y[i]=z[i];
for (i=0; i<nx; i++)
{
y[i]*=pow(alpha,1.0*i/(nx-1)/2);
}
if (r_flag==1)
rotatefunc(y, z, nx, Mr);
else
for (i=0; i<nx; i++)
z[i]=y[i];
f[0] = 0.0;
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 r_flag) /* Noncontinuous Rastrigin's */
{
int i;
double alpha=10.0,beta=0.2;
shiftfunc(x, y, nx, Os);
for (i=0; i<nx; i++)//shrink to the orginal search range
{
y[i]=y[i]*5.12/100;
}
if (r_flag==1)
rotatefunc(y, z, nx, Mr);
else
for (i=0; i<nx; i++)
z[i]=y[i];
for (i=0; i<nx; i++)
{
if (fabs(z[i])>0.5)
z[i]=floor(2*z[i]+0.5)/2;
}
oszfunc (z, y, nx);
asyfunc (y, z, nx, beta);
if (r_flag==1)
rotatefunc(z, y, nx, &Mr[nx*nx]);
else
for (i=0; i<nx; i++)
y[i]=z[i];
for (i=0; i<nx; i++)
{
y[i]*=pow(alpha,1.0*i/(nx-1)/2);
}
if (r_flag==1)
rotatefunc(y, z, nx, Mr);
else
for (i=0; i<nx; i++)
z[i]=y[i];
f[0] = 0.0;
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 r_flag) /* Schwefel's */
{
int i;
double tmp;
shiftfunc(x, y, nx, Os);
for (i=0; i<nx; i++)//shrink to the orginal search range
{
y[i]*=1000/100;
}
if (r_flag==1)
rotatefunc(y, z, nx, Mr);
else
for (i=0; i<nx; i++)
z[i]=y[i];
for (i=0; i<nx; i++)
y[i] = z[i]*pow(10.0,1.0*i/(nx-1)/2.0);
for (i=0; i<nx; i++)
z[i] = y[i]+4.209687462275036e+002;
f[0]=0;
for (i=0; i<nx; i++)
{
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+f[0];
}
void katsuura_func (double *x, double *f, int nx, double *Os,double *Mr,int r_flag) /* Katsuura */
{
int i,j;
double temp,tmp1,tmp2,tmp3;
tmp3=pow(1.0*nx,1.2);
shiftfunc(x, y, nx, Os);
for (i=0; i<nx; i++)//shrink to the orginal search range
{
y[i]*=5.0/100.0;
}
if (r_flag==1)
rotatefunc(y, z, nx, Mr);
else
for (i=0; i<nx; i++)
z[i]=y[i];
for (i=0; i<nx; i++)
z[i] *=pow(100.0,1.0*i/(nx-1)/2.0);
if (r_flag==1)
rotatefunc(z, y, nx, &Mr[nx*nx]);
else
for (i=0; i<nx; i++)
y[i]=z[i];
f[0]=1.0;
for (i=0; i<nx; i++)
{
temp=0.0;
for (j=1; j<=32; j++)
{
tmp1=pow(2.0,j);
tmp2=tmp1*y[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 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);
shiftfunc(x, y, nx, Os);
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.)
tmpx[i] *= -1.;
}
for (i=0; i<nx; i++)
{
z[i]=tmpx[i];
tmpx[i] += mu0;
}
if (r_flag==1)
rotatefunc(z, y, nx, Mr);
else
for (i=0; i<nx; i++)
y[i]=z[i];
for (i=0; i<nx; i++)
y[i] *=pow(100.0,1.0*i/(nx-1)/2.0);
if (r_flag==1)
rotatefunc(y, z, nx, &Mr[nx*nx]);
else
for (i=0; i<nx; i++)
z[i]=y[i];
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;
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 r_flag) /* Griewank-Rosenbrock */
{
int i;
double temp,tmp1,tmp2;
shiftfunc(x, y, nx, Os);
for (i=0; i<nx; i++)//shrink to the orginal search range
{
y[i]=y[i]*5/100;
}
if (r_flag==1)
rotatefunc(y, z, nx, Mr);
else
for (i=0; i<nx; i++)
z[i]=y[i];
for (i=0; i<nx; i++)//shift to orgin
{
z[i]=y[i]+1;
}
f[0]=0.0;
for (i=0; i<nx-1; i++)
{
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 r_flag) /* Expanded Scaffer¡¯s F6 */
{
int i;
double temp1, temp2;
shiftfunc(x, y, nx, Os);
if (r_flag==1)
rotatefunc(y, z, nx, Mr);
else
for (i=0; i<nx; i++)
z[i]=y[i];
asyfunc (z, y, nx, 0.5);
if (r_flag==1)
rotatefunc(y, z, nx, &Mr[nx*nx]);
else
for (i=0; i<nx; i++)
z[i]=y[i];
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 cf01 (double *x, double *f, int nx, double *Os,double *Mr,int r_flag) /* Composition Function 1 */
{
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;
rosenbrock_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=10000*fit[i]/1e+4;
i=1;
dif_powers_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=10000*fit[i]/1e+10;
i=2;
bent_cigar_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=10000*fit[i]/1e+30;
i=3;
discus_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=10000*fit[i]/1e+10;
i=4;
sphere_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],0);
fit[i]=10000*fit[i]/1e+5;
cf_cal(x, f, nx, Os, delta,bias,fit,cf_num);
}
void 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] = {20,20,20};
double bias[3] = {0, 100, 200};
for(i=0;i<cf_num;i++)
{
schwefel_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
}
cf_cal(x, f, nx, Os, delta,bias,fit,cf_num);
}
void cf03 (double *x, double *f, int nx, double *Os,double *Mr,int r_flag) /* Composition Function 3 */
{
int i,cf_num=3;
double fit[3];
double delta[3] = {20,20,20};
double bias[3] = {0, 100, 200};
for(i=0;i<cf_num;i++)
{
schwefel_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
}
cf_cal(x, f, nx, Os, delta,bias,fit,cf_num);
}
void cf04 (double *x, double *f, int nx, double *Os,double *Mr,int r_flag) /* Composition Function 4 */
{
int i,cf_num=3;
double fit[3];
double delta[3] = {20,20,20};
double bias[3] = {0, 100, 200};
i=0;
schwefel_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=1000*fit[i]/4e+3;
i=1;
rastrigin_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=1000*fit[i]/1e+3;
i=2;
weierstrass_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=1000*fit[i]/400;
cf_cal(x, f, nx, Os, delta,bias,fit,cf_num);
}
void cf05 (double *x, double *f, int nx, double *Os,double *Mr,int r_flag) /* Composition Function 4 */
{
int i,cf_num=3;
double fit[3];
double delta[3] = {10,30,50};
double bias[3] = {0, 100, 200};
i=0;
schwefel_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=1000*fit[i]/4e+3;
i=1;
rastrigin_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=1000*fit[i]/1e+3;
i=2;
weierstrass_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=1000*fit[i]/400;
cf_cal(x, f, nx, Os, delta,bias,fit,cf_num);
}
void cf06 (double *x, double *f, int nx, double *Os,double *Mr,int r_flag) /* Composition Function 6 */
{
int i,cf_num=5;
double fit[5];
double delta[5] = {10,10,10,10,10};
double bias[5] = {0, 100, 200, 300, 400};
i=0;
schwefel_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=1000*fit[i]/4e+3;
i=1;
rastrigin_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=1000*fit[i]/1e+3;
i=2;
ellips_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=1000*fit[i]/1e+10;
i=3;
weierstrass_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=1000*fit[i]/400;
i=4;
griewank_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=1000*fit[i]/100;
cf_cal(x, f, nx, Os, delta,bias,fit,cf_num);
}
void cf07 (double *x, double *f, int nx, double *Os,double *Mr,int r_flag) /* Composition Function 7 */
{
int i,cf_num=5;
double fit[5];
double delta[5] = {10,10,10,20,20};
double bias[5] = {0, 100, 200, 300, 400};
i=0;
griewank_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=10000*fit[i]/100;
i=1;
rastrigin_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=10000*fit[i]/1e+3;
i=2;
schwefel_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=10000*fit[i]/4e+3;
i=3;
weierstrass_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=10000*fit[i]/400;
i=4;
sphere_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],0);
fit[i]=10000*fit[i]/1e+5;
cf_cal(x, f, nx, Os, delta,bias,fit,cf_num);
}
void cf08 (double *x, double *f, int nx, double *Os,double *Mr,int r_flag) /* Composition Function 8 */
{
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;
grie_rosen_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=10000*fit[i]/4e+3;
i=1;
schaffer_F7_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=10000*fit[i]/4e+6;
i=2;
schwefel_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=10000*fit[i]/4e+3;
i=3;
escaffer6_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],r_flag);
fit[i]=10000*fit[i]/2e+7;
i=4;
sphere_func(x,&fit[i],nx,&Os[i*nx],&Mr[i*nx*nx],0);
fit[i]=10000*fit[i]/1e+5;
cf_cal(x, f, 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 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 cf_cal(double *x, double *f, int nx, double *Os,double * delta,double * bias,double * fit, int cf_num)
{
int i,j;
double *w;
double w_max=0,w_sum=0;
w=(double *)malloc(cf_num * sizeof(double));
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];
}
free(w);
}
The Working Class Must Lead！
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