?? myfunction.c
字號:
total.f[0]=f1;
total.f[1]=f2;
break;
case 38: // Multiobjective F4
// x1 in (0,1]
// x2 in (0,1]
f1=pos.p.x[ 0];
x2=pos.p.x[ 1];
x=1+9*x2;
x3=f1/x;
f2=x*(1-pow(x3,0.25)-pow(x3,4));
total.f[0]=f1;
total.f[1]=f2;
break;
case 39: // Multiobjective F5
// x1 in (0,1]
// x2 in (0,1]
f1=pos.p.x[ 0];
x2=pos.p.x[ 1];
x=1+9*x2;
x3=f1/x;
f2=x*(1-pow(x3,0.5)-x3*sin(5*two_pi*f1));
total.f[0]=f1;
total.f[1]=f2;
break;
case 40: // Multiobjective F6 (Deb)
// x1 in (0,1]
// x2 in (0,1]
f1=pos.p.x[ 0];
x2=pos.p.x[ 1]; // For 2D
//x2=0; For 1D
x=1+10*x2;
x3=f1/x;
f2=x*(1-x3*x3-x3*sin(4*two_pi*f1));
total.f[0]=f1;
total.f[1]=f2;
break;
case 41:
// Multiobjective Coello F3
f1=pos.p.x[ 0];
x2=pos.p.x[ 1];
x=11+x2*x2-10*cos(two_pi*x2);
if (x>=f1)
{
f2=x*(1-sqrt(f1/x));
}
else
f2=0;
total.f[0]=f1;
total.f[1]=f2;
break;
case 42: // For implicit function
problem[1].target=0;
problem[1].eps=0.1;
problem[1].printlevel=0;
problem[1].funct=42;
problem[1].Max_Eval=problem[0].Max_Eval;
coeff=pos;
post=PSO(1,problem[1].Max_Eval);
total.f[0]=post.f.f[0];
break;
case 43: // Part 2 for implicit function . Here a spherical one
// coeff is a global variable
DD= coeff.p.size;
total.f[0]=0;
for (d=0;d<DD;d++)
{
x=coeff.p.x[d];
total.f[0]=total.f[0]+x*x;
}
total.f[0]=total.f[0]-2+ pos.p.x[ 0];
break;
case 44: // Jeannet_Messine
/*
Ref. ROADEF 2003, p 273
i ={0,1,2,3,4,5} (see static data a1 and a2)
x2 in [-15,25]
x3 in [3,10]
min -112.5 in position (3,-7.5, 10)
The authors define 5 different methods, and
their best result is: 3271 evaluations
TRIBES is _far_ better
*/
i=pos.p.x[ 0];
x2=pos.p.x[ 1];
x3= pos.p.x[ 2];
total.f[0]=20*a1[i]*x2*x2 + 2*a2[i]*x2*x3;
break;
case 45: // MINLP X. Yan
total.f[0]=MINLP(pos,1); // Constraints
total.f[1]=MINLP(pos,0);// Function to minimize
break;
case 46: // Tripod function (Louis Gacogne)
// on [-100, 100], min 0
x1=pos.p.x[0];
x2= pos.p.x[1];
if(x2<0)
{
total.f[0]=fabs(x1)+fabs(x2+50);
}
else
{
if(x1<0)
total.f[0]=1+fabs(x1+50)+fabs(x2-50);
else
total.f[0]=2+fabs(x1-50)+fabs(x2-50);
}
break;
case 47: // Tripod function (Louis Gacogne)
// on [-100, 100], min 0
// using hierarchical multiobjective optimization
// constraint= in circle radius 50, center ( 0,-50)
n1=1;
n2=0;
x1=pos.p.x[0];
x2= pos.p.x[1];
r= x1*x1+(x2+50)*(x2+50);
r=sqrt(r);
total.f[n1]=constrain_positive(50-r);
//printf("\n%f, %f, %f, %f",x1,x2, r,total.f[0]);
if(x2<0)
{
total.f[n2]=fabs(x1)+fabs(x2+50);
}
else
{
if(x1<0)
total.f[n2]=1+fabs(x1+50)+fabs(x2-50);
else
total.f[n2]=2+fabs(x1-50)+fabs(x2-50);
}
break;
case 48: // DeJong f4
// Global min f(x)=0, x(i)=0
total.f[0] = 0;
for( d=0;d<DD;d++)
{
total.f[0] = total.f[0] + pos.p.x[ d]*pos.p.x[ d]*pos.p.x[ d]*pos.p.x[ d];
}
break;
case 49: // Pressure vessel
// Ref New Optim. Tech. in Eng. p 638
/* D=4
1.1 <= x1 <= 12.5 granularity 0.0625
0.6 <= x2 <= 12.5 granularity 0.0625
0 .0 <= x3 <= 240
0.0 <= x4 <= 240
constraints
g1:= 0.0193*x3-x1 <=0
g2 := 0.00954*x3-x2<=0
g3:= 750*1728-pi*x3*x3*(x4-(4/3)*x3) <=0
*/
x1=pos.p.x[0];
x2= pos.p.x[1];
x3=pos.p.x[2];
x4= pos.p.x[3];
f=0.6224*x1*x3*x4 + 1.7781*x2*x3*x3 + 3.1611*x1*x1*x4 + 19.84*x1*x1*x3;
// Constraints
y=0.0193*x3-x1; if ( y>0) {c= 1+pow(10,10)*y; f=f*c*c; }
y= 0.00954*x3-x2; if (y>0) {c=1+y; f=f*c*c; }
y = 750*1728-pi*x3*x3*(x4+(4.0/3)*x3); if (y>0) {c=1+y; f=f*c*c; }
total.f[0]=f;
break;
case 50: // Coil compression spring
// Ref New Optim. Tech. in Eng. p 644
x1=pos.p.x[0];
x2= pos.p.x[1];
x3= pos.p.x[2];
f=pi*pi*x2*x3*x3*(x1+2)*0.25;
// Constraints
Cf=1+0.75*x3/(x2-x3) + 0.615*x3/x2;
K=0.125*G*pow(x3,4)/(x1*x2*x2*x2);
sp=Fp/K;
lf=Fmax/K + 1.05*(x1+2)*x3;
y=8*Cf*Fmax*x2/(pi*x3*x3*x3) -S;
if (y>0) {c=1+y; f=f*c*c*c;}
y=lf-lmax;
if (y>0) {c=1+y; f=f*c*c*c;}
y=sp-spm;
if (y>0) {c=1+y; f=f*c*c*c;}
//y=sp+(Fmax-Fp)/K + 1.05*(x1+2)*x3 - lf;
y=sp-Fp/K;
if (y>0) {c=1+pow(10,10)*y; f=f*c*c*c;}
y=sw- (Fmax-Fp)/K;
if (y>0) {c=1+pow(10,10)*y; f=f*c*c*c;}
total.f[0]=f;
break;
case 51: // Gear train
// Ref New Optim. Tech. in Eng. p 634
x1=pos.p.x[0];
x2= pos.p.x[1];
x3=pos.p.x[2];
x4= pos.p.x[3];
f=1/6.931 - x1*x2/(x3*x4); f=f*f;
total.f[0]=f;
break;
case 52: // Pressure vessel as multiobjective (4 functions)
x1=pos.p.x[0];
x2= pos.p.x[1];
x3=pos.p.x[2];
x4= pos.p.x[3];
total.f[0]=0.6224*x1*x3*x4 + 1.7781*x2*x3*x3 + 3.1611*x1*x1*x4 + 19.84*x1*x1*x3;
// Constraints
y=0.0193*x3-x1;
total.f[1]=y+fabs(y);
y= 0.00954*x3-x2;
total.f[2]=y+fabs(y);
y = 750*1728-pi*x3*x3*(x4+(4.0/3)*x3);
total.f[3]=y+fabs(y);
break;
case 53: // Coil compression spring as multiobjective (6 functions)
x1=pos.p.x[0];
x2= pos.p.x[1];
x3= pos.p.x[2];
total.f[0]=pi*pi*x2*x3*x3*(x1+2)*0.25;
// Constraints
Cf=1+0.75*x3/(x2-x3) + 0.615*x3/x2;
K=0.125*G*pow(x3,4)/(x1*x2*x2*x2);
sp=Fp/K;
lf=Fmax/K + 1.05*(x1+2)*x3;
y=8*Cf*Fmax*x2/(pi*x3*x3*x3) -S;
total.f[1]=y+fabs(y);
y=lf-lmax;
total.f[2]=y+fabs(y);
y=sp-spm;
total.f[3]=y+fabs(y);
y=sp-Fp/K;
total.f[4]=y+fabs(y);
y=sw- (Fmax-Fp)/K;
total.f[5]=y+fabs(y);
break;
case 54: // Pressure vessel by homeomorphism
// WARNING. TO COMPLETE
// May be not possible
alpha=0.0193;
beta=0.00954;
gamma=750*1728;
delta=240;
y1=pos.p.x[0];
y2=pos.p.x[1];
y3=pos.p.x[2];
y4=pos.p.x[3];
x4=y4+delta;
a_1=0.75*x4;
b=0.75*(y3-gamma)/pi;
z=solve_polyn_3(b,0,a_1,1);
y=z.z[0]; choice=1;
root_choice:
x3=y-a_1/3;
x1=alpha*x3-y1;
x2=beta*x3-y2;
printf("\nx1,x2,x3 %f %f %f",x1,x2,x3);
if (x1<0 || x2<0)// || x3<0)
{
if(z.status>1)
{
if (choice==1) {choice=2; y=z.z[1]; goto root_choice;}
if(choice==2) {choice=3;y=z.z[2]; goto root_choice;}
}
printf("\n error my_function case 54. No possible root");
scanf("%i",&d);
}
// x=x3*x3*x3+a_1*x3*x3+b;
// printf("\n x %f =? 0",x); // Should be equal to 0
f=0.6224*x1*x3*x4 + 1.7781*x2*x3*x3 + 3.1611*x1*x1*x4 + 19.84*x1*x1*x3;
// y=gamma-pi*x3*x3*(x4+(4.0/3)*x3); // Should be equal to y3;
// printf("\nx3 %.12f, x4 %f, %f =? %f",x3,x4,y,y3);
printf("\n y %f %f %f %f",y1,y2,y3,y4);
printf("\n x %f %f %f %f",x1,x2,x3,x4);
printf("\n f %f",f);
total.f[0]=f;
break;
case 55: // Neural Network Training. 2 Bit Parity (XOR)
// Dim=9
// min 0.0
total.f[0]= ANNXor(pos.p);
break;
case 56: // Neural Network Training. 4 Bit Parity
// Dim=25
// A good result is 0.11
total.f[0]= ANNParity4(pos.p);
break;
case 57: // Neural Network Training. Three Color Cube
// Dim=46
// A good result is 0.2
total.f[0]=ANNCOLORCUBE(pos.p);
break;
case 58: // Neural Network Training. Diabetes in Pima Indians
// Dim=64
// A good result is 0.16
total.f[0]=ANNPIMA(pos.p);
break;
case 59: // Neural Network Training. Sin Times Sin
// Dim=26
// A good result is 0.23
total.f[0]= ANNSINSIMP(pos.p);
break;
case 60: // Neural Network Training. Rise Time Servomechanism
// Dim=28
// A good result is 0.45
total.f[0]= ANNSERVO(pos.p);
break;
case 61: // Moving Peaks
// Warning. Only for mono-objective non recursive optimization
// (rank 0 in .f and level=0)
for (d=0;d<DD;d++) gen[d]=pos.p.x[d];
total.f[0]=eval_movpeaks (gen);
//printf("\n %f %f",global_max, total.f[0]);
if(recent_change==1 && recurs==0)
{
//printf("\n %f", best_result.f.f[0]);
recurs=1; // myfunction will be called again in reinit_swarm
// so, it is will be then necessary to skip this part
n_change=n_change+1;
// Recompute the memorized f values
reinit_swarm(level,0); // Re-initialise the swarm but keeping the best result
// reinit_swarm(level,1); // Re-initialise the swarm without keeping the best result
offline_error+=total_error(best_result.f);
offline_error_cont+=total_error(best_result.f);
recent_change=0;
recurs=0;
// The current particule has been evaluated twice
eval_f_tot[level]=eval_f_tot[level]-1;
}
break;
case 62: // Goldberg抯 order 3 deceptive problem
// Be sure dimension=3*k
// Interval inside ]-0.5 1.5[
// and granularity=1, so that the only possible x values
// are 0 and 1
// The min value is 0
f=0;
/* // Exact binary form
for (d=0;d<DD-2;d=d+3)
{
bit_sum=0;
for (i=d;i<d+3;i++) bit_sum+=pos.p.x[i];
if (bit_sum==0) {f+=0.9; continue;}
if (bit_sum==1) {f+=0.6; continue;}
if (bit_sum==2) {f+=0.3; continue;}
if (bit_sum==3) {f+=1; continue;}
}
*/
/* // Continuous form
for (d=0;d<DD-2;d=d+3)
{
s=0;
for (i=d;i<d+3;i++) s+=pos.p.x[i];
s=MIN(s,3); s=MAX(s,0);
if(s<=2) f+=0.9-0.3*s;
else f+=0.3+0.7*(s-2);
}
*/
// Continuous integer form
for (d=0;d<DD-2;d=d+3)
{
s=0;
for (i=d;i<d+3;i++) s+=floor(pos.p.x[i]+0.5);
s=MIN(s,3); s=MAX(s,0);
if(s<=2) f+=0.9-0.3*s;
else f+=0.3+0.7*(s-2);
}
total.f[0]=DD/3-f;
break;
case 63: // M黨lenbein's order 5 (MC variant), seen as a 1D function
// Binary optim. Min 0 on 1057 = 100010001000
D=15; // Length of the bit string
f=0;
bit_x=bits(pos.p.x[0],D);
bit.size=5;
for (d=0;d<D-3;d=d+5)
{
for (i=d;i<d+5;i++) bit.x[i-d]=bit_x.x[i];
num=number(0,bit);
if (num==0) {f+=3.0; continue;}
if (num==1) {f+=4.0; continue;}
if (num==3) {f+=2.0; continue;}
if (num==7) {f+=1.0; continue;}
if (num==31) {f+=3.5; continue;}
}
total.f[0]=4*D/5-f;
break;
case 64: // Schaffer'f6 (2D)
x1=pos.p.x[0];
x2= pos.p.x[1];
x1=x1-1; x2=x2-1; // Optional shift
r = x1*x1 + x2*x2;
y= 1 + 0.001*r ;
y1 = y*y;
y=sin(sqrt(r));
y2 = y*y - 0.5;
total.f[0] = 0.5 + y2/y1;
break;
//-----------------------------------------------------------
case 99: // Test functions
// Test
x1=pos.p.x[0];
x2= pos.p.x[1];
f1=2*x1*x2*(1-x2)+ x2*x2;
f2=2*(1-x1)*x2*(1-x2)+(1-x2)*(1-x2);
total.f[0]=1-f1;
break;
// polynomial fitting problem
// Cf. Differential Evolution Homepage, C code
// on [-300 200]^9
f=0; y=-1;
dx = 2/dx;
for (i=0;i<=M;i++)
{
py = pos.p.x[0];
for (j=1;j<DD;j++)
{
py = y*py + pos.p.x[j];
}
if (py<-1 || py>1) f+=(1-py)*(1-py);
y+=dx;
}
py = pos.p.x[0];
for (j=1;j<DD;j++) py=1.2*py+pos.p.x[j];
py = py-72.661;
if (py<0) f+=py*py;
py = pos.p.x[0];
for (j=1;j<DD;j++) py=-1.2*py+pos.p.x[j];
py =py-72.661;
if (py<0) f+=py*py;
total.f[0]=f;
break;
// Stochastic
total.f[0] = 0;
for( d=0;d<DD;d++)
{
xd=pos.p.x[d];
total.f[0]= total.f[0]+(d+1)*pow(xd,4)+alea_normal(0,1);
}
break;
// Step
total.f[0] = 0;
for( d=0;d<DD;d++)
{
total.f[0]= total.f[0]+(int)pos.p.x[d];
}
break;
// Beatle (Luc Heylen)
// Min 0 on (1,1)
// search space [-3 5]^2 => succes rate 76%
x1=pos.p.x[0];
x2= pos.p.x[1];
f = 100*(x2-x1*x1)*(x2-x1*x1)+(1-x1)*(1-x1);
f2=100*(-x2+2-x1*x1)*(-x2+2-x1*x1)+(1-x1)*(1-x1);
//f=log(0.2+f+10*(f*(5.1-mod(sqrt(f+f2),5))))+1.61;
y1=sqrt(f+f2);
y2=y1-5*((int)y1/5);
y3= 0.2+f+10*(f*(5.1-y2));
//f=log(y3)-log(0.2); // Modified function (just one solution)
f=log(y3)+1.61; // Original function
total.f[0]=f;
break;
// Ripple (Luc Heylen)
// Min 0 on (1,1)
// search space [-3 5]^2 => success rate 64%
x1=pos.p.x[0];
x2= pos.p.x[1];
y1=1-exp(-3*(x1-1)*(x1-1)-0.3*(x2-1)*(x2-1));
y2 = 100*(x2-x1*x1)*(x2-x1*x1)+(1-x1)*(1-x1);
f=(12+sqrt(y2)/2-10*cos(20*y1)-abs((cos(3*(x1-1))+cos(10*(x2-1)))))/10;
total.f[0]=f;
break;
// Dynamic Parabola (Sphere)
sigma=0.01;
pr=0.5;
if (alea(0,1)<pr) r=0; else r=1;
total.f[0] = 0;
for( d=0;d<DD;d++)
{
//xd= pos.p.x[ d]*(1+r*alea_normal(0,sigma));
xd= pos.p.x[ d] + r*alea_normal(0,sigma);
total.f[0] = total.f[0] +xd*xd ;
}
DYN=1;
break;
// Leon 2D
// on [-1.2 1.2]^2 min 0 on (1 1)
x1=pos.p.x[0];
x2= pos.p.x[1];
f1=x2-x1*x1*x1;
total.f[0]=100*f1*f1 +(1-x1)*(1-x1);
break;
// Schaffer 2D
// on [-100 100]^2 min 0 on (0 0)
x1=pos.p.x[0];
x2= pos.p.x[1];
f1=1+0.001*(x1*x1+x2*x2);
f1=f1*f1;
total.f[0]=0.5+(sin(sqrt(x1*x1+x2*x2))-0.5)/f1;
break;
// Bukin6 2D
// on [-15 -5]x[-3 3] min 0 on (-10 1)
x1=pos.p.x[0];
x2= pos.p.x[1];
total.f[0]=100*sqrt(abs(x2-0.01*x1*x1)) +0.01*abs(x1+10);
break;
// Schwefel 2D
// on [-500 500]^2, min=-837.9658 on (420.9687, 420.9687)
x1=pos.p.x[0];
x2= pos.p.x[1];
total.f[0]=-x1*sin(sqrt(abs(x1)))-x2*sin(sqrt(abs(x2)));
break;
// somme i*x_i
total.f[0] = 0;
for( d=0;d<DD;d++)
{
total.f[0] = total.f[0] + (d+1)*pos.p.x[ d];
}
break;
// Livre sur l'OEP. Chapitre Contraintes
// hom閛morphisme disque/4=carr?? 快捷鍵說明
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