problemdef.c

nsga2具体算法代码,用来多目标遗传算法的学习和研究

    g = 0.0;
    for (i=1; i<10; i++)
    {
        g += xreal[i];
    }
    g = g/9.0;
    g = pow(g,0.25);
    g = 1.0 + 9.0*g;
    h = 1.0 - pow((f1/g),2.0);
    f2 = g*h;
    obj[0] = f1;
    obj[1] = f2;
    return;
}
#endif

/*  Test problem BNH
    # of real variables = 2
    # of bin variables = 0
    # of objectives = 2
    # of constraints = 2
    */

#ifdef bnh
void test_problem (double *xreal, double *xbin, int **gene, double *obj, double *constr)
{
    obj[0] = 4.0*(xreal[0]*xreal[0] + xreal[1]*xreal[1]);
    obj[1] = pow((xreal[0]-5.0),2.0) + pow((xreal[1]-5.0),2.0);
    constr[0] = 1.0 - (pow((xreal[0]-5.0),2.0) + xreal[1]*xreal[1])/25.0;
    constr[1] = (pow((xreal[0]-8.0),2.0) + pow((xreal[1]+3.0),2.0))/7.7 - 1.0;
    return;
}
#endif

/*  Test problem OSY
    # of real variables = 6
    # of bin variables = 0
    # of objectives = 2
    # of constraints = 6
    */

#ifdef osy
void test_problem (double *xreal, double *xbin, int **gene, double *obj, double *constr)
{
    obj[0] = -(25.0*pow((xreal[0]-2.0),2.0) + pow((xreal[1]-2.0),2.0) + pow((xreal[2]-1.0),2.0) + pow((xreal[3]-4.0),2.0) + pow((xreal[4]-1.0),2.0));
    obj[1] = xreal[0]*xreal[0] +  xreal[1]*xreal[1] + xreal[2]*xreal[2] + xreal[3]*xreal[3] + xreal[4]*xreal[4] + xreal[5]*xreal[5];
    constr[0] = (xreal[0]+xreal[1])/2.0 - 1.0;
    constr[1] = 1.0 - (xreal[0]+xreal[1])/6.0;
    constr[2] = 1.0 - xreal[1]/2.0 + xreal[0]/2.0;
    constr[3] = 1.0 - xreal[0]/2.0 + 3.0*xreal[1]/2.0;
    constr[4] = 1.0 - (pow((xreal[2]-3.0),2.0))/4.0 - xreal[3]/4.0;
    constr[5] = (pow((xreal[4]-3.0),2.0))/4.0 + xreal[5]/4.0 - 1.0;
    return;
}
#endif

/*  Test problem SRN
    # of real variables = 2
    # of bin variables = 0
    # of objectives = 2
    # of constraints = 2
    */

#ifdef srn
void test_problem (double *xreal, double *xbin, int **gene, double *obj, double *constr)
{
    obj[0] = 2.0 + pow((xreal[0]-2.0),2.0) + pow((xreal[1]-1.0),2.0);
    obj[1] = 9.0*xreal[0] - pow((xreal[1]-1.0),2.0);
    constr[0] = 1.0 - (pow(xreal[0],2.0) + pow(xreal[1],2.0))/225.0;
    constr[1] = 3.0*xreal[1]/10.0 - xreal[0]/10.0 - 1.0;
    return;
}
#endif

/*  Test problem TNK
    # of real variables = 2
    # of bin variables = 0
    # of objectives = 2
    # of constraints = 2
    */

#ifdef tnk
void test_problem (double *xreal, double *xbin, int **gene, double *obj, double *constr)
{
    obj[0] = xreal[0];
    obj[1] = xreal[1];
    if (xreal[1] == 0.0)
    {
        constr[0] = -1.0;
    }
    else
    {
        constr[0] = xreal[0]*xreal[0] + xreal[1]*xreal[1] - 0.1*cos(16.0*atan(xreal[0]/xreal[1])) - 1.0;
    }
    constr[1] = 1.0 - 2.0*pow((xreal[0]-0.5),2.0) + 2.0*pow((xreal[1]-0.5),2.0);
    return;
}
#endif

/*  Test problem CTP1
    # of real variables = 2
    # of bin variables = 0
    # of objectives = 2
    # of constraints = 2
    */

#ifdef ctp1
void test_problem (double *xreal, double *xbin, int **gene, double *obj, double *constr)
{
    double g;
    g = 1.0 + xreal[1];
    obj[0] = xreal[0];
    obj[1] = g*exp(-obj[0]/g);
    constr[0] = obj[1]/(0.858*exp(-0.541*obj[0]))-1.0;
    constr[1] = obj[1]/(0.728*exp(-0.295*obj[0]))-1.0;
    return;
}
#endif

/*  Test problem CTP2
    # of real variables = 2
    # of bin variables = 0
    # of objectives = 2
    # of constraints = 1
    */

#ifdef ctp2
void test_problem (double *xreal, double *xbin, int **gene, double *obj, double *constr)
{
    double g;
    double theta, a, b, c, d, e;
    double exp1, exp2;
    theta = -0.2*PI;
    a = 0.2;
    b = 10.0;
    c = 1.0;
    d = 6.0;
    e = 1.0;
    g = 1.0 + xreal[1];
    obj[0] = xreal[0];
    obj[1] = g*(1.0  - sqrt(obj[0]/g));
    exp1 = (obj[1]-e)*cos(theta) - obj[0]*sin(theta);
    exp2 = (obj[1]-e)*sin(theta) + obj[0]*cos(theta);
    exp2 = b*PI*pow(exp2,c);
    exp2 = fabs(sin(exp2));
    exp2 = a*pow(exp2,d);
    constr[0] = exp1/exp2 - 1.0;
    return;
}
#endif

/*  Test problem CTP3
    # of real variables = 2
    # of bin variables = 0
    # of objectives = 2
    # of constraints = 1
    */

#ifdef ctp3
void test_problem (double *xreal, double *xbin, int **gene, double *obj, double *constr)
{
    double g;
    double theta, a, b, c, d, e;
    double exp1, exp2;
    theta = -0.2*PI;
    a = 0.1;
    b = 10.0;
    c = 1.0;
    d = 0.5;
    e = 1.0;
    g = 1.0 + xreal[1];
    obj[0] = xreal[0];
    obj[1] = g*(1.0  - sqrt(obj[0]/g));
    exp1 = (obj[1]-e)*cos(theta) - obj[0]*sin(theta);
    exp2 = (obj[1]-e)*sin(theta) + obj[0]*cos(theta);
    exp2 = b*PI*pow(exp2,c);
    exp2 = fabs(sin(exp2));
    exp2 = a*pow(exp2,d);
    constr[0] = exp1/exp2 - 1.0;
    return;
}
#endif

/*  Test problem CTP4
    # of real variables = 2
    # of bin variables = 0
    # of objectives = 2
    # of constraints = 1
    */

#ifdef ctp4
void test_problem (double *xreal, double *xbin, int **gene, double *obj, double *constr)
{
    double g;
    double theta, a, b, c, d, e;
    double exp1, exp2;
    theta = -0.2*PI;
    a = 0.75;
    b = 10.0;
    c = 1.0;
    d = 0.5;
    e = 1.0;
    g = 1.0 + xreal[1];
    obj[0] = xreal[0];
    obj[1] = g*(1.0  - sqrt(obj[0]/g));
    exp1 = (obj[1]-e)*cos(theta) - obj[0]*sin(theta);
    exp2 = (obj[1]-e)*sin(theta) + obj[0]*cos(theta);
    exp2 = b*PI*pow(exp2,c);
    exp2 = fabs(sin(exp2));
    exp2 = a*pow(exp2,d);
    constr[0] = exp1/exp2 - 1.0;
    return;
}
#endif

/*  Test problem CTP5
    # of real variables = 2
    # of bin variables = 0
    # of objectives = 2
    # of constraints = 1
    */

#ifdef ctp5
void test_problem (double *xreal, double *xbin, int **gene, double *obj, double *constr)
{
    double g;
    double theta, a, b, c, d, e;
    double exp1, exp2;
    theta = -0.2*PI;
    a = 0.1;
    b = 10.0;
    c = 2.0;
    d = 0.5;
    e = 1.0;
    g = 1.0 + xreal[1];
    obj[0] = xreal[0];
    obj[1] = g*(1.0  - sqrt(obj[0]/g));
    exp1 = (obj[1]-e)*cos(theta) - obj[0]*sin(theta);
    exp2 = (obj[1]-e)*sin(theta) + obj[0]*cos(theta);
    exp2 = b*PI*pow(exp2,c);
    exp2 = fabs(sin(exp2));
    exp2 = a*pow(exp2,d);
    constr[0] = exp1/exp2 - 1.0;
    return;
}
#endif

/*  Test problem CTP6
    # of real variables = 2
    # of bin variables = 0
    # of objectives = 2
    # of constraints = 1
    */

#ifdef ctp6
void test_problem (double *xreal, double *xbin, int **gene, double *obj, double *constr)
{
    double g;
    double theta, a, b, c, d, e;
    double exp1, exp2;
    theta = 0.1*PI;
    a = 40.0;
    b = 0.5;
    c = 1.0;
    d = 2.0;
    e = -2.0;
    g = 1.0 + xreal[1];
    obj[0] = xreal[0];
    obj[1] = g*(1.0  - sqrt(obj[0]/g));
    exp1 = (obj[1]-e)*cos(theta) - obj[0]*sin(theta);
    exp2 = (obj[1]-e)*sin(theta) + obj[0]*cos(theta);
    exp2 = b*PI*pow(exp2,c);
    exp2 = fabs(sin(exp2));
    exp2 = a*pow(exp2,d);
    constr[0] = exp1/exp2 - 1.0;
    return;
}
#endif

/*  Test problem CTP7
    # of real variables = 2
    # of bin variables = 0
    # of objectives = 2
    # of constraints = 1
    */

#ifdef ctp7
void test_problem (double *xreal, double *xbin, int **gene, double *obj, double *constr)
{
    double g;
    double theta, a, b, c, d, e;
    double exp1, exp2;
    theta = -0.05*PI;
    a = 40.0;
    b = 5.0;
    c = 1.0;
    d = 6.0;
    e = 0.0;
    g = 1.0 + xreal[1];
    obj[0] = xreal[0];
    obj[1] = g*(1.0  - sqrt(obj[0]/g));
    exp1 = (obj[1]-e)*cos(theta) - obj[0]*sin(theta);
    exp2 = (obj[1]-e)*sin(theta) + obj[0]*cos(theta);
    exp2 = b*PI*pow(exp2,c);
    exp2 = fabs(sin(exp2));
    exp2 = a*pow(exp2,d);
    constr[0] = exp1/exp2 - 1.0;
    return;
}
#endif

/*  Test problem CTP8
    # of real variables = 2
    # of bin variables = 0
    # of objectives = 2
    # of constraints = 2
    */

#ifdef ctp8
void test_problem (double *xreal, double *xbin, int **gene, double *obj, double *constr)
{
    double g;
    double theta, a, b, c, d, e;
    double exp1, exp2;
    g = 1.0 + xreal[1];
    obj[0] = xreal[0];
    obj[1] = g*(1.0  - sqrt(obj[0]/g));
    theta = 0.1*PI;
    a = 40.0;
    b = 0.5;
    c = 1.0;
    d = 2.0;
    e = -2.0;
    exp1 = (obj[1]-e)*cos(theta) - obj[0]*sin(theta);
    exp2 = (obj[1]-e)*sin(theta) + obj[0]*cos(theta);
    exp2 = b*PI*pow(exp2,c);
    exp2 = fabs(sin(exp2));
    exp2 = a*pow(exp2,d);
    constr[0] = exp1/exp2 - 1.0;
    theta = -0.05*PI;
    a = 40.0;
    b = 2.0;
    c = 1.0;
    d = 6.0;
    e = 0.0;
    exp1 = (obj[1]-e)*cos(theta) - obj[0]*sin(theta);
    exp2 = (obj[1]-e)*sin(theta) + obj[0]*cos(theta);
    exp2 = b*PI*pow(exp2,c);
    exp2 = fabs(sin(exp2));
    exp2 = a*pow(exp2,d);
    constr[1] = exp1/exp2 - 1.0;
    return;
}
#endif