Automatically Defined Functions in Problem Solving - Gene Expression Programming - page 261

double ADF2(double d[])
{
double dblTemp = 0.0;
dblTemp = log((sqrt(sqrt((exp(d[0])-(d[0]-d[1]))))/
sqrt(sqrt(sqrt(exp(d[0]))))));
return dblTemp;
}

double ADF3(double d[])
{
double dblTemp = 0.0;
dblTemp = sqrt(sqrt((d[1]+((log(pow(d[1],d[1]))+
(d[2]*d[0]))-d[0]))));
return dblTemp;
}

double ADF5(double d[])
{
double dblTemp = 0.0;
dblTemp = sqrt(sqrt(exp(d[2])));
return dblTemp;
}

double apsModel(double d[])
{
double dblTemp = 0.0;
dblTemp = ((((ADF1(d)+ADF1(d))/(ADF5(d)+ADF0(d)))+
((ADF5(d)+ADF5(d))/ADF5(d)))+
(ADF1(d)-(ADF3(d)*ADF2(d))));
return dblTemp;
}

(6.6b)

where d 0 - d 2 correspond, respectively, to a - c . It is worth pointing out how
different this solution is from the ones created with numerical constants (see
model (6.7) below), as the algorithm had to find some creative ways of
modeling this function without numerical constants at its disposal.
The best solution created by the cellular system with RNCs was found in
generation 4799 of run 46. Its genes and corresponding arrays of random
numerical constants are shown below:

Gene 0: P?c?*E?/-+**abbbbccac?cba7381293446232
C 0 : {76, 4, 59, 83, 37, 52, 1, 45, 66, 42}

Gene 1: a/?/?c-+Lba/cc?cabaabcaa?9486967847808
C 1 : {88, 4, 59, 48, 2, 66, 83, 79, 66, 42}