Automatically Defined Functions in Problem Solving - Gene Expression Programming - page 260

systems perform slightly worse than their acellular counterparts (see Table
5.10 for a comparison); these systems obviously require more time or larger
populations to fine-tune their complex structures. Let's now see what kind of
circuits can be designed with these systems.
The best solution designed with the cellular system without RNCs was
found in generation 4571 of run 59:
0123456789012345678901234
QQEa-QLP*+-+cbaacbbbacaab
EQ+QEQEQP+E-aabbbcaccbccc
L/QQQQ-QE-Eaabaacababacbb
QQ+b-+aL*Pcabbacccaacaabb
PPQabcaPb+PEabacbabccabcb
QQEcaab*abaPacbaacbbaacab
++-//1*+++53211505510 (6.6a)
It has a fitness of 46.4137 and an R-square of 0.9358798486 evaluated over
the training set of 40 fitness cases and is therefore a good solution to the
problem at hand. Note that the R-square of this best-of-experiment solution
is much higher than the average best-of-run R-square obtained in this experi-
ment (0.6708783722), showing that, although harder to find, good solutions
can nevertheless be designed with the cellular system without random nu-
merical constants. Note also how flexible the linking is with this system,
with not only addition being used to link the ADFs but also subtraction,
multiplication, and division. And as we know, this kind of dynamic linking
also allows code reuse. For instance, in the program above, ADF 1 is called
from three different places in the main program. More formally, the model
(6.6a) can be expressed by the following C++ program (ADF 4 is not used in
the main program and, therefore, is not listed):
double ADF0(double d[])
{
double dblTemp = 0.0;
dblTemp = sqrt(sqrt(exp(d[0])));
return dblTemp;
}
double ADF1(double d[])
{
double dblTemp = 0.0;
dblTemp = exp(sqrt((sqrt(sqrt(sqrt((d[0]+d[0]))))+
exp(exp(pow(exp(d[1]),(d[1]-d[1])))))));
return dblTemp;
}