Information Technology Reference
In-Depth Information
expression of sub-ET
2
, as these constants are not used to build this sub-ET.
This is yet another example of how the GEP system explores the idea of
neutrality not only to build the core structure of the expression trees but also
to fine-tune this same structure and all its elements.
On the other hand, it is also worth pointing out that the direct mutation of
random numerical constants might also have a great impact in the overall
solution. This might occur whenever the mutated constant happens to be
used more than once in a particular sub-ET.
Interestingly, the direct mutation of RNCs seems to have a very limited
impact on the creation of good models and better results are indeed obtained
when this operator is switched off. Therefore, we can conclude that a well-
dimensioned initial diversity of RNCs is more than sufficient to allow their
evolutionary tuning, as they are constantly being moved around by all the
genetic operators. Typically, per gene, I use an array length of 10 RNCs for
Dc lengths equal to or less than 20. For larger Dc domains we could increase
the number of elements but, even for bigger structures, an array of length 10
seems to be more than enough.
5.5 Solving a Simple Problem with GEP-RNC
In this section we are going to analyze a successful run in its entirety in order
to understand how populations of such complex entities adapt, not only by
changing the size and shape of their structures but also by fine-tuning the
numerical constants that integrate them.
The simple problem we are going to solve using the GEP-RNC algorithm
is the same simple problem we solved in section 3.4 with the basic gene
expression algorithm. In this case, however, we are going to use just one
gene per chromosome so that both the chromosomal structure and the corre-
sponding array of random numerical constants could fit side-by-side to al-
low a better visualization of the evolutionary process.
For this relatively simple function requiring integer constants, we are go-
ing to use a set of 10 integer random constants and represent them by the
numerals 0-9, that is, R = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, so that the numeral
corresponds to the position each random constant occupies in the array of
RNCs. And the ephemeral random constants “?” will be drawn from the
integer interval [0, 9]. The fitness will be evaluated by equation (3.3a), using
an absolute error of 100 for the selection range and a precision for the error
