Information Technology Reference
In-Depth Information
Let's first study the architectures of both these algorithms and how they
learn and then proceed with the analysis of their performance by optimizing
two different functions: a well-studied two-parameter function and a more
complex five-parameter function.
8.1 The HZero Algorithm
The HZero algorithm is an implementation of the GEP-RNC algorithm at its
utmost simplicity, that is, when the head size
h
is equal to zero (see chapter 5
for a description of the GEP-RNC algorithm). Indeed, when
h
= 0, the length
of the tail evaluated by equation (2.4) gives
t
= 1. And since the Dc length is
equal to the tail length, this means that the Dc's in the HZero algorithm have
just one element. As we will see next, this algorithm is even easier to imple-
ment than the simple GA, and has also the additional advantage of being
more flexible than the GA in evolutionary terms.
8.1.1 The Architecture
Thus, when the head is equal to zero, a normal gene with a Dc domain has the
following structure (the Dc is shown in bold):
01
?
3
(8.1)
where “?” represents the ephemeral random constants and “3” is a numeral
representing a specific random numerical constant, which, for convenience,
also indicates the order that the corresponding numerical constant occupies
in the array of constants. For instance, for the five-element array of random
numerical constants presented below:
C = {-1.144714, -1.80484, 0.936646, 1.509033, -1.157348}
the chromosome (8.1) above encodes the parameter value
p
= 1.509033.
It is worth pointing out that the number of RNCs associated with each
gene is arbitrary and the HZero algorithm is in fact very flexible regarding
the amount of constants it can handle. From configurations with just one
constant per gene to configurations with a few hundreds, the algorithm han-
dles them very fluidly. However, better and faster results are obtained using
simpler configurations of just 1-10 constants per gene.
