Polynomial Induction and Time Series Prediction - Gene Expression Programming - page 276

7.2 Simulating STROGANOFF in GEP
So, by choosing a function set consisting exclusively of function F 9 of Table
7.1, we are exactly simulating the original STROGANOFF system in gene
expression programming. And by choosing a function set containing func-
tions F 1 - F 16 of Table 7.1, we are exactly simulating the enhanced STROGA-
NOFF system in GEP. The performance of both these systems, the GEP-OS
and the GEP-ES, will be analyzed in the next section by comparing them
with other conventional GEP systems.
As stated previously, the implementation of both STROGANOFF sys-
tems (the original and the enhanced) in gene expression programming re-
quires a Dc six times larger than the head, thus, much larger than the Dc
domain of the GEP-RNC algorithm, which, as you recall, equals the tail
length. So, given the much larger number of random numerical constants
required for polynomial induction, it is convenient to use a slightly different
notation to represent in the genome the RNCs that correspond to the polyno-
mial coefficients. For instance, for the gene below with an h = 3:
F9.d6.F7.d8.d2.d0.d5 (7.5)
a Dc with length 18 is already necessary in order to express correctly this
gene. If we choose a set of random numerical constants with 20 members
and represent them by R = {r 0 , ..., r 19 }, then the following structure will be a
valid Dc domain for chromosome (7.5) above:
r19.r12.r15.r9.r2.r19. r13.r6.r5.r19.r12.r7. r17.r10.r7.r15.r7.r11
As before, the values of all the random numerical constants are kept in an
array and are retrieved as needed. For each function node evaluated in the
expression tree, a block of six elements in Dc is processed, independently of
the number of coefficients required for that particular function. So, in the
example above, function F 7 will use the first block of six random constants:
r19.r12.r15.r9.r2.r19
even though it requires just the first four coefficients (see its definition in
Table 7.1), and function F 9 will use the next block of six coefficients:
r13.r6.r5.r19.r12.r7
As you can see, the remaining constants are simply not needed to express
that particular gene and are, therefore, part of a neutral region in the gene.