Information Technology Reference
In-Depth Information
The fitness was evaluated against a set of 25 unbiased ICs (i.e., ICs with
equal probability of having a one or a zero at each cell). For this task, the
fitness
f
i
of an individual program
i
was a function of the number of ICs
n
for
which the system stabilized correctly to a configuration of all 0's or 1's after
2
X
N
time steps, and it was designed in order to privilege individuals capable
of correctly classifying ICs both with a majority of 1's and 0's. Thus, if the
system converged, in all cases, indiscriminately to a configuration of 1's or
0's, only one fitness point was attributed; if, in some cases, the system cor-
rectly converged either to a configuration of 0's or 1's,
f
i
= 2
; in addition,
rules converging to an alternated pattern of all 1's and all 0's were elimi-
nated, as they are easily discovered and disseminate very quickly through
the populations halting the discovery of good rules; and finally, when an
individual program could correctly classify ICs both with majorities of 1's
and 0's, a bonus equal to the number of ICs
C
was added to the number of
correctly classified ICs, being in this case
f
i
= n + C
. For instance, if a pro-
gram correctly classified two ICs, one with a majority of 1's and another
with a majority of 0's, it received 2 + 25 = 27 fitness points.
In this experiment a total of seven runs were made. In generation 27 of run
5, the following rule was discovered (only the K-expression is shown):
01234567890123456789012345678
OAIIAucONObAbIANIb1u23u3a12aa
(4.27)
This program (GEP
1
rule) has an accuracy of 0.82513 tested over 100,000
unbiased ICs in a 149
X
298 lattice, thus better than the 0.824 of the GP rule
tested in a 149
X
320 lattice (Juillé and Pollack 1998, Koza et al. 1999). Its
rule table is shown in Table 4.20. Figure 4.12 shows two space-time dia-
grams obtained with this new rule.
As a comparison, genetic programming used populations of 51,200 indi-
viduals and 1,000 ICs for 51 generations (Koza et al. 1999), thus a total of
51,200
X
1,000
X
51 = 2,611,200,000 fitness evaluations were made, whereas
gene expression programming only made 30
X
25
X
50 = 37,500 fitness evalu-
ations. Thus, at this task, gene expression programming not only discovered
more and better rules than the GP technique, but also managed to do so using
resources that surpassed the GP technique by a factor of 69,632.
In another experiment a rule with an accuracy of 0.8255, thus slightly
better than the GEP
1
rule, was discovered. Again, its performance was evalu-
ated over 100,000 unbiased ICs in a 149
X
298 lattice. In this case F = {I, M}
(“I” represents again the familiar IF function with three arguments and “M”
