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is a function of
N
arguments, the actions of local cells with limited information
and communication must be coordinated with one another in order to classify
correctly the ICs. Indeed, to find, by hand, in a search space of 2
128
transition
states, rules that perform well, is an almost impossible task and, therefore,
several algorithms were used to evolve better than human-written rules (Das
et al. 1994; Juillé and Pollack 1998; Koza et al. 1999; Ferreira 2001). The
best rules with performances of 86.0% (Coevolution
2
) and 85.1%
(Coevolution
1
) were discovered using a coevolutionary approach between
ICs and rules evolved by a GA (Juillé and Pollack 1998). The rules discov-
ered by gene expression programming are better than all the human-written
rules and better than the GP rule or the rules evolved by the GA (Mitchell et
al. 1993 and Mitchell et al. 1994), and were discovered using computational
resources that are more than 60,000 times smaller than those used by the GP
technique.
4.4.2 Two Rules Discovered by GEP
In one experiment, F = {A, O, N, I} (“I” represents the already familiar IF
function of three arguments) and T = {c, b, a, u, 1, 2, 3}. The parameters used
per run are shown in the first column of Table 4.19.
Table 4.19
Parameters for the density-classification task.
GEP1
GEP2
Number of generations
50
50
Population size
30
50
Number of ICs
25
100
Function set
A O N I
I M
Terminal set
c b a u 1 2 3
c b a u 1 2 3
Head length
17
4
Gene length
52
13
Number of genes
1
3
Linking function
--
I
Chromosome length
52
39
Mutation rate
0.038
0.051
One-point recombination rate
0.5
0.7
IS transposition rate
0.2
--
RIS transposition rate
0.1
--
