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Thus, with the symbols drawn from the function and terminal sets, the
chromosomes of the initial population are randomly generated. Obviously,
the heads of the genes are created using elements from both
F
and
T
, whereas
the tails of the genes are created using only elements drawn from
T
. Figure
3.2 shows a small initial population (also called generation 0) of 10 individu-
als randomly created to solve the majority function problem. The chromo-
somes are composed of two genes, each with a length of 7 (
h
= 3 and
t
= 4),
and they encode sub-ETs which are posttranslationally linked by the Boolean
function OR.
Generation N: 0
01234560123456
NaObaacOAbbcca-[0]
AaNcbbaNcOaacc-[1]
OONcbbbNcbcbca-[2]
ANNcaacNcObaab-[3]
AbObcbcOAacaac-[4]
AcNbcbbAONbbcc-[5]
NAcbcacNbOaaba-[6]
NbNbbaaAacbacb-[7]
NAAaccaONacbbb-[8]
AAaccacNcaabab-[9]
Figure 3.2.
The chromosomes of a small initial population created to solve the
Majority(
a
,
b
,
c
) function problem. The randomly generated chromosomes are
composed of two genes, encoding sub-ETs linked by OR.
It is worth emphasizing how easily the initial populations of gene expres-
sion programming are created. The simple structures of the chromosomes
are randomly created using the symbols of the function and terminal sets and
nothing whatsoever needs to be done to monitor their structural soundness:
we know for sure that, without exception, all of them encode valid programs.
As a comparison, the random generation of parse trees in genetic program-
ming must be done with extreme care in order to guarantee the formation of
syntactically correct programs. Not surprisingly, the generation of initial
populations in GP is a complicated, time consuming process.
After the random generation of the chromosomes of the individuals of the
initial population, the chromosomes are expressed, and the fitness of each
individual is evaluated. Figure 3.3 shows the fitness of each individual at the
majority task (for simplicity, only the chromosomes of the individuals are
