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a.
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AbObcbcOAacaac
0123456
b.
O
A
O
a
b
O
A
c
c
a
b
Figure 3.4.
Expression of the best individual of generation 0 (chromosome 4).
a)
The chromosome composed of two genes.
b)
The program encoded in the
chromosome (the linking function is shown in gray). This Boolean function solves
correctly six out of eight fitness cases (see Table 3.1).
terminals can be inserted at the start position of a gene in future generations
by the genetic operators. And if this happens to be advantageous to solve a
certain task, this kind of gene can and will certainly evolve. We will see later
on in this chapter that point mutation and inversion allow the evolution of
genes with a terminal at the start position or, in other words, allow the evolution
of simple sub-ETs composed of only one node.
The problem with the random generation of initial populations is that,
sometimes, especially if the population size is small or the set of fitness
cases is not broad enough or the fitness function is excessively tight, it just
might happen that none of the initial chromosomes encode viable individu-
als and the run is aborted (this is highly improbable for Boolean problems,
though, unless a very restrictive fitness function is used). A simple form of
circumventing this problem consists of introducing a start up control. In gene
expression programming, this control is by default set to one viable indi-
vidual, and was used in all the problems presented in this topic. We will see
that this does not hinder the evolutionary process, as GEP populations can
efficiently evolve even when all the individuals are descendants of a sole
viable founder (Ferreira 2002d; see also the discussion of The Founder Ef-
fect in section 2 of chapter 12). Thus, this control mechanism, together with
the cloning of the best individual (see section 3.1.2 below), prevents the
existence of failed runs in gene expression programming. So, if all the indi-
viduals of the initial population happened to have zero fitness, another initial
population would have been randomly generated. This process is repeated
until at least one viable individual is created and the evolutionary process
can resume.
