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same simple problem so that entire populations could be fully analyzed and
the power of each genetic operator could be completely understood. The
problem used throughout this chapter to illustrate the internal workings of
all the genetic operators is very simple and easy to understand and consists
of the Boolean majority function of three arguments, which will be fully
explained below.
Furthermore, the chapter closes with the exhaustive analysis of a simple
symbolic regression problem, taking us through all the phases in the design
of good models with gene expression programming.
3.1 Populations of Individuals
Like all genetic algorithms, gene expression programming works with
populations of individuals and, therefore, some kind of initial population
must be created in order to get things started. Subsequent populations are
descendants, via genetic modification, of this initial or founder population.
We have already seen that, in the genotype/phenotype system of gene ex-
pression programming, we only need to create the simple, linear chromo-
somes of the individuals without having to bother about the structural sound-
ness of the programs they code for, as we know for sure that their complete
development will always result in syntactically correct programs. Thus, in
GEP, it is only necessary to generate randomly the simple chromosomal struc-
tures of the individuals of the initial population to get things going. And this
is indeed a trivial task and one of the great advantages of this technique.
Thus, for each problem, we must choose the symbols used to create the
chromosomes, that is, we must choose the set of terminals (the variables and
constants used in a problem) and the set of functions we believe to be appro-
priate to solve the problem at hand. We must also choose the length of each
gene, the number of genes per chromosome and how the products of their
expression interact with one another. And, finally, we must provide for a
selection environment (the set of fitness cases) against which the fitness of
each individual is evaluated. Then, according to fitness in that particular
environment, individuals are selected to reproduce with modification, giv-
ing birth to the new members of the next generation. This new population is
then subjected to the same developmental process, giving rise to yet another
new population. This process is repeated for a certain number of generations
or until a good solution has been found.
