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place. In gene expression programming, though, we know exactly when modi-
fications in the genome occur. On the one hand, all of them occur after the
replication of the genome, which in itself is flawless. On the other, the ge-
netic operators perform in an orderly fashion, starting with replication and
continuing with mutation, inversion, transposition, and recombination. It is
worth pointing out, however, that the order in which the latter modify the
genome is not important to the final outcome.
Except for replication, which copies exactly the genomes of all the se-
lected individuals, all the remaining operators randomly pick up the chromo-
somes to be subjected to a certain modification. And, except for mutation,
each operator is not allowed to modify a chromosome more than once. For
instance, for a population of 10 individuals, a crossover rate of 0.8 means
that eight different chromosomes are randomly chosen to recombine.
Thus, in GEP, a chromosome might be randomly chosen to be modified by
more than one modification operator during its reproduction. Therefore, dur-
ing reproduction, the modifications carried out by the different genetic opera-
tors accumulate in the chromosomes, to the extent that the new population is
usually very different from the old one.
Presented below, in the order in which they are usually applied, are the
most commonly used genetic operators, obviously starting with replication
and selection and finishing with the modification operators of mutation, in-
version, transposition, and recombination.
3.3.1 Replication and Selection
Although vital, replication in artificial evolutionary systems is the most unin-
teresting operator of all: by itself, it contributes nothing to genetic variation.
But together with selection, it can already create genetic drift, changing the
proportions of the particular kinds of individuals with time. And most importantly,
together with selection and genetic modification, it allows adaptation and evo-
lution.
So, the selection operator chooses which individuals are going to be re-
produced according to their fitnesses and the luck of the roulette. And this
means that the fitter the individual the higher the probability of leaving more
offspring. When selection is done by roulette-wheel sampling, the roulette is
spun as many times as there are individuals in the population, thus maintain-
ing the same population size from generation to generation. As for the repli-
cation operator, it copies exactly the chromosomes of the individuals picked
