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selection operating, is shown in Figure 3.11, where we can see that by gen-
eration 13 all the individuals are descendants of only one individual: in this
case, chromosome 0 of generation 0. Indeed, replication, together with just
selection, is only capable of causing genetic drift. And, although useful for
searching the fitness landscape, genetic drift by itself cannot create genetic
diversity. Only the modification operators have that power.
Generation N: 13
01234560123456
OOOaaabAAAcabb-[0] = 6
OOOaaabAAAcabb-[1] = 6
OOOaaabAAAcabb-[2] = 6
OOOaaabAAAcabb-[3] = 6
OOOaaabAAAcabb-[4] = 6
OOOaaabAAAcabb-[5] = 6
OOOaaabAAAcabb-[6] = 6
OOOaaabAAAcabb-[7] = 6
OOOaaabAAAcabb-[8] = 6
OOOaaabAAAcabb-[9] = 6
Figure 3.11.
Illustration of genetic drift. In this extreme case, after 13 generations
the population lost all genetic diversity, and all its members are descendants of one
chromosome, in this case, chromosome 0 of generation 0 (see Figure 3.10).
3.3.2 Mutation
Of the operators with intrinsic modification power, mutation is the most effi-
cient (see a discussion of the Genetic Operators and Their Power in chapter
12). With mutation, populations of individuals adapt very efficiently, allow-
ing the evolution of good solutions to virtually all problems. Typically, I use
a mutation rate
p
m
equivalent to two one-point mutations per chromosome.
Considering the relatively small length of GEP genomes, this mutation rate
is much higher than the mutation rates found in nature (see, e.g., Futuyma
1998). Indeed, thanks to elitism, we can have GEP populations subjected to
very high mutation rates and, nevertheless, evolving very efficiently. As a
comparison, the human genome is about 6
X
10
9
base pairs long and only
about 120 new mutations are introduced per genome per generation.
In gene expression programming, mutations are allowed to occur any-
where in the chromosome. However, the structural organization of chromo-
somes must be obviously preserved. Thus, in the heads of genes, any symbol
