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sqrt
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Figure 1.12.
Illustration of a hypothetical event of point mutation in genetic
programming. Note that the daughter tree is an invalid structure.
operators such as transposition or inversion raises similar difficulties and the
search space in GP remains vastly unexplored.
Although Koza described these three operators as the basic GP operators,
tree crossover is practically the only genetic operator used in most GP appli-
cations (Koza 1992, 1994; Koza et al. 1999). Consequently, no new genetic
material is introduced in the genetic pool of GP populations. Not surpris-
ingly, huge populations of parse trees must be used in order to prime the
initial population with all the necessary building blocks so that good solu-
tions could be discovered by just moving these initial building blocks around.
Finally, due to the dual role of the parse trees (genotype and phenotype),
genetic programming is also incapable of a simple, rudimentary expression;
in all cases, the entire parse tree is the solution: nothing more, nothing less.
1.6 Gene Expression Programming
Gene expression programming was invented by myself in 1999 (Ferreira
2001), and incorporates both the simple, linear chromosomes of fixed length
similar to the ones used in GAs and the ramified structures of different sizes
and shapes similar to the parse trees of GP. And since the ramified structures
of different sizes and shapes are totally encoded in the linear chromosomes
of fixed length, this is equivalent to say that, in GEP, the genotype and phe-
notype are finally separated from one another and the system can now ben-
efit from all the evolutionary advantages this brings about.
Thus, the phenotype of gene expression programming consists of the same
kind of ramified structure used in GP. But the ramified structures evolved by
GEP (called expression trees) are the expression of a totally autonomous
