For the sake of simplicity, we are going to illustrate the mechanisms of one-point recombination using the compact, linear representation of chromosomes used to describe the
structural organization of
chromosomes in the previous chapter. In this representation, each element (function or terminal) is represented by a single character so that each element can be easily identified by its position in the chromosome.
In one-point recombination the parent chromosomes are paired and split up at exactly the same point. The material downstream of the recombination point is afterwards exchanged between the two chromosomes.
The default value for the one-point recombination rate in APS 3.0 is 0.3, as this operator is usually used together with other, more powerful operators such as
mutation. But if you want to introduce genetic modification by using this operator alone, the better results are obtained with one-point recombination rates of 1.0.
Consider the following parent chromosomes, each composed of three genes:
012345678901234012345678901234012345678901234
+++*-QQbbdddbbb*-d*cbbbcdaddbd+-baaaaacdccbba
Q+-Q///bbaacccb-cda+-dbcacadad+d/c**abdbcabdb
Suppose bond 4 in gene 2 (between positions 3 and 4) was randomly chosen as the crossover point. Then, the paired chromosomes are both cut at this bond, and exchange between them the material downstream of the crossover point, forming the offspring below:
012345678901234012345678901234012345678901234
+++*-QQbbdddbbb*-d*+-dbcacadad+d/c**abdbcabdb
Q+-Q///bbaacccb-cdacbbbcdaddbd+-baaaaacdccbba
It is worth emphasizing that the chromosomes of gene
expression programming (GEP) can cross over any point in the genome, continually disrupting old building blocks and continually forming new ones. Furthermore, due to both the
multigenic nature of GEP chromosomes and the existence of
noncoding regions in most genes, entire genes and intact
K-expressions can be swapped between parent chromosomes. Thus, the disruptive tendencies of one-point recombination (splitting of building blocks) coexist side by side with its more conservative tendencies (swapping of genes and K-expressions), making one-point recombination (and of course
two-point recombination too) a very well balanced genetic operator. Furthermore, like all the other
recombinational operators, when one-point recombination is used together with
gene transposition, it is also capable of duplicating genes.
Notwithstanding, if the goal is to evolve good solutions, one-point or two-point recombination should never be used as the only source of genetic variation as, with time, they tend to homogenize populations. However, together with
mutation, inversion and
transposition, these operators are an excellent source of genetic variation and are more than sufficient to evolve good solutions to virtually all problems.
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