For the sake of simplicity, we are going to illustrate the mechanisms of gene 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 gene recombination, entire genes are exchanged between two parent chromosomes, forming two daughter chromosomes containing genes from both parents. The exchanged genes are randomly chosen and occupy exactly the same position in the parent chromosomes.
The default value for the gene recombination rate in APS 3.0 is 0.1, 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 gene recombination rates of 1.0.
Consider the following parent chromosomes, each composed of three genes:
012345678901234012345678901234012345678901234
+Qaa-dcabdaddac-a*b-/aabdbbdba+caQ*bQcdcbdcac
//Q//bacdacabba/b/d+/acddbbdac*-c*-/acdbacddd
Suppose gene 2 was chosen to be exchanged. In this case the following offspring is formed:
012345678901234012345678901234012345678901234
+Qaa-dcabdaddac/b/d+/acddbbdac+caQ*bQcdcbdcac
//Q//bacdacabba-a*b-/aabdbbdba*-c*-/acdbacddd
Note that, with this kind of recombination, similar genes can be exchanged but, most of the times, the exchanged genes are very different and new material is introduced in the population.
It is worth emphasizing that gene recombination is unable to create new genes: the individuals created by this operator are different arrangements of existing genes. Obviously, if gene recombination were used as the unique source of genetic variation, more complex problems could only be solved using very large initial populations in order to provide for the necessary diversity of genes. However,
the evolvability of gene
expression programming is based not only in the shuffling of genes (achieved by gene recombination and
gene transposition), but also in the constant creation of new genetic material which is carried out essentially by
mutation, inversion and
transposition (both IS and
RIS transposition) and, to a lesser extent, by
recombination (both one-point and
two-point recombination).
So, if the goal is to evolve good solutions, gene recombination should never be used as the only source of genetic variation as, with time, it tends to homogenize populations. However, as observed for
one-point and two-point
recombination, gene recombination can also give rise to duplicated genes if it were used together with
gene transposition.
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