For the sake of simplicity, we are going to illustrate the mechanisms of two-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 two-point recombination two parent chromosomes are paired and two points are randomly chosen as crossover points. The material between the recombination points is afterwards exchanged between the parent chromosomes, forming two new daughter chromosomes.
The default value for the two-point recombination rate in GeneXproTools 4.0
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,
you will obtain better results with two-point recombination rates of 1.0.
Consider the following parent chromosomes, each composed of three genes:
012345678901234012345678901234012345678901234
+ca*-+cdacabbca/Qdd-c+cddacdac+/ccbd/bcbadabb
Qcb+b+acddaadad*/*b/adadaddcba/bc-a+Qacdbbbaa
Suppose bond 7 in gene 1 (between positions 6 and 7) and bond 4 in gene 3 (between positions 3 and 4) were chosen as crossover points. Then, the following daughter chromosomes are created:
012345678901234012345678901234012345678901234
+ca*-+ccddaadad*/*b/adadaddcba/bc-bd/bcbadabb
Qcb+b+adacabbca/Qdd-c+cddacdac+/cca+Qacdbbbaa
It is worth emphasizing that two-point recombination is more disruptive than
one-point recombination in the sense that it recombines the genetic material more thoroughly, constantly destroying old building blocks and creating new ones. But like one-point recombination, two-point recombination has also a conservative side and it is good at swapping entire genes and
K-expressions. And, as observed for one-point recombination, two-point recombination can also give rise to duplicated genes if it were used together with
gene transposition.
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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