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(swapping of genes and ORFs), making one-point recombination (and of course
two-point recombination too) a very well balanced genetic operator.
Also worth pointing out is the fact that, like all the other recombinational
operators, when used together with gene transposition, one-point recombi-
nation is also capable of duplicating genes, which is also very important for
an efficient and innovative evolution.
Two-point Recombination
In two-point recombination the parent chromosomes are paired side by side
and two points are randomly chosen by which both chromosomes are split.
The material between the recombination points is then exchanged between
the two chromosomes, forming two new daughter chromosomes.
Figure 3.26 shows two-point recombination at work. An initial population
and its immediate descendants obtained in a run are shown. In this experi-
ment, the only source of genetic variation was a two-point recombination rate
p
2r
of 0.8. Note that a perfect solution was obtained early in generation 1 (chromo-
some 3). Indeed, when recombination is the only source of genetic variation,
most of the times, perfect solutions are either found early on in the run or are not
found at all, as populations become less and less diverse with time (see the Evo-
lutionary Studies in chapter 12 for a discussion of the homogenizing tenden-
cies of recombination). Note that chromosomes 1 and 3 of generation 1 are the
daughters of chromosomes 4 and 6 of the initial population.
The event that led to the creation of this perfect solution in generation 1 is
shown in Figure 3.27. In this case, the parent chromosomes exchanged the
genetic material between point 7 (between positions 6 and 7 of gene 1) and
point 14 (between positions 2 and 3 of gene 2). Note that the first gene is, in
both parents, split downstream of the termination point. Note also that the
second gene of chromosome 4 was also cut downstream of the termination
point. Indeed, the noncoding regions of GEP chromosomes are ideal regions
where chromosomes can be split to cross over without disrupting the ORFs.
We have already seen that these regions are also ideal places where neutral
mutations can accumulate and then such operators as two-point and one-
point recombination can activate these neutral regions by integrating them in
the coding regions of a new gene. Note, however, that gene 2 of chromosome
6 was split upstream of the termination point, changing profoundly the en-
coded sub-ET. Note also that when these chromosomes recombined, the
noncoding region of chromosome 4 was activated and became part of the
perfect solution found in generation 1 (chromosome 3).
