The GEP-RNC algorithm
of APS 3.0 uses an additional gene domain
(Dc) for encoding random numerical constants (RNCs). In the Dc, the symbols used to represent the random numerical constants can obviously be replaced by other symbols of the same kind.
For the sake of simplicity, we are going to illustrate the mechanisms of Dc IS transposition 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, terminal, or random constant) is represented by a single character so that each element can be easily identified by its position in the chromosome.
Dc IS transposition similar to the IS transposition that occurs in the
heads of genes, extending this operator also to Dc. Thus, the default value for the
Dc IS transposition rate in APS 3.0 is also 0.1.
The Dc IS transposition operator randomly chooses the chromosome, the start and termination points of the IS element, and the target site.
Consider the following chromosome composed of two genes, each with a Dc length of 8:
0123456789012345678901201234567890123456789012
/---Q+c??a?cddb05829607--?//*-ab?dd?cb25391083
Suppose that the sequence “108” in gene 2 (positions 19-21) was picked up as an IS element to be then inserted between positions 15 and 16 in gene 2, obtaining:
0123456789012345678901201234567890123456789012
/---Q+c??a?cddb05829607--?//*-ab?dd?cb21085391
Note that a sequence with as many symbols as the IS element is deleted at the end of the Dc of gene 2 (in this case, the sequence “083” was deleted).
Now suppose that the arrays below represent the random numerical constants of the respective genes:
C1 = {-0.148, 1.83, -0.503, -1.786, 0.313, -0.302, 0.768, -0.947, 1.487, 0.075}
C2 = {-0.256, -0.026, 1.874, 1.488, -0.8, -0.804, 0.039, -0.957, 0.462, 1.677}
As you can see (you’ll need to draw the expression
trees, of course), these chromosomes encode different solutions because the random constants expressed in the original chromosome are slightly different from the ones expressed in the daughter chromosome.
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