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 inversion 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 inversion is similar to the inversion that occurs in the
heads of genes, extending this operator also to Dc. Thus, the default value for the
Dc inversion rate in APS 3.0 is also 0.1.
The Dc inversion operator randomly chooses the chromosome, the gene to be modified, and the start and termination points of the sequence to be inverted.
Consider the following chromosome composed of two genes, each with a Dc length of 8:
0123456789012345678901201234567890123456789012
-Q/*?-?da?bac?b21650337Q*+b?/*?addb??b10715948
Suppose that the sequence “1650” in gene 1 (positions 16-19) was picked up to be inverted. Then the following chromosome is formed:
0123456789012345678901201234567890123456789012
-Q/*?-?da?bac?b20561337Q*+b?/*?addb??b10715948
Now suppose that the arrays below represent the random numerical constants of the respective genes:
C1 = {-0.78, -0.521, -1.224, 1.891, 0.554, 1.237, -0.444, 0.472, 1.012, 0.679}
C2 = {-1.553, 1.425, -1.606, -0.487, 1.255, -0.253, -1.91, 1.427, -0.103, -1.625}
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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