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 mutation 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 mutation is similar to the mutation that occurs in the
heads and tails of genes, extending this powerful operator also to Dc. Thus, the default value for the
Dc mutation rate in APS 3.0 is also 0.044.
Consider the following chromosome composed of two genes, each with a Dc length of 8:
0123456789012345678901201234567890123456789012
*/-?c++?c?acadc60569331+-?Q*?/cd?ddc?a86358705
Suppose a mutation changed the numeral “5” at position 17 in gene 1 to “4”; and the “8” at position 15 in gene 2 to “1”. In this case the following chromosome is obtained:
0123456789012345678901201234567890123456789012
*/-?c++?c?acadc60469331+-?Q*?/cd?ddc?a16358705
Now suppose that the arrays below represent the random numerical constants of the respective genes:
C1 = {-1.64, -1.834, -0.295, 1.205, -0.807, 0.856, 1.702, -1.026, -0.417, -1.061}
C2 = {-1.14, 1.177, -1.179, -0.74, 0.393, 1.135, -0.625, 1.643, -0.029, -1.639}
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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