The R-square fitness function of APS 3.0 is, as expected, based on the standard
R-square, which returns the square of the Pearson product moment correlation coefficient.
The Pearson product moment correlation coefficient is a dimensionless index that ranges from -1 to 1 and reflects the extent of a linear relationship between two data sets.
The Pearson product moment correlation coefficient Ri of an individual program i is evaluated by the equation:
where P(ij) is the value predicted by the individual program
i for fitness case j (out of n fitness cases);
and Tj is the target value for fitness case j.
The fitness fi of an individual program
i is expressed by the equation:
fi = 1000*Ri*Ri
which allows a fairer distribution of fitnesses for selection.
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