Choosing the Fitness Function
R-square Based Fitness Function
 
For all classification problems, in order to be able to apply a particular fitness function, the learning algorithms APS 3.0 must convert the value returned by the evolved model into “1” or “0” using the 0/1 Rounding Threshold. If the value returned by the evolved model is equal to or greater than the rounding threshold, then the record is classified as “1”, “0” otherwise.

Thus, the 0/1 Rounding Threshold is an integral part of all fitness functions used for classification and must be appropriately set in the Settings Panel -> Fitness Function Tab.

The R-square fitness function 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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