Choosing the Fitness Function
Relative Squared Error Based Fitness Function
 
The relative squared error fitness function (RSE) of APS 3.0 is, as expected, based on the standard relative squared error.

The relative squared error Ei 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); Tj is the target value for fitness case j; andis given by the formula:

For a perfect fit, the numerator is equal to 0 and Ei = 0. So, the RSE index ranges from 0 to infinity, with 0 corresponding to the ideal.

As it stands, Ei can not be used directly as fitness since, for fitness proportionate selection, the value of fitness must increase with efficiency.

Thus, for evaluating the fitness fi of an individual program i, the following equation is used:

which obviously ranges from 0 to 1000, with 1000 corresponding to the ideal (the coefficient 1000 allows a fairer distribution of fitnesses for selection).
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