The root mean squared error fitness function (RMSE) of APS 3.0 is, as expected, based on the
standard root mean squared
error.
The root mean 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); and
Tj is the target value for fitness case j.
For a perfect fit, P(ij) = Tj
and Ei = 0. So, the RMSE 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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