The Relative Error With Selection Range fitness function explores the idea of a
selection range and a precision. The selection range is used as a limit for selection to operate, above which the performance of a program on a particular fitness case contributes nothing to its fitness. And the precision is the limit for improvement, as it allows the fine-tuning of the evolved solutions as accurately as possible.
Mathematically, the fitness fi of an individual program
i is expressed by the equation:
where R is the selection range, P(ij) 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. Note that the absolute value term corresponds to the relative error. This term is what is called the
precision and if the error is smaller than or equal to the
precision then the error becomes zero. Thus, for a good match the
absolute value term is zero and fi
= fmax = nR.
Note that when the target value for a particular fitness case is zero, the relative error is undefined but, for fitness evaluation purposes
during training, APS 3.0 salvages these cases so that they can also be used for fine-tuning solutions.
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