Choosing the Fitness Function
Relative/Hits
 
For some Time Series Prediction problems it is important to evolve a model that performs well for all fitness cases within a certain relative error (the precision) of the correct value.

For those cases, the fitness f(ij) of an individual program i for fitness case j is evaluated by the formula:

where p is the precision and E(ij) is the relative error of an individual program i for fitness case j evaluated by the equation:

where P(ij) is the value predicted by the individual program i for fitness case j and Tj is the target value for fitness case j.

So, for this fitness function, maximum fitness fmax is given by:

fmax = n

where n is the number of fitness cases.

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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