Choosing the Fitness Function

Absolute/Hits

 GeneXproTools 4.0 implements the Absolute/Hits fitness function both with and without parsimony pressure. The version with parsimony pressure puts a little pressure on the size of the evolving solutions, allowing the discovery of more compact models. For some Function Finding problems it is important to evolve a model that performs well for all fitness cases within a certain absolute 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 absolute 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. And overall, the fitness fi of an individual program i is expressed by the equation: where n is the total number of fitness cases. So, for this fitness function, maximum fitness fmax is given by:fmax = nIts counterpart with parsimony pressure, uses this fitness measure fi as raw fitness rfi and complements it with a parsimony term. Thus, in this case, raw maximum fitness rfmax = n. And the overall fitness fppi (that is, fitness with parsimony pressure) is evaluated by the formula: where Si is the size of the program, Smax and Smin represent, respectively, maximum and minimum program sizes and are evaluated by the formulas: Smax = G (h + t) Smin = G where G is the number of genes, and h and t are the head and tail sizes (note that, for simplicity, the linking function was not taken into account). Thus, when rfi = rfmax and Si = Smin (highly improbable, though, as this can only happen for very simple functions as this means that all the sub-ETs are composed of just one node), fppi = fppmax, with fppmax evaluated by the formula:
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