GeneXproTools 4.0 implements the Accuracy 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.
The Accuracy
fitness function of
GeneXproTools is, as expected, based on the classification accuracy.
The classification accuracy Ai of an individual program
i depends on the number of fitness cases correctly classified
(true positives plus
true
negatives) and is evaluated by the formula:
where t is the number of sample cases correctly classified, and
n is the total number of sample cases.
The fitness fi of an individual program
i is expressed by the equation: fi = 1000*Ai
and therefore ranges from 0 to 1000, with 1000 corresponding to the ideal.
Its 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 =
1000.
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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