The Basic Gene Expression Algorithm - Gene Expression Programming - page 71

where h is the number of fitness cases correctly evaluated (or number of hits,
which obviously corresponds to h = TP i + TN i ). So, for a perfect solution,
maximum fitness corresponds to the total number of fitness cases and is also
evaluated by equation (3.9).

Sensitivity / Specificity
The sensitivity/specificity fitness function is based both on the sensitivity
and specificity indicators, both commonly used in the medical field. The
sensitivity reflects the probability of the diagnostic test finding disease among
those who have the disease or the proportion of people with disease who
have a positive test result. And the specificity reflects the probability of the
diagnostic test finding no disease among those who do not have the disease
or the proportion of people free of a disease who have a negative test.
More formally, and perhaps more clearly, the sensitivity SE i of an indi-
vidual program i is evaluated by the equation:

TP

i

SE (3.11)

i

TP FN

i i

and the specificity SP i is evaluated by:

TN

i

SP

(3.12)

i

TN FP

i i

By multiplying both these indicators and using this new index as basis to
measure the fitness of the evolved models, one forces the discovery of mod-
els that have both high sensitivity and specificity, since it would be relatively
simple to maximize the sensitivity by minimizing the specificity and vice
versa. Indeed, this kind of fitness function is extremely valuable in situations
where highly unbalanced training sets are being used, that is, datasets with
an excess of positive or negative instances. So, the sensitivity/specificity SS i
of an individual program i is evaluated by the equation:

(3.13)

And for evaluating the fitness f i of an individual program i , the following
equation is used:

f 1000 SS

(3.14)

i i

which obviously ranges from 0 to 1000, with 1000 corresponding to the ideal.