Information Technology Reference
In-Depth Information
Number of Hits
The number of hits fitness function is very simple and corresponds to the
number of samples correctly classified. More formally, the fitness f i of an
individual program i is evaluated by the formula:
f i = h (3.8)
where h is the number of fitness cases correctly evaluated (number of hits).
So, for this fitness function, maximum fitness f max is given by the formula:
f max = n (3.9)
where n is the total number of fitness cases.
As you would recall, this fitness function was efficiently used to solve the
Majority( a , b , c ) function problem of section 3.1. But sometimes a more
sophisticated fitness function is needed because, both in classification and
logic synthesis, it is indeed very easy to discover lots of simple programs
with relatively high fitness that are not particularly good predictors. On the
one hand, the fitness of most programs will only reflect the 50% likelihood
of correctly solving a binary function; and on the other, such simple pro-
grams as the constant zero f ( x 1 , ..., x n ) = 0 or constant one f ( x 1 , ..., x n ) = 1
functions are very easily discovered and will most probably also score a high
fitness. For more complex applications, all these simple programs might hinder
the evolutionary process and therefore it is advisable to reduce them to a
minimum. A simple way of doing this is shown below.
Hits with Penalty
The hits with penalty fitness function was designed in order to avoid the
dissemination of useless programs that could indefinitely trap the system in
local optima. For that the following simple strategy can be used: for each
program i , both the number of true positives TP i and true negatives TN i is
evaluated and as long as either TP i or TN i remain equal to zero, this model
will be considered unviable and therefore it won't be selected to reproduce.
More formally, the fitness f i of an individual program i is evaluated by the
formula:
IF ( TP i = 0 OR TN i = 0), THEN f i = 0; ELSE f i = h (3.10)
Search WWH ::




Custom Search