Information Technology Reference
In-Depth Information
More formally, the fitness
f
(
ij
)
of an individual program
i
for fitness case
j
is evaluated by the formula:
If
E
d
p
,
then
f
1
else
f
0
(3.1)
ij
ij
ij
where
p
is the precision and
E
(
ij
)
is the error of an individual program
i
for
fitness case
j
, and is expressed by equation (3.2a) if the error chosen is the
absolute error, and by equation (3.2b) if the error chosen is the relative error:
E
P
T
(3.2a)
ij
(
ij
)
j
P
T
(
ij
)
j
E
100
(3.2b)
ij
T
j
where
P
(
ij
)
is the value predicted by the individual program
i
for fitness case
j
and
T
j
is the target value for fitness case
j
. So, for these fitness functions,
maximum fitness
f
max
=
n
, where
n
is the number of fitness cases.
Precision and Selection Range
The
precision and selection range
fitness function explores the idea of a
selection range and a precision. The selection range is used as a limit for
selection to operate, above which the performance of a program on a particu-
lar fitness case contributes nothing to its fitness. And the precision is the
limit for improvement as it allows the fine-tuning of the evolved solutions as
accurately as possible.
More formally, the fitness
f
i
of an individual program
i
is expressed by
equation (3.3a) if the error chosen is the absolute error, and by equation
(3.3b) if the error chosen is the relative:
n
¦
f
R
P
T
(3.3a)
i
(
ij
)
j
j
1
§
·
P
T
n
¦
¨
©
¸
¹
(
ij
)
j
f
R
100
(3.3b)
i
T
j
1
j
where
R
is the selection range,
P
(
ij
)
the value predicted by the individual
program
i
for fitness case
j
(out of
n
fitness cases) and
T
j
is the target value
for fitness case
j
. Note that the absolute value term corresponds, in both
equations, to the error (absolute in the former, relative in the latter). This
