Information Technology Reference
In-Depth Information
||
≤ε
||
=ε
x
x'
∈
M
ε
(
x
−
x'
x
−
x'
)
x
●
●
●
●
●
x
1
−ε
x
1
x
1
+ε
Fig. 3.
Example of an incremental group in a 2 dimensional space
consecutively shifted into one dimension. The distance is given by an increment
ε>
0
which shifts the position of the pivot element in both directions of the dimension. In
each dimension
i
Incremental Probing
considers two points (see figure 3 for a 2 dimen-
sonal example). For a given pivot element
x
=(
x
1
,...x
n
)
and a given increment
ε>
0
these positions are determined by
=
ε
|
i
=
j
x
i
|
|
x
i
−
(2)
0
|
i
=
j
where
j, i
n
. The increment
ε
is defined relatively to the domain. For instance, in a
restricted
n
-dimensional domain
≤
I
n
, where the interval
I
i
=[
a
i
,b
i
]
defines the valid subspace, the increment is applied as
ε
A
=
I
1
×
...
×
b
i
−
a
i
100
. For each dimension the
position of the pivot element is shifted into two directions. This leads to a set of
2
n
+1
points including the pivot element. The fitness value of each valid point is calculated
and these fitness values are used for the extraction of objective features
1
. In this group
of features, nine features are created with the use of three increments of
ε
1
=1
,
ε
2
=2
and
ε
5
=5
.Let
n
be the dimension of the domain, then
2
n
+1
evaluations are required
to calculate the fitness values of the relevant points. Since three increments are used
there are
(3
×
2
n
)+1
evaluations required to calculate the features of
Incremental
Probing
.
The features
Incremental Min
,
Incremental Max
and
Incremental
Range
are computed similar to the features of
Random Probing
. For each increment the
minimum, maximum and the spread of the fitness values are computed.
Incremental
·
1
In case that the point is invalid, that is it lies outside the valid domain, the evaluation of the
fitness value is skipped and the fitness value of the pivot element is used instead.
