Information Technology Reference
In-Depth Information
Chromosome tree representation
Control
Center
Radius
Lower corner
Upper corner
Center
Semi-axis
Orientation matrix
Chromosome linear representation
01
Center
d
Radius
Lower-corner
d
Upper-corner
d
Center
d
Semi-axis
d
Orientation matrix
dxd
Control
Hypersphere
Hyperrectangle
Hyperellipse
Figure 4.16 A single chromosome having a high-level control and low-level
parameters encoding three different hypershapes: hyperspheres, hyperrectangles,
and hyperellipses.
deactivates genes at level 2. Any gene set at level 2 can be expressed for fi tness mea-
sure (shown in Figure 4.16).
Although each individual (chromosome) encodes multiple shapes, namely,
hypersphere, hyperrectangle, and hyperellipse, it expresses only one shape in the
“phenotypic space.” Accordingly, “hypersphere genes” indicate the hypersphere
n
-dimensional center
c
and radius
R
, “hyperrectangle genes” hold information
of the two points that specify the minimum and maximum coordinates in each
dimension (e.g., the lower-left and upper-right corners of a rectangle in two dimen-
sions), and “hyperellipse genes” contain its
n
-dimensional center
ω
,
n
semi-axes
lengths
l
i
, and a square “orthonormal matrix V” of size
n
×
n
, which specifi es the
orientation of the hyperellipse.
h us, each detector shape,
d
in
n
-dimensional unit hyperspace is represented as
Hypersphere,
d(c, r)
, with the center and the radius
Hyperrectangle,
d[min
i
,
max
i
]
for each
i
=
1, 2, …
,
n
dimension
−
ω
)
T
A
(
p
−
ω
)
<
=
Λ
V
T
and
Λ
=
(
λ
i,j
) is an
Hyperellipse,
d(p
1, where
A
V
×
=
n
n
diagonal matrix such that
λ
i i
1/
l
i
2
Accordingly, a sample (with center
x
and variability
v
) forming the hypersphere
s(x, v)
is considered matched (using
some distance measure
dist(·)
) by a detector
, d
of shape
<
+
Hyper-sphere-shaped detector if
dist
(
c
,
x
)
r
)
Hyper-rectangle-shaped detector if the circumscribed hypercube around the
sample hypersphere intersects the detector
(
v
Search WWH ::
Custom Search