Biomedical Engineering Reference
In-Depth Information
r
Wmax,0
r
2,Rmax
δ/2
δ
δ/2
δ
Figure 1.3:
An example of a non-uniform grid
G
.
In the 2D space, the parameter set is reduced to
x
,
y
, and the angle of
rotation
θ
. These parameters are represented by binary notation to minimize as
much as possible the length of the schemata
d
(
H
) and the order of the schemata
O
(
H
). The number of bits
n
p
, assigned to each parameter,
p
, depends on the
type of application and the required degree of accuracy. The number of bits
should be chosen as small as possible to minimize the time of convergence of
the genetic algorithm. For example, you can assign 8 bits each, thus allowing a
displacement of
±
127 units. A range of
±
31 can also enforced over the angles
of rotation. Therefore 6 bits are assigned for each angle of rotation. As shown
in Fig. 1.4, the genes are formed from the concatenation of the binary coded
parameters.
The selection operator chooses the highest fitted genes for mating using a
Roulette wheel selection [24]. The crossover and mutation operators are imple-
mented by choosing a random crossover and mutation point with probabilities
P
c
and
P
m
, respectively, for each coded parameter
p
. The generated strings
are concatenated together to form one string from which the populations are
formed (see Fig. 1.5).
More details and error analysis of the GCP technique can be found in [9]. The
major drawback of the GCP/GA algorithm is that the range of the transformation
