Digital Signal Processing Reference
In-Depth Information
Table 13.1 Topologies and quality indices of the ANN classifiers obtained with the GA for
various combinations of selection method and probabilities of genetic operations
Probability values
Optimization results (best ANN size and quality) for selection process
realized with the method of
Wheel of
roulette
Ranking
place
Tournament with
deterministic
choice
Tournament
with random
choice
p
m
= 0.25 p
c
= 0.65
(p
l
= 0.75
p
gn
= 0.20)
ANN-R1:
(11-1)
Q
eff
= 0.9637
ANN-Rn1:
(14-1)
Q
eff
= 0.9742
ANN-Td1:
(5-9-3-1)
Q
eff
= 0.9720
ANN-Tr1:
(6-10-1)
Q
eff
= 0.9563
p
m
= 0.25 p
c
= 0.65
(p
l
= 0.40
p
gn
= 0.55)
ANN-R2:
(4-11-1)
Q
eff
= 0.9707
ANN-Rn2:
(6-15-1)
Q
eff
= 0.9720
ANN-Td2:
(11-8-8-1)
Q
eff
= 0.9670
ANN-Tr2:
(11-11-4-4-1)
Q
eff
= 0.9683
p
m
= 0.60
p
c
= 0.30
(p
l
= 0.75
p
gn
= 0.20)
ANN-R3:
(6-7-7-1)
Q
eff
= 0.9720
ANN-Rn3:
(7-11-12-1)
Q
eff
= 0.9733
ANN-Td3:
(9-6-1)
Q
eff
= 0.9650
ANN-Tr3:
(9-11-4-1)
Q
eff
= 0.9574
p
m
= 0.60
p
c
= 0.30
(p
l
= 0.40
p
gn
= 0.55)
ANN-R4:
(4-8-7-7-1)
Q
eff
= 0.9653
ANN-Rn4:
(13-1)
Q
eff
= 0.9783
ANN-Td4:
(15-3-11-5-1)
Q
eff
= 0.9723
ANN-Tr4:
(6-2-1)
Q
eff
= 0.9687
crossover for group of neurons p
gn
is higher than for the whole layers p
l
. Not going
into detail it is worth to mention that the probability values do not have to be
constant during the run of GA. Usually the value of p
c
is higher at the beginning of
the optimization process and decreases with time to the advantage of probability
p
m
, which becomes higher for later generations.
In Fig.
13.11
the course of quality index Q
eff
during the run of GA algorithm
(version with ''wheel of roulette'' selection method R2) is shown. Looking at the
curve of quality index for the best ANN in current population (Q
eff_max
) one can
find that the process convergence is the fastest for the first few iterations. After
several generations the pace of optimization decreases and from ca. 25th gener-
ation no significant improvement of the neural classifiers is observed. The average
quality index (Q
eff_av
) calculated for the entire population of ANNs is not a
monotonic function, however, it increases slowly with time, which means that
consecutive populations of nets consist of individuals on better average and better
adapted for the task they are trained to.
The research performed also included an attempt of ANN structure design with
heuristic ''trial and error'' approach. A number of 1,000 neural networks were
randomly created, trained and then tested with EMTP-ATP simulation signals. It
allowed getting the neural classifiers with 94% efficiency at the most (the best out
of 1,000 created ANNs was characterized by efficiency Q
eff
index equal to 0.94
and size (9-7-1), i.e. consisting of 17 neurones), which is less than obtained with
the genetic optimization approach, independent of the selection method and
probabilities of genetic operations.
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