Genetic and Evolutionary Algorithms for PSP - Digital Signal Processing in Power System Protection and Control - page 283

classification abilities. After further investigations the Q eff/size index in form of
Eq. ( 13.2 ) was adopted. The analyses confirmed that such an approach could
provide

much better optimization results in both ANN efficiency and size

aspects.
The best ANNs obtained for respective quality indices were:

• For Q eff index—ANN having 14 neurons (13-1), classification efficiency equal
to 0.978, and
• for Q eff/size index—ANN having 6 neurons (3-2-1), classification efficiency of
0.954.

As one can see, optimization with combined index ( 13.2 ) ceased with twice
smaller neural network by only slight decrease of ANN classification abilities.
The operation of described genetic optimization algorithm was thoroughly
tested taking also into account various ways of selection procedure realization
(Fig. 13.9 ) as well as various probability values for occurrence of particular
genetic operations. The genetic operations mentioned above were realized with
regard to neural networks in the following way:

• Crossover operation (with probability p c ) consisted in exchange of some neu-
rons between two ANN individuals; the crossover could concern single neurons
(with probability p sn ), groups of neurons (p gn ) or whole layers (p l ).
• Mutation operation (with probability p m ) was realized in one of the following
versions: delete a neuron, duplicate a neuron, delete a layer of neurons or
duplicate a layer of neurons.

In Table 13.1 the optimization results of the neural CT-saturation detectors are
gathered for various selection methods applied and probability values of the
genetic operands adopted. Here, the ANNs were being assessed with the efficiency
index Q eff . It is seen that the resulting neural networks are characterized by similar
effectiveness of CT-state identification. The best ANN (Q eff = 0.9783) was
obtained for the algorithm Rn4, i.e. for selection with ranking place method,
probability of crossover set low (p c = 0.3) and probability of mutation set high
(p m = 0.6). Apart from high-classification abilities, its important advantage is also
quite small size (the considered ANN consisted only of 14 neurons laid out in two
layers). Such a compact neural structure can easily be implemented even in on-line
operating protection and control systems. From Table 13.1 one can also draw
some conclusions with regard to the influence of the selection method applied on
the results of GA operation. Independent of the values of probabilities of genetic
operations, the selection method based on ''ranking place'' approach brought about
the ANNs with the highest values of efficiency index Q eff . With this respect the
worst one turned out to be the ''tournament'' selection algorithm with random
choice of individuals.
The analysis of results gathered in Table 13.1 with respect to influence of the
probabilities of genetic operations reveals the fact that the best optimization results
are obtained for the algorithms with probability of mutation p m set higher than
probability of crossover p c . It is also advantageous when the probability of