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For the experiment summarized in the first column of Table 10.3, unigenic
chromosomes were chosen in order to simulate more faithfully a neural net-
work. One of the most parsimonious solutions found in this experiment has a
total of 32 nodes and is shown in Figure 10.7.
Obviously, we could explore the multigenic nature of GEP systems and
also evolve multigenic neural networks for the 6-multiplexer. The solutions
found are, however, structurally more constrained as we have to choose some
kind of linking function to link the sub-NNs encoded by each gene. In this
case, the Boolean function OR was chosen to link the sub-NNs. (If the mix-
ing of OR with “U”, “D”, and “T” functions is confusing, think of OR as a
function with connectivity two and weights and thresholds all equal to one,
and you have a neural network solution to the OR function.)
In the experiment summarized in the second column of Table 10.3, four
genes posttranslationally linked by OR were used. The first solution found
in this experiment is shown in Figure 10.8. Note that some of the weights in
genes 1 and 2 have identical values, and that the same happens for genes 3
and 4. This most probably means that these genes share a common ancestor
and were, therefore, created by an event of gene duplication, which, as you
would recall, can only be achieved by the concerted action of gene transpo-
sition and gene recombination.
The fact that the problems chosen to illustrate the workings of GEP-nets
are Boolean in nature and that the neurons we used belong to the simplest
class of McCullouch-Pitts neurons, doesn't mean that only this kind of crisp
Boolean problems with binary inputs and binary outputs can be solved by
the GEP-NN algorithm. In fact, all kinds of neurons (linear neuron, tanh
neuron, atan neuron, logistic neuron, limit neuron, radial basis and triangu-
lar basis neurons, all kinds of step neurons, and so on) can be implemented
in GEP-nets as no restrictions whatsoever exist about the kind of functions
the system can handle. And the exciting thing about this is that one can try
different combinations of different neurons and let evolution work out which
ones are the most appropriate to solve the problem at hand. So, GEP-nets can
be used to solve not only Boolean problems but also classification and sym-
bolic regression problems using not only unigenic and multigenic systems
but also acellular and cellular systems. Furthermore, classification problems
with multiple outputs can also be solved in one go by GEP-nets either by
using a multigenic system or a multicellular system. All these different kinds
of neural network systems work beautifully and can be used not only as an
