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a.
01234567890123456
TDbabaabb73899388
W = {0.713, -0.774, -0.221, 0.773, -0.789, 1.792, -1.77, 0.443, -1.924, 1.161}
b.
T
a
D
b
a
b
Figure 10.6.
A perfect, extremely parsimonious solution to the exclusive-or
problem designed with the GEP-NN algorithm.
a)
Its chromosome and respective
array of weights.
b)
The fully expressed NN encoded in the chromosome.
10.3.2 Neural Network for the 6-Multiplexer
Multiplexers are logic circuits frequently used in communications and input/
output operations for transmitting a number of separated signals simultane-
ously over a single channel. And in particular, the task of the 6-bit Boolean
multiplexer is to decode a 2-bit binary address (00, 01, 10, 11) and return the
value of the corresponding data register (d
0
, d
1
, d
2
, d
3
). Thus, the 6-multi-
plexer is a function of six activities: two,
a
0
and
a
1
, determine the address,
and four,
d
0
through
d
3
, determine the answer.
There are therefore 2
6
= 64 possible combinations for the six arguments of
the 6-multiplexer function (Table 10.2) and, for this problem, the entire set
of 64 combinations was used as the selection environment. The fitness was
evaluated by equation (3.10), thus giving
f
max
= 64.
In order to simplify the analysis, I chose a rather compact (hence, less
efficient) organization and used only neurons with connectivities one, two,
and three, which were respectively represented by “U”, “D”, and “T”, thus
Table 10.2
Lookup table for the 6-multiplexer. The output bits are given in
lexicographic order starting with 000000 and finishing with 111111.
00000000 11111111 00001111 00001111 00110011 00110011 01010101 01010101
