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desired fitness, then the corresponding chromosome is picked and, thereafter, is
decoded into network parameter values. The network parameters generated are the
final output of the GA run and a further GA run is not required (Figure 5.1).
However, if the best fitness is less than the desired fitness, then the GA run is
further continued as per Figure 5.1. Once the fitness values are all arranged in
descending orders, the best 70% population are collected to form the mating pool
in this example. Now, from the mating pool, the next-generation populations are
created by applying the various genetic operations as described earlier in this
chapter.
In order to test the efficiency of the GA-based neuro-fuzzy network training the
Mackey-Glass chaotic time series was considered. The network in this case, as
usual, had four inputs and only five rules were implemented. As described above,
only 20 populations were selected in each generation. It can be seen from the
Figure 5.3 that in only a few generations the GA could improve the fitness function
to 8.4149, which corresponds to SSE = 0.1188 or MSE = 0.0012. However,
because of the very slow progress of the generation run, the GA run was
terminated after only a few generations. If a higher fitness value (say, a few
hundred) is required, then the GA run may have to be continued for several
thousands of generations so that the network can correctly approximate the
nonlinear chaotic time series model.
5.3 Genetic Programming
Koza (1992) proposed an evolutionary algorithm for solving intelligent
computational problems by automated generation of computer programs required
for problem solution. He viewed the new algorithm as a model for machine
learning in the space of programs and, therefore, named it genetic programming .
a
+
bc
LISP program chunk: a+b*c
Figure 5.4. Example of a LISP program “ a + b * c
Instead of operating with individuals, genetic programming operates with the
computer programs and uses computer languages, preferably functional
programming languages, for its implementation. Functional programming
languages are based on syntax suitable for presenting parse trees used in genetic
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