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Reed-Muller system of ANDs, XORs, and NOTs; and the MUX system.
Furthermore, we will see how to enrich the evolutionary toolkit of GEP through
the use of user defined functions in order to design parsimonious solutions to
complex modular functions using smaller building blocks.
And finally, we will see how gene expression programming can be used to
evolve cellular automata rules for the density-classification task. The rules
evolved by gene expression programming have accuracy levels of 82.513%
and 82.55%, exceeding all human-written rules and the rule evolved by ge-
netic programming. And most impressive of all, we will see that this was
achieved using computational resources more than four orders of magnitude
smaller than those used by the GP technique.
4.1 Symbolic Regression
We have already seen how gene expression programming can be used to do
symbolic regression in the simple example of section 3.4. Here, we will
analyze more complex problems of symbolic regression in order to evaluate
the performance of the algorithm. The first is a simple test function that can
be exactly solved by the basic GEA and, therefore, is ideal for showing the
importance of the fundamental parameters of the algorithm, such as the popu-
lation size, the number of generations, fitness function, chromosome size,
number of genes, head size, and the linking function. The second consists of
a complex test function with five arguments that shows how gene expression
programming can be efficiently applied to model complex realities with great
accuracy. And the third problem was chosen to illustrate how gene expres-
sion programming can be efficiently used for mining relevant information
from extremely noisy data.
4.1.1 Function Finding on a One-dimensional Parameter Space
The target function of this section is the simple cubic polynomial:
y
=
a
3
+
a
2
+
a
+ 1 (4.1)
This function was chosen not only because it allows the execution of hun-
dreds of runs in a few seconds but also because it can be solved exactly by
the algorithm and, therefore, is ideal for rigorously evaluating the perform-
ance in terms of success rate. Consequently, it can be used to illustrate how
