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It has a fitness of 9.00806 and an R-square of 0.9110742575 evaluated against
the training set of 90 fitness cases and, therefore, is slightly better than the
model (7.11) designed with the cellular system without random numerical
constants and also considerably better than all the models designed with
Kolmogorov-Gabor polynomials. More formally, the model (7.12a) can be
expressed by the following function (the contribution of each ADF is shown
in brackets):
2
§
·
a
j
2
h
2
¨
©
j
¸
¹
e
g
y
(7.12b)
§
·
a
j
2
h
¨
©
j
¸
¹
(
0
0018847
d
0
518463
i
)
(
i
)
e
g
Several conclusions can be drawn from the experiments presented here.
First, a STROGANOFF-like system exploring second-order bivariate basis
polynomials, although mathematically appealing, is extremely inefficient in
evolutionary terms. For one thing, its performance is significantly worse than
all the much simpler GEP systems. For another, the structural complexity of
the solutions it designs is overwhelmingly complicated, making it almost
impossible to extract knowledge from them. And second, any conventional
GEP system with a simple set of arithmetical functions is not only much
more efficient but also considerably simpler than the extravagantly compli-
cated and computationally expensive STROGANOFF systems.
In the next section we are going to use the settings of the simplest of the
GEP systems (the basic GEA with the basic arithmetical operators) to design
a model and then make predictions about sunspots with it.
7.4 Predicting Sunspots with GEP
In this section we are going to explore all the fundamental steps in time series
prediction. As an example, we are going to learn how to make predictions
about sunspots but, indeed, we could be predicting anything from financial
markets to the price of peanuts for all such tasks are solved using exactly the
same time series prediction framework.
Time series analysis is a special case of symbolic regression and, there-
fore, can be easily done using the familiar framework of gene expression
programming. Indeed, one has only to prepare the data to fit a conventional
symbolic regression task, which means that we must have a dependent vari-
able and a set of independent variables. For this problem, we are going to use
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