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lurk into populations, they can seriously hinder evolution for they have usu-
ally very simple structures that are not only easily discovered but also ex-
tremely resilient. And because they can have a relatively high fitness, they
will compete fiercely with any generalist that might appear, trapping the
system in a local optimum for an indefinite length of time.
Irrespective of unbalanced or unrepresentative datasets, populations do
sometimes get stuck in local optima for long periods of time and might need
a little help to get out of there. A way of doing this consists of using a differ-
ent measure to evaluate fitness. Indeed, by changing the fitness function we
are changing the fitness landscape, and what was a peak on the previous
landscape might now be a valley, and the population might be able to find a
new path to the elusive global optimum. This is the reason why it is handy to
have more than one fitness function at our disposal so that we can try a few
of them on a problem. With this in mind, some of the most common fitness
functions, used not only in symbolic regression but also in classification and
logic synthesis, are described below.
3.2.2 Fitness Functions for Symbolic Regression
One important application of evolutionary computation is symbolic regres-
sion, where the goal is to find a symbolic expression that performs well for
all fitness cases or, in other words, to find a model that is good at numeric
prediction. And there are several measures that can be used to evaluate how
good these models are. Some of them are based on the absolute error be-
tween predicted and target values. Others are based on the relative rather
than absolute error. Others still are based on statistical indexes that measure
the correlation between the values predicted by the model and the target
values. Which of these fitness functions is more appropriate to search the
fitness landscape in any given problem is a matter that can only be deter-
mined by studying the problem itself. But fitness functions based on stand-
ard measures such as the mean squared error or R-square are virtually uni-
versal and can be used to evolve very good models for all kinds of problems.
Number of Hits
The
number of hits
fitness function favors models that perform well for all
fitness cases within a certain error (that is, the precision that is chosen for the
evolved models) of the correct value. This error can be either the absolute or
relative error.
