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Daida et al. (2001)
provided a thorough investigation of why increasing the ephemeral
constant range makes the Binomial-3 problem `harder'. The authors
draw attention to the inter-play between content and context
of functions and terminals in the representation. Many different
solutions exist to the Binomial-3 problem and combining parts of different
solutions does not always make sense. A level of deception
exists that is similar to the Ant problem,
due to the many different solutions.
However,
in the Ant problem the functions and terminals preserve, to some degree,
semantic meaning in different contexts. Moving constants and arithmetic
functions between
programs in Regression problems does not ensure their meaning in new contexts.
A DAG (directed acyclic graph) representation of genetic programming
was used on a Regression problem [Monsieurs and Flerackers, 2003] where the author
introduced a diversity method
that was also highly elitist. Performance showed that best fitness was
achieved much faster with smaller population sizes using the elitist
diversity measure.
Regression problems appear to pose a two-fold problem,
finding a good approximation to fit the data points and attempting
to reduce semantic changes of nodes during crossover.
In this case, increasing genetic diversity could increase the chance
that crossover will have problems with nodes changing context. A converged
population may contain fewer nodes but with similar contexts and
improve search performance. However, too little or too much
selection or diversity
would cause problems as well, making this a complex problem domain.

** Next:** 4 Remarks
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S Gustafson
2004-05-20