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Two challenging problems in genetic programming are the application
of genetic programming on increasingly difficult problem instances and
the increase of solution size which is not correlated with improvement.
Daida et al. (2001) recently demonstrated that when
genetic programming has difficulty solving harder problem instances,
solutions are generally larger in size, take longer to find, and are
less numerous in the population.
Of these traits, the increase in size without corresponding
fitness improvement is the most worrying to genetic programming
practitioners.
The continued
growth of solutions for difficult problems
will become a limiting factor of the applicability of the
algorithm; computational resources will be exhausted and the algorithm
will halt before reaching a good solution.
The existing theories of code growth [Langdon and Poli, 2002,Luke, 2003,Soule and Heckendorn, 2002]
provide the
mechanical basis for understanding why programs in a variable-length
representation tend to
grow in size, but do not predict the rate of growth or explain
why optimal solutions can vary in size by a large degree.
Additionally, the many methods used to limit code growth, or to
remove non-functional code from solutions, may often lead to
worse performance [Ekárt, 2000,Luke and Panait, 2002a,Soule and Foster, 1998,Zhang and Mühlenbein, 1995].
Two symbolic regression problems are used that are differently
scaled in difficulty to observe the
behaviour of fitness, code growth and diversity.
If growth is related to instance difficulty, it will be likely
that the dynamics of the population, viewed with measures of
diversity, will aid in understanding the phenomenon.
Symbolic regression problems are used for two main reasons.
Firstly, there is a large body of existing theoretical studies using
regression problems to understand genetic programming.
Secondly, it is easier to reason about increasing the difficulty
of fitting mathematical functions than it might be for increasing the
difficulty of other types of problems.

** Next:** 2 Regression Problems and
** Up:** 6 Effects of Population
** Previous:** 6 Effects of Population
** Contents**
S Gustafson
2004-05-20