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For the increasing range of ERCs, the instances (*control*,
*unity*, *ten* and *hundred*) become increasingly difficult for genetic programming
to solve. As shown in Figure 6.5, fitness (adjusted fitness) converges less quickly,
fewer good fitness values
are found and individuals become larger and deeper for the larger ERC ranges.
Additionally, the edit distance diversity is slightly
higher for the easier instances. This would seem counterintuitive
as one would expect earlier convergence toward similar programs
for easier instances. In the bottom graph of Figure 6.5,
the entropy quickly falls and rises, then continues
to decrease. This confirms that once good solutions are found,
the population loses unique fitness values. As more
and more solutions have the same fitness value, entropy decreases.
However,
the easier instances, in contrast to the difficult instances, are
also more likely to be solved by
more *different* programs. This explains why diversity
is higher in this case. While the populations do converge and lose diversity,
the easier instances converge to a more varied selection of fit individuals.
Note that the time when entropy begins to slowly decrease
also marks the time when code growth begins to slow down. For the
easier instances, this occurs just before generation 40, and for the
*hundred* instance, somewhere between generation 60 and 80.

** Next:** 3 Random Polynomials
** Up:** 4 Binomial-3 and Random
** Previous:** 1 Establishing Difficulty
** Contents**
S Gustafson
2004-05-20