2 Binomial-3 Results

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.