For the Quartic and Rastrigin experiments, the phenotype diversity in Figures 4.7 shows an initial decrease followed by a sharp increase. This behaviour was also seen with genotype diversity and entropy: an initial sharp decrease was followed by an increase within the Quartic and Rastrigin experiments and in all experiments with genotype diversity. Intuitively, the cause of this initial fluctuation is due to the ease with which improvements can be found in the initial solutions. This initial phase highlights the differences between the experiments. Also, note that phenotype diversity for the Parity experiments continues to increase until the final generation.
For all experiments, the edit distance One in Figure 4.9 generally decreases after the initial generation. Also, in Figure 4.10, the populations measured with edit distance Two behave similarly. With this in mind, and because the edit distance Two measure places more importance on the root and higher portions of trees, one can conclude the following: While trees are changing (according to edit distance One) to be more like the best fit tree in each population, the differences between the roots and top portions of the tree also become more similar (according to the edit distance Two measure). This supports previous conclusions [Igel and Chellapilla, 1999,McPhee and Hopper, 1999,Soule and Foster, 1998] that roots become fixed early on in the evolutionary process. Structural convergence is important when considering using a method to control diversity. If structural convergence is beneficial to genetic programming search, then encouraging or forcing structural diversity (edit distance in this case) could have negative consequences. However, the loss of edit distance diversity does not necessarily mean a loss of phenotype diversity or the worsening of fitness, as seen in Figure 4.7 and 4.4.
Lastly, the figures show the behaviour that in some runs fitness continues to increase until the final generation. Identifying the dynamics and properties that allowed for this continued increase is critical for genetic programming practitioners. This is a goal of this research: understanding how to make populations more amenable to improvement. Given the wide range of fitness and diversity, one would like to know if these measures correlate with fitness in any way. Addressing this question is key to understanding if controlling diversity is likely to be effective and how it should be applied to different problem domains.