5 Summary

This chapter has provided a survey of measures used to capture diversity and methods employed to control diversity in genetic programming. An experimental study enabled the analysis of correlation between selected measures of diversity and fitness. The results showed three important behaviours:

1. The generation to generation behaviour of specific diversity measures is problem specific. In fact, representation changes of the same problem are likely to have different diversity behaviours. Thus, the pursuit of a single measure with which to control diversity in order to improve fitness is likely to be difficult.
2. Entropy and edit distance diversity showed some correlation with fitness. This is likely related to a change of selection pressure and the level of structural convergence which allows a form of hill-climbing search.
3. Regression problems had the weakest correlation between any measure of diversity and fitness overall, suggesting that the things that make these populations achieve good fitness may not be captured by any of the measures used here.

The introduction of different recombination operators, large changes in parameter values and applications on different problem domains are all likely to effect the results and interpretations made here. However, the methodology of using several informative and complimentary measures of diversity should allow one to gain a deeper understanding of the search space and algorithm. As search spaces become larger and more complex, fine grain measures will become too inefficient. Therefore, using measures which capture the right level of information while still being efficient will be critical. Based on these results, the following recommendations are made:

• Before applying new methods to control diversity in order to improve fitness, the correlation between fitness and diversity should be investigated. Knowledge of the correlation between fitness and a measure of diversity can help to enhance the diversity measure or diversity control method and give insight into results.
• Care should be taken to distinguish between correlation and causation.
• Lastly, when a many-to-one relationship exists between the genotype and phenotype encoding, measures which are based on genotype uniqueness will probably not be as useful as those which capture phenotype uniqueness.

Next, a measure of diversity, genetic lineages, is used to increase population diversity (both edit distance and entropy). The effects of this change in population dynamics is examined to better understand the relationship between diversity and fitness, and also the type of search genetic programming carries out during the evolutionary process.