3 Regression Remarks

The range of symbolic regression instances used throughout this thesis provided a set of very different behaviours. From the very difficult, the Rastrigin function, to much easier ones, the Quartic and Binomial-3 functions, diversity measures did not capture a similar dynamic in previous problems that was important to search. One reason for this is that the continuous fitness space in Regression experiments allows genetic programming to easily maintain high fitness-based diversity. This can most easily be seen in the phenotype and entropy measures in Chapter 4 that remained at much higher levels than other domains.

The Tree-String problem from Chapter 7 would appear to be most closely related to Regression problems with its dual and often conflicting objectives of structure and content. Applying the results from the Tree-String experiments to the Regression problem suggests that much of the future populations come from diverse individuals that may not necessarily be the most fit in the population. That is, in the Tree-String experiments, when considering the definition of outliers as better-than or equivalent-to more than half the population, the outliers contributed a considerably higher rates of survivability than selection. The results of the Binomial-3 instance in Chapter 7 also show that outliers play an important part in the search process.