6 Summary

This chapter investigated the effects of population diversity by examining the relationship between problem difficulty and varied rates of code growth. Two problems with different types of difficulty and a simplified model of genetic programming have been used to understand this relationship. A causal hypothesis is formed that links difficulty to higher entropy, which in turn causes more selection pressure and loss of diversity. Increased selection pressure and lower diversity are then responsible for a higher rate of code-growth. This hypothesis is consistent with previous research. A recommendation for controlling genetic diversity, entropy and selection pressure is made to gradually effect the rate of code growth, in response to more direct methods which often have negative effects.

The results in this chapter were based on experiments in the regression domain, using a variety of problem instances. Earlier chapters displayed varying levels of results between problem domains, but diversity and fitness trends were generally consistent. Thus, the conclusions and recommendations from this chapter are relevant for other domains as well. The correlation between fitness and diversity was investigated in Chapter 4, which was complemented in this chapter with the investigation of the relationship between size and fitness, size and edit distance diversity, and size and entropy. Lastly, while the causal hypothesis of code growth appears consistent with results presented in earlier chapters and in the literature, additional research would be beneficial to confirm specific aspects of the hypothesis as well as its validity on other problem domains.

To further understand the role of population diversity in genetic programming, the next chapter examines the ability of dissimilar individuals to produce good offspring.