4 Analysis of Diversity Measures

Previous investigations into measures of diversity have given the community a clearer view of populations and the search process of genetic programming [McPhee and Hopper, 1999,Darwen and Yao, 2001,Ekárt and Németh, 2002,Rosca, 1995a,Keijzer, 1996,Langdon and Poli, 2002]. However, the many different possible definitions of diversity can be conflicting. Identifying the measures that correlate with run performance will enable the design of more efficient operators and genetic programming algorithms.

The three main issues addressed in this chapter are:

1. The ways of measuring and controlling diversity,
2. The correlation between the best fitness and diversity of populations, and
3. The importance of diversity at different stages of the evolutionary process.

As genetic programming is a stochastic algorithm, clear (and always applicable) rules about exact ideal levels of diversity are not expected to be found. The goal is instead to draw general conclusions and `rules of thumb' about expected diversity and search performance. A survey of diversity measures and diversity preserving methods is presented next. This is followed by an experimental study of the trends of various measures, the correlation between fitness and diversity measures and a discussion about the overall effects of diversity.