2 Evolving Populations' Correlation

Is diversity more important at different stages of the evolutionary process? The fact that several methods have been previously used to adaptively control the level of diversity would suggest so. Figure 4.13 shows the correlation between diversity and best fitness for each generation. Note that each point represents the correlation between 100 populations, sampled from 100 runs where there is a dependency of later generations on preceding ones.

Both the Ant and Parity experiments contain varying levels of correlation between edit distance and fitness and between phenotype diversity and fitness. The Quartic experiments contains a period of early fluctuation, followed by an increase in positive correlation between entropy (and phenotype diversity) and fitness. As runs typically achieve the best fitness early, this effect may be due to many copies of the best fit individual accumulating in the population. That is, populations which achieve good local optima begin to have lower entropy.

The Rastrigin experiments contain an early period of varying correlation between diversity and fitness, after which most measures lost correlation with fitness. In this problem and representation, the relationship between fitness and diversity becomes less important, probably due to other more critical relationships like node-to-node dependencies [Daida et al., 2001]. A positive correlation between fitness and edit distance occurs together with a negative correlation between fitness and phenotype diversity is seen in the Ant and Parity experiments. These results suggest that the fitness landscape induced by the representation, operator and fitness function is uncorrelated. Small differences between individuals are still capable of expressing a wide range of behaviours. However, this statement should be considered in the light of the operator not being used to define distance and the actual difference between behaviours is not considered. The measures used here only give approximate descriptions of the fitness landscape.

Figure 4.14: Ant, Parity, Quartic and Rastrigin best fitness in population plotted against that population's entropy. Note that each point represents one population from each run. We sample 10 different runs for each population at generation $g$, requiring $50 \times 10 = 500$ runs for all 50 generations.