6 Alternative Definitions

Figure 7.5 shows the average and 95 % confidence bars for the random runs, but now the fitness component used to define outliers (and in-liers) is that of better-than or equivalent-to. With this change, the number of outliers and in-liers has increased significantly. This increase highlights the equivalence of fitness in the population. The ratios in the right plot of Figure 7.5 show dramatically different selection and survival ratios than before. The outlier survival rates are highly sporadic and seem to increase later in the evolutionary process. In the presence of many equivalent fitness relationships, diverse solutions appear to play a more important role in creating offspring which survive to create more offspring. Also, the ratios of survival are much higher in the un-fit than the in-liers. This suggests that while their overall numbers are lower, individuals that are both similarly fit and genetically similar are unable to produce viable offspring. By changing the view of outliers and in-liers to include equivalent fitness values in their definition, the in-lier class increased in numbers but decreased in overall survivability.

Depending on the problem representation and operator, one may wish to consider an alternative definition of genetic dissimilarity, such as the distance from the mean of only one standard deviation. Next, the the original fitness definition for outliers is used, but the genetic difference will now be based on one standard deviation. This change should allow more individuals to be considered as dissimilar.

Figure 7.6: The average number in the population, the number of times selected and the survivability of the outliers, in-liers and un-fit for the Tree-String experiments using the (better-than, 1 standard deviation) definition of outliers.

Figure 7.6 shows the same plots as above for the number of outliers and the ratios of selection and survivability, but now using the one standard deviation criterion. Here, one can see again how a slight increase in the number of outliers causes their selection and survival rates to increase. The right plot of this figure emphasises the large spikes of the survival ratio of outliers. In contrast to Figure 7.5, the survivability of outliers, while still unstable, tends to decrease during the evolutionary process. The in-lier survivability frequently intersects the selected ratio, while the un-fit individuals tend to have lower survived ratios compared to the selected ratio. These results show that as the population loses diversity and becomes genetically converged, the outlier survivability becomes more unstable. When the number of outliers are high enough to be selected, they produce children with high survivability, but at an increasingly varied rate during the course of the run. This view of outliers, compared with Figure 7.5, shows that outliers, which have a dissimilarity between 1 and 2 standard deviations from the population's mean, play a more important role initially in search. As Figure 7.5 shows outliers with a dissimilarity greater than 2 standard deviations, Figure 7.6 confirms that the addition of outliers with a dissimilarity greater than 1 and less than 2 standard deviations account for this increased dissimilarity. However, in the later stages of the evolutionary process, the outliers have a lower survivability.

Finally, the above two methods are combined to define an outlier as being one standard deviation from the mean average pair-wise edit distance and being better-than or equivalent-to half the population in fitness. Figure 7.7 shows that when the outlier class is made larger by including equivalent fitness and only being one standard deviation from the pair-wise distance mean, the survivability rate of outliers is consistently higher than its selection rate, but still unstable. This view of outliers, combined with Figures 7.4 and 7.5, shows clearly how the population converges to be mostly equivalent and genetically similar. Also, Figure 7.7 shows that when outliers are viewed using the equivalent fitness criterion, their survivability is higher for longer periods.