5 Genetic Properties Contributing to the Evolutionary Process

Figure 7.3 shows the fitness points visited by 40 runs of the Tree-String problem. The tree objective is along the X-Axis, and the string objective is on the Y-Axis. A randomly chosen run is highlighted by connecting the successive points this run visits. Points are randomly offset by a small amount to better illustrate their distribution. The Tree-String problem creates a complex fitness landscape where improving one objective often conflicts with the other, and vice versa.

Figure 7.4 shows the average over 10 runs of the number of outliers, in-liers and un-fit individuals (from left to right) at each generation (increasing from left to right) in the left plot. The number of selected individuals and the number of those which produced offspring that were selected in the following generation (the survivability) are shown in heavier lines. 95% confidence bars are plotted every ten generations for the in-lier and outlier individuals. The un-fit population is the total population size minus the in-lier and outlier populations. This measure of survivability is similar to that in [Luke, 2003] where the selection of an individual represents the relative rank of that individual in the population. The measure considers the selection method being used and is a better indicator of an individual's contribution toward the search process than the change in fitness from parent to offspring.

Figure 7.4: 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. Outliers are defined by the (fitness, similarity) tuple as (better-than, 2 standard deviations).

Every generation has a number of outliers which are rarely selected, due to their low numbers and subsequently low probability of selection. Thus, these outliers have almost no survivability. The right plot in Figure 7.4 of ratios of selected over total number and survived over selected emphasise these effects. Here the in-liers generally have a higher ratio of selection, which is expected, and a higher survivability than the un-fit. The un-fit tend to have worse survivability, which emphasizes that the in-liers produce more offspring that are able to survive and contribute offspring in the next generation. The survivability of the in-liers tends to lower toward the end of the run, which is likely due to convergence, i.e. the in-liers are unable to produce useful variations.

In this initial experiment, outlier individuals have an average pair-wise edit distance greater than 2 standard deviations from the population mean and are better than over half of the population in fitness. The number of outliers in Figure 7.4 highlights the fact that the population contains good individuals that are structurally unlike the rest of the population, are unlikely to be selected due to their few numbers, and, without more experimental results, have an intuitively lower chance of producing good offspring.

The above definition of outliers addresses the concepts of fitness and genetic diversity, but it is not the only possibility. For example, the fitness component in the outlier definition requires an outlier to be better-than more than half the current population. It may be beneficial to also consider individuals with equivalent fitness values in this definition. To further investigate the role of genetic diversity and survivability, three additional experiments are performed, summarised in Table 7.2, by adjusting the fitness and dissimilarity components that define outliers. The following alternative definitions provide alternative views of the survivability of different regions of the population. The evolutionary process is the same for all definitions of outliers, and as above, each alternative is considered using the averages of 10 random runs.

Table 7.2: The Tree-String outlier definition variations and respective figures.

	fitness component		difference component
Fig. 7.4	better-than	,	2 standard deviations
Fig. 7.6	better-than	,	1 standard deviations
Fig. 7.5	(better-than $\lor$ equivalent-to)	,	2 standard deviations
Fig. 7.7	(better-than $\lor$ equivalent-to)	,	1 standard deviations

Figure 7.5: 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 $\lor$ equivalent-to , 2 standard deviation) definition of outliers.