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7 Discussion of Experimental Results

The previous experiments have provided an initial exploration into the role of diverse individuals in the population using a constructed problem. The results showed the existence of varying types of structurally diverse and fit individuals and their ability to produce successful offspring. Each of the varying definitions described in Table 7.2 shows a different perspective of the role of diversity.
Figure 7.7: 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 , 1 standard deviation) definition of outliers.

The view of the population using the equivalent definition of fitness showed how the survivability of in-liers goes below their selection rates. This, combined with the previous views using the better-than relationship, shows how the increase of the number of equally fit individuals is correlated with poorer search ability. Or, a decrease in phenotype diversity is correlated with poorer search ability. This was also seen in Chapter 4, where high fitness entropy and phenotype diversity were positively correlated with fitness improvements.

When considering the outlier dissimilarity to be one standard deviation from the population mean pair-wise distance, the low selection of these individuals still produced high rates of survival, becoming lower and more sporadic over time (Figure 7.6). What is consistent in these experiments, and with others that examine diversity with similar algorithms [McPhee and Hopper, 1999], is that the population becomes more similar in structure over time. Thus, the number of outlier individuals in all experiments tends to decrease as the population becomes more homogeneous. When that occurs, seen in Figure 7.6, the survivability of outliers becomes more sporadic. However, in Figure 7.5, using the equivalent fitness definition for outliers, the sporadic survivability of outliers increases as the population converges. With this view of outliers, they become more important as they contain diverse genetic material that the population needs to produce useful variations.

Among the possible interpretations of these results, two are initially highlighted here. First, dissimilar individuals have an unstable ability in producing offspring with high survivability. Secondly, as the population converges, and in light of equivalent fitness values, the role of dissimilar individuals becomes more important. Without considering equivalence, dissimilar individuals become less effective when the population converges. With the equivalence relationship, dissimilar individuals provide key variation necessary for variation and improvement. That is, when the space of fit individuals contain many equally fit individuals, the dissimilar individuals with the same fitness play an increasingly important role, albeit an unstable one.

Lastly, this study has grouped similar and dissimilar individuals with low fitness into the un-fit class. However, it is interesting to note the change of survivability rates under the varying views of the population. Most noticeably is the change between using the stricter better-than definition (Figures 7.4 and 7.6) to the better-than or equivalent definition (Figure 7.5 and 7.7). In the latter cases, the un-fit consistently produces higher survivability ratios than the outliers or the in-liers. Also, this ratio is typically higher than its own selection ratio. The loss of genetic and phenotype diversity probably increases deception and lowers selection pressure, causing search to rely on new solutions produced by the un-fit subpopulation.

An effort has been made throughout this thesis to consistently analyse genetic programming on a similar set of problem domains. In order to add to this growing body of analysis for these domains, and to provide additional validation of the above analysis using the Tree-String problem, an initial study of survivability is carried out using the Ant, Parity and regression problems.

Table 7.3: Experiment and problem parameters for Ant, Parity and Binomial-3 outlier experiments.
        Ant if_food_ahead,progn2
        Parity and,or,nand,nor
        Binomial3 +,-,*,p/
        Ant left,right,move
        Parity D1,D2,D3,D4,D5
        Binomial3 x, ERCs
ERC range $[-10,10]$
Other parameters same as for Tree-String experiments

next up previous contents
Next: 4 The Ant, Parity Up: 3 Genetic Outliers and Previous: 6 Alternative Definitions   Contents
S Gustafson 2004-05-20