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4 The Ant, Parity and Regression Domains

The Ant, Parity and Binomial-3 regression problem instances are used with the same definitions and parameters as presented in Chapter 5. All problems are minimisation of errors; the number of missed food pellets in the Ant problem, the mean squared error in regression of the Binomial-3 problem and the number of misclassified bit-strings in the Parity problem. The genetic measure of diversity is the Levenshtein distance between tree structures denoted with [n,l]. The same experimental parameters were used as in the Tree-String experiments. The better-than relationship and 2 standard deviations are used as the fitness and difference components to define outliers.

The outliers, in-liers and un-fit distributions are shown in Figures 7.8 to 7.9. These graphs show the averages over 30 runs for each problem, where the left plot represents the numbers in each category. Survival numbers were based on the number of selected individuals that produced offspring which were selected in the next generation. 95% confidence bars are shown for the left plots and the right plots in Figures 7.8 to 7.9 show the ratios of selection and survivability.

For the Ant experiments in Figure 7.8, the rate of survival of outliers is initially high compared to their number and rate of selection, especially in the early generations. As discussed earlier in this thesis, the Ant problem contains deception and benefits from more exploration in early generations. The decrease of in-liers in the later generations is due to the increasing number of individuals which have equivalent fitness. However, even though the number and rate of selection of in-liers dramatically reduces, their offspring have a considerably higher and increasing rate of survival compared to selection.

Figure 7.8: The average number in the population, the number of times selected and the survivability of the outliers, in-liers and un-fit for the Ant experiments.
\begin{figure}\centerline{\psfig{figure=chapters/ch7figs/ant-surv-conf.eps,width...
...}
\psfig{figure=chapters/ch7figs/ant-surv-rate-ave.eps,width=8.0cm}}\end{figure}
Figure 7.9: The average number in the population, the number of times selected and the survivability of the outliers, in-liers and un-fit for the Parity experiments.
\begin{figure}\centerline{\psfig{figure=chapters/ch7figs/parity-surv-conf.eps,wi...
...psfig{figure=chapters/ch7figs/parity-surv-rate-ave.eps,width=8.0cm}}\end{figure}
Figure 7.10: The average number in the population, the number of times selected and the survivability of the outliers, in-liers and un-fit for the Binomial-3 experiments.
\begin{figure}\centerline{\psfig{figure=chapters/ch7figs/binomial3-surv-conf.eps...
...ig{figure=chapters/ch7figs/binomial3-surv-rate-ave.eps,width=8.0cm}}\end{figure}

Similar results are seen with the Parity experiments in Figure 7.9. The few number of outliers have high survival rates that are also very sporadic. In this problem, the role of in-liers and the un-fit change similarly to the Ant problem. The early stages in the evolutionary process rely on the un-fit and outliers to produce much of the surviving offspring relative to the rate of selection. However, this role shifts to the in-liers having higher survival rates in later generations. The Parity problem differs from other problems (including the Tree-String problem) in that the un-fit subpopulation increases in numbers considerably. Previous chapters, particularly Chapter 5, showed the large effort genetic programming spends in sampling different solutions that have equally poor fitness. Thus, in the later stages of the evolutionary process, the un-fit subpopulation increases in numbers but becomes less effective in producing good offspring. The Ant problem has a similar behaviour, but starts the run with an already high number of un-fit.

The Binomial-3 experiments have somewhat different results, shown in Figure 7.10. These experiments contain a relatively higher numbers of outliers compared to the other problems. Outliers are selected more and achieve higher rates of survival more often. The in-liers and un-fit maintain fairly constant and similar rates of selection and survival. Outliers achieve higher rates of survival compared to their numbers and selection rates, which decreases during the run. However, it is important to remember that the definition of outliers, particularly with the difference component, is problem dependent. Performing a more extensive study of different definitions of outliers would yield more informative results, as done earlier with the Tree-String problem. Based on the above empirical study and survey of related work, a niche for islands models is proposed.


next up previous contents
Next: 5 A Niche for Up: 7 Diversity, Survivability and Previous: 7 Discussion of Experimental   Contents
S Gustafson 2004-05-20