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3 Scatter Plots of Diversity and Fitness

The Spearman correlation coefficient only describes linear relationships. A series of scatter plots are also examined to assess the data for any nonlinear relationships. Figure 4.14 and 4.15 plot a population's performance (best fitness found in the population is plotted along the x-axis, where values to the left are better) versus that population's diversity (on the y-axis). Each point represents a population sampled from a different run, where no run is used twice and 10 populations are sampled for each generation, requiring 500 runs. Also note that all points for the Parity experiments have their fitness values randomly offset in the range of [-0.2,0.2] to allow for better visualisation of the points at each fitness value.

A few general comments can be made about the scatter plots in Figures 4.14 and 4.15. There are clear trends of best fitness occurring with lower edit distance and with higher entropy. However, many populations with low fitness also have a wide range of entropy (Rastrigin and Quartic experiments) and edit distance (Quartic experiments). The Ant experiments, in particular, show a transition from high to low fitness with populations in the middle containing a wide range of entropy and edit distance values. The populations which achieve the lower fitness then also have lower entropy and edit distance. It is likely that this problem suffers the most from local optima, where populations that get stuck with sub-optimal individuals also have sub-optimal diversity. Too high edit distance diversity and either too-low or too-high entropy would appear to be sub-optimal for the Ant problem.

Figure 4.15: Best fitness vs. edit distance One diversity for the Ant, Parity, Quartic and Rastrigin experiments. 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.
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\psfig{figure=chapters/ch4figs/ant-10.eps,height=5.5c...
...5cm}
\psfig{figure=chapters/ch4figs/rastrigin-10.eps,height=5.5cm}
}\end{figure}

An important observation is that better populations tend to occur near the end of evolution and resulting populations will be less diverse simply because of the search and selection mechanisms. In Figure 4.15, when populations have large edit distances they are unlikely to have better fitness values. A reason for this could be that large edit distances only occur at the beginning of runs. The question of whether these populations always occur late in evolutionary process is analysed next.

For Figure 4.16, the same populations from Figure 4.15 are used, except now the z-axis shows a vertical line representing the generation in which that population occurred. A common trend is that the worse fit populations occur in early generations, which is to be expected as Fig. 4.4 showed fitness to always improve (decrease in value) initially. In general, moving from right to left in fitness values (from worse to better), the lines get taller on the z-axis. However, it is not the case that the best populations are always at the end of runs for all problems. Many populations achieve good fitness early and in the middle of runs. Furthermore, Fig. 4.16 emphasises that populations have different diversity at similar times in the evolutionary process. Later evolutionary periods do not always imply high or low values of diversity and fitness.

Figure 4.16: Ant, Parity, Quartic and Rastrigin best fitness in population (x-axis) plotted against that population's edit distance One diversity, (y-axis) and the generation the population occurred (z-axis). Note that each point represents one population from each run.
\begin{figure}\centerline{
\psfig{figure=chapters/ch4figs/3dant-10.eps,height=5....
...m}
\psfig{figure=chapters/ch4figs/3drastrigin-10.eps,height=5.5cm}
}\end{figure}


next up previous contents
Next: 4 Discussion of Diversity Up: 3 Analysis of Results Previous: 2 Evolving Populations' Correlation   Contents
S Gustafson 2004-05-20