Index of Graphs

Overview

These graphs are intended to highlight the differences that I have discovered while testing the genetic Othello player, factoring complexity into the fitness measure in one case, and ignoring complexity when computing fitness in the other. I have created graphs for all of the categories of the resulting data that I could have; these seem to highlight the differences between the two approaches the best. (For example, I have omitted graphs of the depth of the population because depth is very closely related to complexity, and I have omitted the complexity of the worst individuals because it is similar to the data contained in the graphs of the worst fitness and the average complexity, and the graph itself is rather erratic).

Graphs

Best fitness

This contains the comparison of the fitness measures of the best individual per five generations between the two methods. Since both methods produced best individuals with similar fitnesses, the graph is not too insightful.

Average fitness

This graph contains the comparison of the average fitness measures of the entire population per five generations between the two methods, which could be interpreted as the fitness of the entire population at that generation. This graph reveals quite a bit about the drawback of constraining the population by complexity.

Worst fitness

This graph contains the comparison of the worst fitness measures of the entire population per five generations between the two methods. Like the graph of the best fitness measures, it is not too revealing, but does demonstrate some possible correlation between complexity and performance.

Best Complexity

This graph contains the comparison of the complexity of the best individuals in the populations. While there is not much that can be drawn from the graph of the best fitnesses themselves, the way that the population that is evaluated on complexity is constrained to a low complexity is interesting, while the constrast of the increasing complexity of the population that was not evaluated on complexity demonstrates that there may be some benefit (or no loss, at least) in not evaluating fitness with complexity.

Average Complexity

This graph contains the comparison of the complexity of the average complexity of the two populations, or how complex the population is at at a particular generation. When coupled with the display of the average fitness between the two methods, it makes a compelling case for the benefits of a population that is not constrained by complexity.

Variety

This graph contains the comparison of the variety of the two populations over the generations. The interesting point here is the manner in which the population that is evaluated by complexity is reduced to a small, repetitive population over many generations. I purposefully made the complexity factor very small in comparison to the overall fitness measure (on average, complexity increases the fitness measure by .5 to 1.5 percent, and goes as low as .05 percent for some individuals). However, over time, complexity in evaluation will grow a very small population; this, combined with the evaluation of performance, effectively restricts the search space to a small subset of possible individuals. Ignoring complexity when evaluating fitness expanded the search space considerably, leading to a greater variety of individuals in each generation.
William Bauder
wjb14@columbia.edu