A comment that we often receive is that our final structures are not optimized: they contain redundant bricks that do not serve any apparent purpose. Of course, these irregularities are useful during the search process. Since we are not rewarding nor punishing for the number of bricks used, the evolutionary search freely generates variations with different numbers of bricks. All of them are potentially useful in the process of finding new combinations with higher fitness.
In a new run of the diagonal crane arm experiment, we added a little reward for lightness, inversely proportional to the number of bricks, but three orders of magnitude smaller than the raw fitness function. Fig. 2.28 shows two solutions for a crane arm the same length (a fitness value of 24). The structure on the right has a bigger premium, so we will prefer it.
Since we are willing to sacrifice everything else for the length of the arm,
the fitness weight of the `simplicity' factor has to be very small compared
with the raw fitness measure (arm length). Among cranes of the same size and
resistance, however, we prefer those with a smaller number of bricks. The evolutionary
process is not biased against heavier versions of the crane; it just detects
the simpler ones. In the example shown in fig. 2.28, fitness
values of 24.0029 and 24.0040 have nearly identical chances of being selected
in a fitness proportional selection scheme. But among otherwise identical cranes,
the premium for implies that the cleanest one makes the final cut.
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