It may seem that I have been neglecting this genetic algorithm project, but my computer has been busy crunching numbers, repeatedly evolving images with 128, 256 or 384 circles. Below shows the average distance values from four separate runs of evolution with 128 circles, 256 circles and 384 circles. It is purely bad luck that the Darwins evolved from 256 circles started with a much higher distance from the target images. However, by ~500 generations, the 256-circle Darwins had caught up with the 384-circle Darwins.
The more circles the image has, the slower it evolves. This is what one would expect because the circles that make the most difference to the distance from the target image are those on top. The more circles there are, the less chance there is that a mutation will affect one of the more important circles. However, we would expect that while evolution is slower when there are more circles, the rate at which evolution slows should also be slower, such at that, at some point, the images with more circles will overtake those with fewer circles. I will have to analyse the actual numbers to see if this really holds.
One idea I had, based on this result, is to start evolution with one or two circles, allow those to evolve until there are no successful mutations for a while, and then adding an additional random circle (or perhaps have a random circle replicate).
The image below is a collection of the resulting images from each run of evolution after 100 000 generations, with their d values. I also averaged the four images with a given number of circles. Again shows that the 128-circle images are slightly better than the 256-circle images, while the 384-circle images are considerable worse.