A few people hear are pointing out that in a GA, individuals should be complete solutions to the problem. That's generally true, but there are evolutionary methods that do the opposite. Within the field of Learning Classifier Systems, the two approaches corresponding to your question are called the Michigan approach (each individual is only one rule or circle) and the Pittsburgh approach (each individual encodes the entire set of rules or circles). Currently, Michigan approaches (namely XCS and its variants) dominate the field, so there is evidence that you can craft such algorithms successfully. More generally, there are coevolutionary methods that have similar ideas.
The only restrictions you really have on an evolutionary method is that you need to be able to go from genotype to fitness value in some way, and you need some ability to perform transformations on the genotype like mutation and/or recombination. Mutation and crossover don't necessarily give you trouble whether or not you have one circle per individual or one solution per individual. The only issue is how do you assign fitness to one circle? If you solve that problem, then you can build algorithms that use one individual per circle.
It's certainly easier to write a fitness function that takes the entire solution as one individual, but you can do it the other way. If this is something you want to pursue, look at how XCS works and look into cooperative coevolutionary algorithms.