I also had no problem in understanding the question, and have been amused at how many monks are assuming that the use of genetic algorithms has anything to do with bioinformatics.

I don't know how many species you're aiming to attempt, but I would guess it's high enough you can't just keep a singleton registry of all tried genomes (or even a registry of digests of all tried genomes). tye's suggestion seems to limit the types of mutations (consecutive pair swaps). I'm a bit worried about how non-general that is, but we really don't have much to go on, for the actual problem at hand.