Is there a name for this approach to evolutionary algorithms? I am considering an approach to evolutionary algorithms, in which instead of maintaining a population of individuals, we maintain a pool of $N$ mutations that can be applied to a base genome.  For every possible subset (or many possible subsets) of the mutation pool, we apply that subset to the base genome to produce an individual, then test that individual.  We discard mutations for which the population with that mutation performs worse than the population without it.  We merge the best-performing mutations into the base genome for the next generation.  Then we replace the discarded or merged mutations with new ones.
Is this known under some name?  Is it a good idea?
It's just a genetic algorithm, only your population is a set of instructions that generate a subject to be tested. There are minor differences in the way you apply multiple mutations, so you evaluate groups of them instead of each individually, but for the scoring you effectively single out the commonalities among the worse individuals.
Hard to tell whether it's a good idea; discarding poor mutations based on them being part of a sub-optimal individual might not be as straight forward as it sounds. And where do you get new mutations from?