How difficult of a problem is it to break out of local optimums several generations down in a genetic algorithm? If we prune the domain space from the get-go ra

How difficult of a problem is it to break out of local optimums several generations down in a genetic algorithm? If we prune the domain space from the get-go randomly, and then keep on creating sub-domains of the original large (or potentially non-finite) domain, wouldn't we generally only head towards local optimums, albeit, quickly?