I feel like we need a better name for this type of approach, because many people (myself included) take "brute force" to mean naively checking every solution candidate. If you're doing something clever like reducing the search space and/or lowering the big-O, that doesn't seem "brute." Even if you're throwing dozens of core-years at the problem, that seems like "force" but not "brute."

I can't think of anything snappy, though. "Clever brute force" is the best I've got, and it's a mouthful. I tried looking for antonyms for "brute," the options aren't great. Well-bred? Polished? Humanitarian?