Evolutionary algorithms

Search by breeding. The system starts with a population of random, mostly bad solutions, scores each one, discards the worst, combines the best, and adds small mutations to stop the process settling on a dead end. Repeat for enough generations and a strong answer surfaces.

Use it when the possible combinations run into the billions and no analysis can work through them: scheduling a fleet, laying out a warehouse, designing a component with competing constraints. It does not promise the perfect answer. It finds a very good one in a space where nothing else finishes at all.