Exact methods will always find the global optimum and recognize it too. That being said, they don't scale (not even beyond toy problems) and are therefor mostly useless.
The brute force algorithm creates and evaluates every possible solution.
Notice that it creates a search tree that explodes as the problem size increases. Brute force is mostly unusable for a real-world problem due to time limitations.
Branch and bound is an improvement over brute force, as it prunes away subsets of solutions which cannot have a better solution than the best solution already found at that point.
Notice that it (like brute force) creates a search tree that explodes (but less than brute force) as the problem size increases. Branch and bound is mostly unusable for a real-world problem due to time limitations.
It can determine a lower bound of problem. A lower bound is a score which is proven to be higher than the optimal score of a problem. So it gives an indication of the quality of any best solution found for that problem: the closer to best score is to the lower bound, the better.