Optimal
Part of speech: adjective
Definition: The best, most favourable or desirable, especially under some restriction # Describing a search algorithm that always returns the best result.
Example sentence: The Cowles Commission was the optimal environment for the type of research that I wanted to do.
Optimum
Part of speech: noun
Definition: The best or most favorable condition, or the greatest amount or degree possible under specific circumstances.
Part of speech: adjective
Definition: best or most advantageous; surpassing all others
Example sentence: The optimum telephone is one that I think some day is gonna be embedded behind your ear. It's gonna have an extraordinarily powerful computer running the cell phone.