I'm pretty sure MIT teaches some sort of AI 101.* CSP, local search (and genetic algorithms) is what you're looking for.
Also make sure to check out the paper by Wolpert and Macready on "no free lunch in search and optimization" for a perspective on "best way"
*I also think it's a non-trivial connection to make that these types of problems are covered in AI or at least that's the feedback I get from students. "Oh didn't expect this search stuff thought it was about brainnnnnnz"
I think a lot of that classic work on search, heuristics, and problem-solving has been overshadowed lately by the emphasis on more 'modern' statistical machine learning. There's definitely value to both perspectives.
*I also think it's a non-trivial connection to make that these types of problems are covered in AI or at least that's the feedback I get from students. "Oh didn't expect this search stuff thought it was about brainnnnnnz"
Pretty cool read though, thx for posting.