a well-defined, formalized process (an algorithm) which eventually converges to a local (or global) optimum.
Back-tracking is a fundamental notion of returning back to the last fork from a dead-end or when a limit for depth is exceeded. It is how to recover from failures and to avoid of getting lost.
An informed search process which is guided by a heuristic - a procedure that generates highly informed guesses.
Converges much faster than a brute-force enumerating, or a "blind" exploration processes.
Pruning of a search space =
Pruning is removing of branches which, according to some heuristic learned by a prior experience, is known to be empty or sub-optimal or leading to a dead-end.
Pruning is also heuristic-based.