What is the most efficient scheduling algorithm?

Scheduling is an optimisation problem. There are “no free lunch” theorems about optimisation problems saying that there is no “best” algorithm for all possible problems.

Intuitively, “efficient” algorithms beat simple checking all of possible permutations for a specific class of problems by exploiting features of the structure of problems in that class.

So if you have a specific scheduling or optimisation problem to solve, start by figuring out if it belongs to a well-known class of problems, and then look for the algorithms developed to deal with this class.