Beyond No Free Lunch: Realistic Algorithms for Arbitrary Problem Classes

We show how the necessary and sufficient conditions for the NFL to apply can be reduced to the single requirement of the set of objectives under consideration being closed under permutation, and quantify the extent to which a set of objectives not closed under permutation can give rise to a performance difference between two algorithms. Then we provide a more refined definition of performance under we to show that revisiting algorithms are always trumped by enumerative ones.