Beyond no free lunch: realistic algorithms for arbitrary problem classesJames Marshall, Thomas Hinton, Beyond no free lunch: realistic algorithms for arbitrary problem classes. CSTR-09-003, University of Bristol. July 2009. No electronic version available. External information
We show how the necessary and sufficient conditions for the NFL to apply can be reduced to the single requirement of the set of objective functions 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 which we show that revisiting algorithms are always trumped by enumerative ones.