No Free Lunch and Benchmarks

We extend previous results concerning black box search algorithms, presenting new theoretical tools related to no free lunch (NFL) where functions are restricted to some benchmark (that need not be permutation closed), algorithms are restricted to some collection (that need not be permutation closed) or limited to some number of steps, or the performance measure is given. Minimax distinctions are considered from a geometric perspective, and basic results on performance matching are also presented.