On classes of functions for which No Free Lunch results hold
Information Processing Letters
Focused no free lunch theorems
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Two broad classes of functions for which a no free lunch result does not hold
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartII
A study of some implications of the no free lunch theorem
Evo'08 Proceedings of the 2008 conference on Applications of evolutionary computing
No free lunch theorems for optimization
IEEE Transactions on Evolutionary Computation
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The Sharpened No Free Lunch theorem states that all optimization algorithms have the same performance on sets of functions that are closed under permutation, independently of the considered performance measure. However, not all performance measures are informative on how fast or how accurately an algorithm can solve a given problem. In this paper we focus on a particular performance measure, called optimization speed, that quantifies how fast a search algorithm is able to find an optimal solution, and we try to characterize the set of functions on which all possible search algorithms have the same optimization speed. We call fair these sets, and we prove some results about their structure, the number of such sets and the computational complexity of checking fairness.