No Free Lunch Theorem: A Review

The “No Free Lunch” theorem states that, averaged over all optimization problems, without re-sampling, all optimization algorithms perform equally well. Optimization, search, and supervised learning are the areas that have benefited more from this important theoretical concept. Formulation of the initial No Free Lunch theorem, very soon, gave rise to a number of research works which resulted in a suite of theorems that define an entire research field with significant results in other scientific areas where successfully exploring a search space is an essential and critical task. The objective of this paper is to go through the main research efforts that contributed to this research field, reveal the main issues, and disclose those points that are helpful in understanding the hypotheses, the restrictions, or even the inability of applying No Free Lunch theorems.