Simple explanation of the no-free-lunch theorem and its implications

Abstract

The no-free-lunch theorem of optimization (NFLT) is an impossibility theorem telling us that a general-purpose, universal optimization strategy is impossible. The only way one strategy can outperform another is if it is specialized to the structure of the specific problem under consideration. Since optimization is a central human activity, an appreciation of the NFLT and its consequences is essential. In this paper, we present a framework for conceptualizing optimization that leads to a simple but rigorous explanation of the NFLT and its implications.