The no free lunch theorem and the human-machine interface

Abstract

The no free lunch (NFL) theorem tells us that without any structural assumptions on an optimization problem, no algorithm can perform better on average than blind search. Although for most such impossibility theorems, the proofs are lengthy, difficult, and often not at all intuitive, we can get a feel for the NFL theorem by considering the proverbial needle in a haystack problem. Clearly, in this instance, no algorithm has any better chance of finding the optimum than blind search. The title also refers to the human-machine interface (HMI). Traditionally, this term has had the narrow meaning of facilitating communication between humans and computing machines, such as via the graphical user interface or head-up displays. But as technology advances, this communication interface will also evolve. Certainly, in the future we can see voice, fuzzy, and natural language inputs and outputs. Here, however, we are using the term in an even broader sense: to demarcate the dividing line between what humans do and what machines do in problem solving or optimization. The twin purposes of the article are to explore the implications of NFL and to address the proper allocation of natural and computational intelligence in optimization problem solving.