# When and Why Metaheuristics Researchers Can Ignore "No Free Lunch" Theorems

## TL;DR

This paper clarifies misconceptions about the No Free Lunch theorems, providing counterexamples and arguing that in many practical cases, researchers can disregard NFL results when designing algorithms.

## Contribution

It offers new counterexamples and a nuanced interpretation of NFL, challenging common beliefs and clarifying when NFL theorems are relevant or ignorable in practice.

## Key findings

- Counterexamples where NFL does not apply
- Misunderstandings about NFL implications clarified
- Justification for ignoring NFL in many real-world scenarios

## Abstract

The No Free Lunch (NFL) theorem for search and optimisation states that averaged across all possible objective functions on a fixed search space, all search algorithms perform equally well. Several refined versions of the theorem find a similar outcome when averaging across smaller sets of functions. This paper argues that NFL results continue to be misunderstood by many researchers, and addresses this issue in several ways. Existing arguments against real-world implications of NFL results are collected and re-stated for accessibility, and new ones are added. Specific misunderstandings extant in the literature are identified, with speculation as to how they may have arisen. This paper presents an argument against a common paraphrase of NFL findings -- that algorithms must be specialised to problem domains in order to do well -- after problematising the usually undefined term "domain". It provides novel concrete counter-examples illustrating cases where NFL theorems do not apply. In conclusion it offers a novel view of the real meaning of NFL, incorporating the anthropic principle and justifying the position that in many common situations researchers can ignore NFL.