Properties of symmetric fitness functions

Abstract

The properties of symmetric fitness functions are investigated. We show that a well-known encoding scheme inducing symmetric functions has the non-synonymous property and the search spaces obtained from symmetric functions have the zero-correlation structures. The Walsh analysis reveals the properties of symmetric functions related to additive separability, problem difficulty measures and so on. Our results support the claim of other researchers that the search spaces with symmetry induce relatively difficult problems. The results also present some limitations of existing problem difficulty measures for symmetric fitness functions.