Properties of symmetric fitness functions

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. Categories and Subject Descriptors F.2.2 [Nonnumerical Algorithms and Problems]: Computations on discrete structures General Terms Theory Keywords Symmetric fitness functions, encoding scheme, search space analysis, problem difficulty measures, Walsh analysis

• Type: Conference
• Year: 2006
• Where: GECCO
• Authors: Sung-Soon Choi, Yung-Keun Kwon, Byung Ro Moon
• Keywords: GECCO 2006, Optimization, Problem Difficulty Measures, Symmetric Fitness Functions, Symmetric Functions