Locality in Continuous Fitness-Valued Cases and Genetic Programming Difficulty
It is commonly accepted that a mapping is local if it preserves neighbourhood. In Evolutionary Computation, locality is generally described as the property that neighbouring genotypes correspond to neighbouring phenotypes. Locality has been classified in one of two categories: high and low locality. It is said that a representation has high locality if most genotypic neighbours correspond to phenotypic neighbours. The opposite is true for a representation that has low locality. It is argued that a representation with high locality performs better in evolutionary search compared to a representation that has low locality. In this work, we explore, for the first time, a study on Genetic Programming (GP) locality in continuous fitnessvalued cases. For this, we extended the original definition of locality (first defined and used in Genetic Algorithms using bitstrings) from genotype-phenotype mapping to the genotype-fitness mapping. Then, we defined three possible variants of locality in GP regarding neighbourhood. The experimental tests presented here use a set of symbolic regression problems, two different encoding and two different mutation operators. We show how locality can be studied in this type of scenarios (continuous fitness-valued cases) and that locality can successfully been used as a performance prediction tool.
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