Studying Grammatical Evolution’s Mapping Processes for Symbolic Regression Problems

Abstract

Grammatical Evolution (GE) is a variant of Genetic Programming (GP) that uses a BNF-grammar to create syntactically correct solutions. GE is composed of the following components: the Problem Instance, the BNF-grammar (BNF), the Search Engine (SE) and the Mapping Process (MP). GE allows creating a distinction between the solution and search spaces using an MP and the BNF to translate from genotype to phenotype, that avoids invalid solutions that can be obtained with GP. One genotype can generate different phenotypes using a different MP. There exist at least three MPs widely used in the art-state: Depth-first (DF), Breadth-first (BF) and Π Grammatical Evolution (piGE). In the present work DF, BF, and piGE have been studied in the Symbolic Regression Problem. The results were compared using a statistical test to determine which MP gives the best results.