A new decoding method of the grammatical evolution

GE (grammatical Evolution) is an evolutionary algorithm that evolves programs in an arbitrary language using a variable-length binary string. The binary genome determines which production rules from the grammar definition of the Backs-Naur form(BNF) are used for the program in the genotype-phenotype mapping process. However, the matter relating to the completeness of individual phenotype throughout population formation isn't well self-addressed, so limiting both the convergence speed and the accuracy of the evaluations to some extent. In this paper, we propose an improved GE algorithm that aims to guarantee the completeness of individual phenotypes during initialization as well as subsequent evolution. A comparison of the improved algorithm (IGE) with the classical GE algorithm (CGE) and NGE(integer-coded grammatical evolution) conducted on the symbolic regression problems shows that the improved algorithm (IGE) not only reduces the search space and improves the accuracy of the algorithm, but also speeds up the convergence of the algorithm in constructing both. Definition 1. “Incomplete”: An individual is called an incomplete individual if its corresponding sentential form contains a non-terminal symbol, and its corresponding mapping process is called incomplete mapping. Definition 2. "Recursive" production rule: Refers to the BNF in which the same non-terminal symbol appears on the left and right sides of the production rule. Definition 3. Combined production rule: For a production rule with a non-terminal symbol in the right part, if it can be followed by only one type of production rule, it is said that the production rule and its subsequent followable production rule are combined production rules. Definition 4. Non-combined production rule: Production rule except for combined production rule