Model approach to grammatical evolution: theory and case study

Many deficiencies with grammatical evolution (GE) such as inconvenience in solution derivations, modularity analysis, and semantic computing can partly be explained from the angle of genotypic representations. In this paper, we deepen some of our previous work in visualizing concept relationships, individual structures and total evolutionary process, contributing new ideas, perspectives, and methods in these aspects; reveal the principle hidden in early work so that to develop a practical methodology; provide formal proofs for issues of concern which will be helpful for understanding of mathematical essence of issues, establishing of an unified formal framework as well as practical implementation; exploit genotypic modularity like modular discovery systematically which for the lack of supporting mechanism, if not impossible, is done poorly in many existing systems, and finally demonstrate the possible gains through semantic analysis and modular reuse. As shown in this work, the search space and the number of nodes in the parser tree are reduced using concepts from building blocks, and concepts such as the codon-to-grammar mapping and the integer modulo arithmetic used in most existing GE can be abnegated.