An improved semantic schema modeling for genetic programming

Abstract

A considerable research effort has been performed recently to improve the power of genetic programming (GP) by accommodating semantic awareness. The semantics of a tree implies its behavior during the execution. A reliable theoretical modeling of GP should be aware of the behavior of individuals. Schema theory is a theoretical tool used to model the distribution of the population over a set of similar points in the search space, referred by schema. There are several major issues with relying on prior schema theories, which define schemata in syntactic level. Incorporating semantic awareness in schema theory has been scarcely studied in the literature. In this paper, we present an improved approach for developing the semantic schema in GP. The semantics of a tree is interpreted as the normalized mutual information between its output vector and the target. A new model of the semantic search space is introduced according to semantics definition, and the semantic building block space is presented as an intermediate space between semantic and genotype ones. An improved approach is provided for representing trees in building block space. The presented schema is characterized by Poisson distribution of trees in this space. The corresponding schema theory is developed for predicting the expected number of individuals belonging to proposed schema, in the next generation. The suggested schema theory provides new insight on the relation between syntactic and semantic spaces. It has been shown to be efficient in comparison with the existing semantic schema, in both generalization and diversity-preserving aspects. Experimental results also indicate that the proposed schema is much less computationally expensive than the similar work.