Deterministic Crossover Based on Target Semantics in Geometric Semantic Genetic Programming

Abstract

In this paper, we focus on solving symbolic regression problems, in which we find functions approximating the relationships between given input and output data. Genetic Programming (GP) is often used for evolving tree structural numerical expressions. Recently, new crossover operators based on semantics of tree structures have attracted many attentions for efficient search. In the semantics-based crossover, offspring is created from its parental individuals so that the offspring can be similar to the parents not structurally but semantically. Geometric Semantic Genetic Programming (GSGP) is a method in which offspring is produced by a convex combination of two parental individuals. In order to improve the search performance of GSGP, we propose an improved Geometric Semantic Crossover utilizing the information of the target semantics. In conventional GSGP, ratios of convex combinations are determined at random. On the other hand, our proposed method can use optimal ratios for affine combinations of parental individuals. We confirmed that our method showed better performance than conventional GSGP in several symbolic regression problems.