Deterministic Geometric Semantic Genetic Programming with Optimal Mate Selection

Abstract

To solve symbolic regression problems, 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. In the semantics-based crossover, offspring is created from its parental individuals so that the offspring can inherit the characteristics of the parents not structurally but semantically. Geometric Semantic GP (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, deterministic Geometric Semantic Crossover utilizing the information of the target semantics has been proposed. In conventional GSGP, ratios of convex combinations are determined at random. On the other hand, the deterministic crossover can use optimal ratios for affine combinations of parental individuals so that created offspring can be closest to the target solution. In these methods, parents which crossover operators will be applied to are selected based only on their fitness. In this paper, we propose a new selection method of parents for generating offspring which can approach to a target solution more efficiently. In this method, we select a pair of parents so that a distance between a straight line connecting the parents and a target point can be smallest in semantic space. We confirmed that our method showed better performance than conventional GSGP in several symbolic regression problems.