Geometric Semantic Genetic Programming Using External Division of Parents

In this paper, we focus on symbolic regression problems, in which we find functions approximating the relationships between given input and output data. If we do not have the knowledge on the structure (e.g. Degree) of the true functions, Genetic Programming (GP) is often used for evolving tree structural numerical expressions. In GP, crossover operator has a great influence on the quality of the acquired solutions. Therefore, various crossover operators have been proposed. 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. This operation corresponds to the internal division of two parents. This method can optimize solutions efficiently because the crossover operator always produces better solution than a worse parent. But, in GSGP, if the true function exists outside of two parents in semantic space, it is difficult to produce better solution than both of the parents. In this paper, we propose an improved GSGP which can also consider external divisions as well as internal ones. By comparing the search performance among several crossover operators in symbolic regression problems, we showed that our methods are superior to the standard GP and conventional GSGP.