Versatile function in GPA

The paper, devoted to continuous versatile function application in the Genetic Programming Algorithm (GPA), begins with a discussion of similarities between GPA with versatile function and neural network. Then, the function set influence on GPA efficiency is discussed. In the next part, there is described a hybrid evolutionary algorithm that combines GPA for structure development and Evolutionary Strategy (ES) for parameters and constant optimization; which is herein much more significant than in the standard GPA. There is also discussed the setting of parameters of this hybrid algorithm and due to a different function set. The original idea of a versatile function, which origins come from the area of fuzzy control systems, is formulated and explained. Four different implementations of this versatile function are discussed. On the base of experiments with the hybrid evolutionary algorithm providing symbolic regression of precomputed Lorenz attractor system data representing its dynamic behaviour; the comparison of three variants of versatile functions was formulated. The paper also presents ways how to set up hybrid evolutionary algorithm parameters like population sizes as well as limits of maximal population numbers for both algorithms: GPA for structural development and nested ES for parameters optimization. The versatile function concept is applicable but it requires the hybrid evolutionary algorithm use as it is explained in the paper.