Symbolic Regression Using Genetic Programming with Chaotic Method-Based Probability Mappings

Abstract

In this study, we propose a novel pre-learning approach for genetic programming (GP) that aims to investigate the effect of the probability of being selected for each operator. Furthermore, we present a technique that combines chaos theory and searches for a relatively good possibility mapping for each operator using one-dimensional chaotic mapping. We conducted several sets of comparative experiments on real-world data to test the viability of the proposal. These experiments included comparisons with conventional GP, examination of the impact of various chaotic mappings on the proposed algorithm, and implementation of different optimization strategies to find the relative optimal probability mapping. The experimental results demonstrate that the proposed method can achieve better results than conventional GP in the tested dataset, without considering the total quantitative calculation amount. Through statistical tests, it has been proven that the proposed method is significantly different from the conventional method. However, the discussion regarding the circumstances under which the proposed method can obtain better results when the total calculation amount is limited is not yet fully explored due to the small-scale nature of the experiments. Our future studies will focus on improving and fully discussing this idea.