Uma técnica de programação genética gramatical e semântica para regressão simbólica

Abstract

Symbolic Regression (SR) is a modeling technique aimed at finding a complete expression, rather than just adjusting coefficients in a fixed model, as is done in conventional regression methods. SR involves automatically discovering the structure of a model from data, which can result in more accurate and interpretable solutions for complex problems. The use of Genetic Programming (GP) to solve SR problems is particularly advantageous because GP explores the solution space efficiently and ensures that the generated mathematical expressions are syntactically valid. Additionally, the use of context-free grammars (CFG) leads to Grammatical Genetic Programming (GGP), which allows for the definition of rules and boundaries within the solution space to be explored during regression. This is crucial in SR, where simplicity and interpretability of models are key factors. However, the unrestricted generation of candidates in SR methods often leads to redundant or irrelevant solutions. Semantic Genetic Programming (SGP), by considering the semantics of candidates during its operations, has shown the ability to avoid these issues across various approaches, enhancing both search efficiency and solution quality. This results in SR models that more accurately capture the intrinsic relationships within the data. Grammatical and Semantic Genetic Programming (GSGP) combines the context-free grammars of GGP with the use of semantics, further enhancing the ability to guide the search towards producing expressions that are both valid and semantically relevant to the problem at hand. In this study, GSGP is analyzed in depth, focusing on its recombination operator and considering different approaches and their effects on search and solution quality. We propose the Roulette Semantic Crossover (RSC) as a new recombination operator that creates a roulette among candidate solutions based on their semantics, increasing the likelihood of generating relevant new candidates. Furthermore, a parametric analysis of these operators and the technique’s performance is conducted on a benchmark set of problems developed to evaluate SR methods, highlighting the advantages and limitations of the proposed approach. RSC demonstrated robustness, achieving the highest area under the curve in Performance Profiles (PP) and obtaining the highest number of successes in the tests. These results indicate that GSGP is a promising approach for SR.