Improving Symbolic Regression through a semantics-driven framework

Abstract

The process of identifying analytical relationships among variables and responses in observed data is commonly referred to as Symbolic Regression (SR). Genetic Programming is one of the commonly used approaches for SR, which operates by evolving expressions. Such relationships could be explicit or implicit in nature, of which the former has been more extensively studied in literature. Even though extensive studies have been done in SR, the fundamental challenges such as bloat, loss of diversity and accurate determination of coefficients still persist. Recently, semantics and multi-objective formulation have been suggested as potential tools to alleviate these issues by building more intelligence in the search process. However, studies along both these directions have been in isolation and applied only to selected components of SR so far. In this paper, we intend to build a framework that integrates semantics deeper into more components of SR. The framework could be operated in conventional single objective as well as multi-objective mode and is capable of dealing with both explicit and implicit functions. Semantics are used in the proposed framework for improving compactness and diversity of expressions, crossover and local exploitation. Numerical experiments are presented on a set of benchmark problems to demonstrate the strengths of the proposed approach.