Adaptive Evolution Strategy for Symbolic Regression

This paper presents an adaptive evolutionary strategy that combines a genetic algorithm with an evolution strategy to solve symbolic regression problems. Symbolic regression aims to determine a regression model. Although genetic programming has been widely used to solve this problem in the past, it has to choose coefficients from a set of randomly selected constants, which prohibits gradual searching towards optimal or near optimal coefficients. To address this limitation, the proposed technique leverages the strengths of an evolution strategy in evolving coefficients and a genetic algorithm in evolving the rest of functional forms. In each learning step, the evolution strategy gradually adjusts the values of coefficients based on fitness values. Experimental results on symbolic regression problems demonstrate that the proposed technique outperforms traditional genetic programming, with statistically significant improvement demonstrated through a hypothesis test. With 95% confidence, the latter incurs the average error 1.81 times that of our proposed method.