An efficient memetic genetic programming framework for symbolic regression

Background Symbolic regression is one of the most common applications of genetic programming (GP), which is a popular evolutionary algorithm in automatic computer program generation. Despite existing success of GP on symbolic regression, the accuracy and efficiency of GP can still be improved especially on complicated symbolic regression problems, enabling GP to be applied to more fields. Purpose This paper proposes a novel memetic GP framework to improve the accuracy and search efficiency of GP on complicated symbolic regression problems. The proposed framework consists of two components: feature construction and feature combination. The first component focuses on constructing diverse features. The second component aims to filter redundant features and linearly combines these independent features. Methods The first component (feature construction) focuses on constructing polynomial features derived from polynomial functions, and evolves features by a GP solver. In addition, a gradient-based nonlinear least squares algorithm named Levenberg-Marquardt (LM) is embedded in the second component (feature combination) to locally adjust the weights of independent features. A filtering mechanism is put forward to discard redundant features in the second component. Hence, the polynomial features and evolved features can work together in the framework to improve the performance of GP. Results Experimental results demonstrate that the proposed framework offers enhanced performance compared with several state-of-the-art algorithms in terms of accuracy and search efficiency on nine benchmark regression problems and three real-world regression problems. Conclusion In this study, a novel memetic genetic programming framework is proposed to improve the performance of GP on symbolic regression. Experimental results demonstrate that the proposed framework can improve the accuracy and search efficiency of GP on complicated symbolic regression problems compared with four state-of-the-art algorithms.