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.

中文翻译：

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用于符号回归的有效模因遗传程序设计框架

背景

符号回归是遗传编程（GP）的最常见应用之一，它是自动计算机程序生成中的一种流行的进化算法。尽管GP在符号回归方面已经取得了成功，但是GP的准确性和效率仍然可以提高，尤其是在复杂的符号回归问题上，这使得GP可以应用于更多领域。

目的

本文提出了一种新颖的模因GP框架，以提高GP在复杂符号回归问题上的准确性和搜索效率。所提出的框架包括两个部分：特征构造和特征组合。第一部分着重于构建各种功能。第二个组件旨在过滤冗余特征并线性组合这些独立特征。

方法

第一个组件（特征构造）着重于构造从多项式函数派生的多项式特征，并通过GP求解器扩展特征。此外，名为Levenberg-Marquardt（LM）的基于梯度的非线性最小二乘算法被嵌入到第二个组件（特征组合）中，以局部调整独立特征的权重。提出了一种过滤机制来丢弃第二个组件中的冗余功能。因此，多项式特征和演化特征可以在框架中协同工作，以提高GP的性能。

结果

实验结果表明，相对于几种最新算法，该框架在9个基准回归问题和3个实际回归问题上的准确性和搜索效率方面均提供了增强的性能。

结论

在这项研究中，提出了一种新颖的模因遗传程序设计框架，以提高符号回归上GP的性能。实验结果表明，与四种最新算法相比，该框架可以提高GP在复杂符号回归问题上的准确性和搜索效率。