In this paper we analyze the effects of using nonlinear least squares for parameter identification of symbolic regression models and integrate it as local search mechanism in tree-based genetic programming. We employ the Levenberg–Marquardt algorithm for parameter optimization and calculate gradients via automatic differentiation. We provide examples where the parameter identification succeeds and fails and highlight its computational overhead. Using an extensive suite of symbolic regression benchmark problems we demonstrate the increased performance when incorporating nonlinear least squares within genetic programming. Our results are compared with recently published results obtained by several genetic programming variants and state of the art machine learning algorithms. Genetic programming with nonlinear least squares performs among the best on the defined benchmark suite and the local search can be easily integrated in different genetic programming algorithms as long as only differentiable functions are used within the models.

中文翻译：

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使用非线性最小二乘法进行符号回归的参数识别

在本文中，我们分析了使用非线性最小二乘法对符号回归模型进行参数识别的效果，并将其集成为基于树的遗传规划中的局​​部搜索机制。我们采用 Levenberg-Marquardt 算法进行参数优化并通过自动微分计算梯度。我们提供了参数识别成功和失败的示例，并强调了其计算开销。使用一套广泛的符号回归基准问题，我们证明了在遗传编程中加入非线性最小二乘法时性能的提高。我们的结果与最近发表的通过几种遗传编程变体和最先进的机器学习算法获得的结果进行了比较。