Parameter identification for symbolic regression using nonlinear least squares

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 gradient...

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Bibliographic Details
Published in:Genetic programming and evolvable machines 2020-09, Vol.21 (3), p.471-501
Main Authors: Kommenda, Michael, Burlacu, Bogdan, Kronberger, Gabriel, Affenzeller, Michael
Format: Article
Language:English
Subjects:
Algorithms
Artificial Intelligence
Benchmarks
Biomedical Engineering and Bioengineering
Compilers
Computer Science
Electrical Engineering
Genetic algorithms
Interpreters
Least squares
Machine learning
Optimization
Parameter identification
Programming
Programming Languages
Programming Techniques
Regression analysis
Regression models
Software Engineering/Programming and Operating Systems
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Summary: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.
ISSN:1389-2576
1573-7632
DOI:10.1007/s10710-019-09371-3