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Performance of Differential Evolution Method in Least Squares Fitting of Some Typical Nonlinear Curves

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Abstract

No foolproof method exists to fit nonlinear curves to data or estimate the parameters of an intrinsically nonlinear function. Some methods succeed at solving a set of problems but fail at the others. The Differential Evolution (DE) method of global optimization is an upcoming method that has shown its power to solve difficult nonlinear optimization problems. In this study we use the DE to solve some nonlinear least squares problems given by the National Institute of Standards and Technology (NIST), US Department of Commerce, USA and some other challenge problems posed by the CPC-X Software (the makers of the AUTO2FIT software). The DE solves the test problems given by the NIST and most of the challenge problems posed by the CPC-X, doing marginally better than the AUTO2FIT software in a few cases.

Suggested Citation

  • Mishra, SK, 2007. "Performance of Differential Evolution Method in Least Squares Fitting of Some Typical Nonlinear Curves," MPRA Paper 4634, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:4634
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    File URL: https://mpra.ub.uni-muenchen.de/4656/1/MPRA_paper_4656.pdf
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    References listed on IDEAS

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    1. Goffe, William L. & Ferrier, Gary D. & Rogers, John, 1994. "Global optimization of statistical functions with simulated annealing," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 65-99.
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    Cited by:

    1. repec:ebl:ecbull:v:3:y:2007:i:51:p:1-13 is not listed on IDEAS
    2. Sudhanshu Mishra, 2007. "Least squares estimation of joint production functions by the differential evolution method of global optimization," Economics Bulletin, AccessEcon, vol. 3(51), pages 1-13.
    3. Mishra, SK, 2008. "Construction of composite indices in presence of outliers," MPRA Paper 8874, University Library of Munich, Germany.
    4. Sudhanshu K. MISHRA, 2016. "Shapley Value Regression and the Resolution of Multicollinearity," Journal of Economics Bibliography, KSP Journals, vol. 3(3), pages 498-515, September.

    More about this item

    Keywords

    Nonlinear least squares; curve fitting; Differential Evolution; global optimization; AUTO2FIT; CPC-X Software; NIST; National Institute of Standards and Technology; test problems;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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