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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.

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  • 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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    References listed on IDEAS

    as
    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.
    2. George E. P. Box, 1957. "Evolutionary Operation: A Method for Increasing Industrial Productivity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 6(2), pages 81-101, June.
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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. Mishra, SK, 2008. "Construction of composite indices in presence of outliers," MPRA Paper 8874, University Library of Munich, Germany.
    3. 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.
    4. S K Mishra, 2010. "A Brief History of Production Functions," The IUP Journal of Managerial Economics, IUP Publications, vol. 0(4), pages 6-34, November.
    5. 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.

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    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;
    All these keywords.

    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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