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Some Experiments on Fitting of Gielis Curves by Simulated Annealing and Particle Swarm Methods of Global Optimization

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Abstract

In this paper an attempt has been made to fit the Gielis curves (modified by various functions) to simulated data. The estimation has been done by two methods - the Classical Simulated Annealing (CSA) and the Particle Swarm (PS) methods - of global optimization. The Repulsive Particle Swarm (RPS) optimization algorithm has been used. It has been found that both methods are quite successful in fitting the modified Gielis curves to the data. However, the lack of uniqueness of Gielis parameters to data (from which they are estimated) is corroborated. From a technical viewpoint, this exercise may be considered as an application of CSA and RPS to extremely nonlinear least-squares curve-fitting to data that may exhibit a large number of local optima.

Suggested Citation

  • Mishra, SK, 2006. "Some Experiments on Fitting of Gielis Curves by Simulated Annealing and Particle Swarm Methods of Global Optimization," MPRA Paper 465, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:465
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    File URL: https://mpra.ub.uni-muenchen.de/465/1/MPRA_paper_465.pdf
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    Cited by:

    1. Mishra, SK, 2006. "Performance of Differential Evolution and Particle Swarm Methods on Some Relatively Harder Multi-modal Benchmark Functions," MPRA Paper 1743, University Library of Munich, Germany.
    2. Mishra, SK, 2006. "Global Optimization by Particle Swarm Method:A Fortran Program," MPRA Paper 874, University Library of Munich, Germany.

    More about this item

    Keywords

    Gielis curves; superformula; nonlinear curve-fitting; Least squares; multi-modal; local optima; global optimization; simulated annealing; particle swarm; parameters estimation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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