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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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  • Mishra, SK


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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 465.

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Date of creation: 02 Jul 2006
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Handle: RePEc:pra:mprapa:465

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Related research

Keywords: Gielis curves; superformula; nonlinear curve-fitting; Least squares; multi-modal; local optima; global optimization; simulated annealing; particle swarm; parameters estimation;

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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.


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