Least Squares Fitting of Chacón-Gielis Curves by the Particle Swarm Method of Optimization

Mishra, SK (2006): Least Squares Fitting of Chacón-Gielis Curves by the Particle Swarm Method of Optimization.

Abstract

Ricardo Chacón generalized Johan Gielis's superformula by introducing elliptic functions in place of trigonometric functions. In this paper an attempt has been made to fit the Chacón-Gielis curves (modified by various functions) to simulated data by the least squares principle. Estimation has been done by the Particle Swarm (PS) methods of global optimization. The Repulsive Particle Swarm optimization algorithm has been used. It has been found that although the curve-fitting exercise may be satisfactory, a lack of uniqueness of Chacón-Gielis parameters to data (from which they are estimated) poses an insurmountable difficulty to interpretation of findings.

• Item Type: MPRA Paper
• Language: English
• Keywords: Least squares multimodal nonlinear curve-fitting; Ricardo Chacón; Jacobian Elliptic functions; Weierstrass ; Gielis super-formula; supershapes; Particle Swarm method; Repulsive Particle Swarm method of Global optimization; nonlinear programming; multiple sub-optima; global; local optima; fit; empirical; estimation; cellular automata; fractals
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C44 - Operations Research ; Statistical Decision Theory; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis

References

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