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

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 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.

Number of Pages in PDF File: 7

Keywords: Gielis super-formula, supershapes, Simulated annealing, Particle Swarm method, Repulsive Particle Swarm method of Global optimization, nonlinear programming, multiple sub-optimum, global, local optima, fit, data, empirical, estimation, parameters, curve fitting, Shape Recovery

JEL Classification: C15, C63

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