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. 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.

Keywords: Ricardo Chacón, Jacobian Elliptic functions, Weierstrass , Gielis super-formula, supershapes, Particle Swarm method, Repulsive Particle Swarm method of Global optimization, nonlinear programming, multiple sub-optimum, global, local optima, fit, empirical, estimation, cellular automata, fractals

JEL Classifications: C15, C63

Working Paper Series