Experiments on Estimation of the Parameters of Gielis Super-Formula by Simulated Annealing Method of Optimization

Abstract:     
In this paper an attempt has been made to estimate the parameters of Gielis superformula (modified by various functions). Simulated data have been used for this purpose. The estimation has been done by the method of simulated annealing. It has been found that the simulated annealing method is quite successful in fitting the modified Gielis curves to observed data. However, lack of empirical uniqueness of Gielis parameters has been corroborated. Due to this, it is quite unlikely to succeed at an estimation of the true parameters of Gielis superformula, more so when it is modified by an unknown function, and seek a scientific explanation behind them.

Keywords: Gielis super-formula, supershapes, Simulated annealing, nonlinear programming, multiple sub-optimum, global, local optima, genetic algorithm, Box's algorithm, Nelder-Mead, fit, data, empirical, estimation, parameters, curve fitting

JEL Classifications: C15, C63

Working Paper Series