THE USE OF GENETIC ALGORITHMS IN THE NONLINEAR-REGRESSION OF IMMITTANCE DATA

A genetic algorithm (GA) approach to curve fitting of immittance data is presented. This approach offers a solution to all of the problems a ssociated with traditional non-linear regression of immittance data, s uch as multiple local minima, the inability to constrain the fitting p arameters, and the need for initial estimates of the fitting parameter s. The GA works with a 'population' of possible answers (e.g. sets of parameter values). Because of this, it does not require initial estima tes of the fitting parameters, but requires only the allowable range o f each parameter. Constraints are easily included by rejecting members of the population which fall outside the allowable range for one or m ore parameters. The fact that there is a population of answers and gra dients are not calculated, means that it is more difficult, but not im possible, for a GA to become trapped in a local minimum unlike the mor e conventional gradient methods. The fitting of simulated noisy Randle s data was used to illustrate the method. Populations of 100 individua ls were used. The genetic operators were mutation, crossover and a pai r of novel line operators. These were selected for use with probabilit ies, respectively, of 40, 40 and 20% each. A global fit to the data co uld be achieved within 20000 function evaluations which took 1 min on a 100-MHz 486 PC. Uncertainties were calculated numerically by locatin g a specified number of points which lay upon the 95% confidence hyper surface. The performance of the GA was compared to that of a quasi-New ton algorithm which calculated the gradients numerically. The quasi-Ne wton algorithm typically required approximately 2000 function evaluati ons to converge, but it often converged to a local minimum especially with noisier data. (C) 1998 Elsevier Science S.A. All rights reserved.