The use of genetic algorithms in the non-linear regression of immittance data

Abstract

A genetic algorithm (GA) approach to curve fitting of immittance data is presented. This approach offers a solution to all of the problems associated with traditional non-linear regression of immittance data, such as multiple local minima, the inability to constrain the fitting parameters, and the need for initial estimates of the fitting parameters. The GA works with a `population' of possible answers (e.g. sets of parameter values). Because of this, it does not require initial estimates of the fitting parameters, but requires only the allowable range of each parameter. Constraints are easily included by rejecting members of the population which fall outside the allowable range for one or more parameters. The fact that there is a population of answers and gradients are not calculated, means that it is more difficult, but not impossible, for a GA to become trapped in a local minimum unlike the more conventional gradient methods. The fitting of simulated noisy Randles data was used to illustrate the method. Populations of 100 individuals were used. The genetic operators were mutation, crossover and a pair of novel line operators. These were selected for use with probabilities, respectively, of 40, 40 and 20% each. A global fit to the data could be achieved within 20 000 function evaluations which took 1 min on a 100-MHz 486 PC. Uncertainties were calculated numerically by locating a specified number of points which lay upon the 95% confidence hypersurface. The performance of the GA was compared to that of a quasi-Newton algorithm which calculated the gradients numerically. The quasi-Newton algorithm typically required approximately 2000 function evaluations to converge, but it often converged to a local minimum especially with noisier data.