A Genetic Algorithm -Based Method for Solving an Inverse Problem. Application to the Estimation of the Particle Size Distribution in Colloidal Systems

CLEMENTI, L.A.; GUGLIOTTA, L.M.; VEGA, J.R.

Rosario

Congreso; RPIC 2009 - XIII Reunión de Trabajo en Procesamiento de la Información y Control; 2009

Dynamic Light Scattering (DLS) is an optical technique widely used to estimate the particle size distribution (PSD) in colloidal systems. The PSD estimation requires to solve an ill-conditioned inverse problem through some regularization method. In this paper a new method to estimate the PSD of a colloidal system from DLS measurement is proposed. The method utilizes a two-steps optimiza-tion algorithm, which is able to estimate an arbi-trary-shaped PSD on the basis of the average diame-ters derived from DLS measurements. In the first step, a genetic algorithm (GA) is used to find the lo-cation of the global minimum among several possible local minima. In the second step, a sequential quad-ratic programming (SQP) method is used to deter-mine the optimum solution by refining the first step estimate. The proposed method was tested with both simulated and experimental examples. Additionally, each PSD was estimated through: i) a GA-based method that assumes a PSD of known shape; and ii) a Tikhonov regularization method. The results showed that the PSD estimated through the GA-based methods are more accurate than those ob-tained with more standard regularization methods used for solving inverse problems.