Radiation Measurements 41 (2006) 897 – 902 www.elsevier.com/locate/radmeas Finding model parameters: Genetic algorithms and the numerical modelling of quartz luminescence Grzegorz Adamiec a , Andrzej Bluszcz a , Richard Bailey b , Marta Garcia-Talavera c , ∗ a Department of Radioisotopes, Institute of Physics, Silesian University of Technology, ul. Krzywoustego 2, 44-100 Gliwice, Poland b Department of Geography, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK c LIBRA, Centro I + D, Campus Miguel Delibes, 47011 Valladolid, Spain Received 10 August 2005; received in revised form 26 April 2006; accepted 24 May 2006 Abstract The paper presents an application of genetic algorithms (GAs) to the problem of finding appropriate parameter values for the numerical simulation of quartz thermoluminescence (TL). We show that with the use of GAs it is possible to achieve a very good match between simulated and experimentally measured characteristics of quartz, for example the thermal activation characteristics of fired quartz. The rate equations of charge transport in the numerical model of luminescence in quartz contain a large number of parameters (trap depths, frequency factors, populations, charge capture probabilities, optical detrapping probabilities, and recombination probabilities). Given that comprehensive models consist of over 10 traps, finding model parameters proves a very difficult task. Manual parameter changes are very time consuming and allow only a limited degree of accuracy. GAs provide a semi-automatic way of finding appropriate parameters. © 2006 Elsevier Ltd. All rights reserved. 1. Introduction Quartz remains the main material used for luminescence dat- ing. Numerical simulations of its properties can be a useful means for testing various measurement procedures. It was pos- sible to produce a plausible trap model (at least for homoge- nous samples) of this material. However, finding the optimal set of model parameters in luminescence simulations in quartz is always a challenge. The current work was undertaken in an attempt to automate and improve the process of finding the op- timal set of parameters. Originally, the numerical model did not allow for inter- grain variability of quartz properties. Bailey (2004) attempted to simulate a random variability of single grain properties by randomising the concentrations of various trapping levels. However, there still remains the question of finding the “real” variability for a given sample. ∗ Corresponding author. Current address: Consejo de Seguridad Nuclear, Justo Dorado 11, 28040 Madrid, Spain. E-mail address: grzegorz.adamiec@polsl.pl (G. Adamiec). 1350-4487/$ - see front matter © 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2006.05.005 The model under investigation is a band model of quartz with several electron and hole trapping centres and it is an extended model of Zimmermann (1971). The interaction between the centres and the charge trapped in them and present in the delo- calised bands results in a complex behaviour during irradiation, heating, and OSL measurements. Sensitivity changes resulting from irradiation and heating can be accommodated for by the appropriate selection of trap parameters and populations. The model is described by a set of first-order differential equations, which describe the time evolution of the electron and hole populations under a whole range of conditions includ- ing irradiation, heating, and illumination. Finding the set of trap parameters and trap populations that reflect the behaviour of real samples traditionally has been done by the modeller through a trial and error process. Considering the large number of parameters in question, this is a time-consuming procedure. Using such process, a good general model has been developed (Bailey, 2001). Applying traditional deterministic optimum search methods, such as the Levenberg–Marquardt method, to finding model parameters inevitably leads to problems associated with local minima since such algorithms usually do not work well in