A genetic algorithm for fitting Lorentzian line shapes in Mössbauer spectra

Abstract

A genetic algorithm was implemented for finding an approximative solution to the problem of fitting a combination of Lorentzian lines to a measured Mössbauer spectrum. This iterative algorithm exploits the idea of letting several solutions (individuals) compete with each other for the opportunity of being selected to create new solutions (reproduction). Each solution was represented as a string of binary digits (chromosome). New individuals were created by pairwise exchanging bits in the binary representations of two selected solutions (crossover). In addition, the bits in the new solutions may be switched randomly from zero to one or conversely (mutation). The input of the program that implements the genetic algorithm consists of the measured spectrum, the maximum velocity, the peak positions and the expected number of Lorentzian lines in the spectrum. Each line is represented with the help of three variables, which correspond to its intensity, full line width at half maxima and peak position. An additional parameter was associated to the background level in the spectrum. A χ 2 test was used for determining the quality of each parameter combination (fitness). The results of the genetic algorithm have been compared with those obtained by a widely used commercial program. The preliminary results obtained seem to be very promising and encourage to further development of the algorithm and its implementation.