New Particle Swarm Optimizer Algorithm with Chaotic Maps for Combinatorial Global Optimization Problems. An Application to the Deconvolution of Mössbauer Spectra

In this chapter, we present a novel method for addressing global optimization problems inspired by evolutionary algorithms found in nature. We integrate the Comprehensive Learning Particle Swarm Optimization (CLPSO) algorithm with random value generation based on chaotic maps. The resulting algorithm is applied to the computationally complex task of deconvoluting Mossbauer spectra. We implement ten chaotic maps to generate random values and compare their performance with traditional random number generators. Through experiments, we demonstrate that the developed algorithm excels in exploring the search space and exhibits fast intensification in finding the global minimum. In addition, we perform a comprehensive review of existing solutions to the Mossbauer spectrum deconvolution problem, highlighting the scarce availability of developments in this area. We also present a user-friendly program designed with an intuitive interface to facilitate the deconvolution process by Spector Mossbauer. This program will be freely distributed without operational restrictions. Experimental validation is performed on Mossbauer spectra generated using the developed program and those obtained by experimental means, affirming the efficiency of the new algorithm conceived.