Aplicação da transformada discreta Wavelet no controle da diversidade populacional nos algoritmos genéticos em problemas de otimização

Abstract

In modern society marked by globalization and consumption, the rational and sustainable use of natural resources and the constant quest for higher quality and lower costs in production processes are getting more and more importance. In both aspects, the use of optimization tools is salutary. In this scenario highlights the technique of genetic algorithms, which are search algorithms based on Darwin's theory of evolution and genetic mutation of Mendel. Genetic algorithms work with a set of possible solutions (individuals) to the problem, which evolve according to some criteria for genetic ideally converge to the best solution. Despite provide satisfactory solutions even for complex problems and maybe therefore are widely used, this technique can suffer from convergence problems. In many situations, individuals can set the focus on certain regions of the search space that do not contain the best solution, meaning a premature convergence of the method. This problem of concentration of individuals in the search space represents what is called loss of population diversity. This study addresses the issue of population diversity of the AG from the perspective of the size of the choice set of possible solutions (the population) and the control of its diversity throughout the evolutionary process. To this end, proposes the use of discrete wavelet transform to a set of individuals in order to create a set of approximation by eliminating the correlation between its individuals. The technique of k-means clustering is used to group the individuals who suffer joint action of the wavelet transform. The proposed approach, called AGkW was tested on benchmark problems commonly used for evaluation of global search techniques. Results show that in general, the method proposed behave effectively to the problems addressed and tested as good as or superior as compared to the AG. In particular, a number of problems tested, the method AGkW performance was about 50% higher with only 25% of the average objective function evaluations, approximately.