Algoritmos genéticos: uso de lógica nebulosa e análise de convergência por cadeia de Markov

摘要

In this work, the Markov chain will be the tool used in the modeling and analysis ofconvergence of the genetic algorithm, both the standard version as for the other versionsthat allows the genetic algorithm. In addition, we intend to compare the performance ofthe standard version with the fuzzy version, believing that this version gives the genetic algorithma great ability to find a global optimum, own the global optimization algorithms.The choice of this algorithm is due to the fact that it has become, over the past thirty yares,one of the more importan tool used to find a solution of de optimization problem. Thischoice is due to its effectiveness in finding a good quality solution to the problem, consideringthat the knowledge of a good quality solution becomes acceptable given that theremay not be another algorithm able to get the optimal solution for many of these problems.However, this algorithm can be set, taking into account, that it is not only dependent onhow the problem is represented as but also some of the operators are defined, to the standardversion of this, when the parameters are kept fixed, to their versions with variablesparameters. Therefore to achieve good performance with the aforementioned algorithmis necessary that it has an adequate criterion in the choice of its parameters, especially therate of mutation and crossover rate or even the size of the population. It is important toremember that those implementations in which parameters are kept fixed throughout theexecution, the modeling algorithm by Markov chain results in a homogeneous chain andwhen it allows the variation of parameters during the execution, the Markov chain thatmodels becomes be non - homogeneous. Therefore, in an attempt to improve the algorithmperformance, few studies have tried to make the setting of the parameters throughstrategies that capture the intrinsic characteristics of the problem. These characteristicsare extracted from the present state of execution, in order to identify and preserve a patternrelated to a solution of good quality and at the same time that standard discarding oflow quality. Strategies for feature extraction can either use precise techniques as fuzzytechniques, in the latter case being made through a fuzzy controller. A Markov chain isused for modeling and convergence analysis of the algorithm, both in its standard versionas for the other. In order to evaluate the performance of a non-homogeneous algorithmtests will be applied to compare the standard fuzzy algorithm with the genetic algorithm,and the rate of change adjusted by a fuzzy controller. To do so, pick up optimizationproblems whose number of solutions varies exponentially with the number of variables