Evolutionary algorithms are an important branch of soft computing, being able to provide approximate solutions to problems in a reasonable amount of time. The underlying principle can be realized in an almost unlimited number of ways. This paper presents four main variants of evolutionary algorithms, and a method of running them in a topology consisting of multiple populations. The resources given to each population and migration are altered dynamically throughout the test, based on the effectiveness they show. Along with evolutionary methods, the solutions are also adjusted by gradient-based numerical optimization, in our case the Levenberg-Marquardt algorithm. These steps are added to the evolutionary processes as an extension, resulting in what are called memetic algorithms. The specific application for these methods here is optimizing fuzzy rule-bases, thereby making inference systems better at emulating a desired behavior, such as modeling a certain objective function. ©2010 IEEE.