Using Multiple Populations of Memetic Algorithms for Fuzzy Rule-base Optimization Zsolt Dányádi * , Krisztián Balázs ** and László T. Kóczy **,*** * Institute of Logistics, Electrical and Mechanical Engineering, Faculty of Engineering Sciences, Széchenyi István University, Győr, Hungary ** Department of Telecommunications and Media Informatics, Budapest University of Technology and Economics, Hungary *** Institute of Informatics, Electrical and Mechanical Engineering, Faculty of Engineering Sciences, Széchenyi István University, Győr, Hungary danyadi@sze.hu balazs@tmit.bme.hu koczy@tmit.bme.hu Abstract—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. I. INTRODUCTION Evolutionary algorithms are stochastic optimization processes, which attempt to find approximate solutions to a problem by altering parts of the solution candidates and creating new ones based on the previous. These candidates are known as individuals, and they comprise the population the algorithm works on. Each of the individuals describes a solution with the information stored in it, otherwise known as its genome. The genes of an individual range from representing parameter values to prescribing specific operations. In this paper, the task these algorithms were used for was to optimize the rule-base of a fuzzy inference system, making sure that its output matches the ideal values found in training and test samples as accurately as possible. The most common way to represent a specific evolutionary method is to split its main generation cycle into parts, also called operators, all of which describe a major step in creating the new generation of individuals. Such operators include making new individuals from existing ones (cloning or cross-over), and changing parts of old or newly created individuals (mutation). A most significant effect of evolutionary processes is that genes that correlate with better solutions spread throughout the population, a phenomenon known as genetic drift. This leads to convergence of the individuals, which is useful in that it aids worse members of the population with beneficial genes, but also negatively effects genetic diversity. Therefore it is preferable that a sufficient level of diversity be maintained, in order to help new solutions arise. Gradient-based numerical optimization is another technique that is employed here, in conjunction with the evolutionary algorithms. These additions can be demanding on computational cost, but are more suited to approximating objective functions than the relatively undirected evolutionary processes. This paper, as a continuation of our previous works [1][12][13][14], compares various combinations of these algorithms with a dynamic multi-population approach. The multiple populations evolve independently, but at certain intervals they trade individuals via a topology of migration routes. The populations may use arbitrary evolutionary methods and parameters, which, along with random factors, makes them exhibit different convergence properties as the simulation progresses. Since certain populations use the allotted computation time more effectively with regards to increasing the fitness values of solutions, it is reasonable to base the distribution of time on the expected performance of each population. We employ a method of keeping track of the effectiveness and allocating computation time accordingly. The properties of migration routes are handled in much the same way as populations are, allowing migrations that are more beneficial to the destination population to copy over individuals more frequently. The goal of the paper is to provide a comparison between static and dynamically adjusted multi-population topologies, as well as the single- population version of each algorithm. The next section details the four evolutionary algorithms that make up the topologies of the multi- population processes, while the third one presents the gradient-based numerical optimization that is also used as a helpful extension. The fourth section describes how the multi-population topologies were set up, and the way the dynamic allocation of time between them took place. The fifth talks about the fuzzy inference methods that use the individuals generated by the evolutionary algorithms, and also the CINTI 2010  11th IEEE International Symposium on Computational Intelligence and Informatics  18–20 November, 2010  Budapest, Hungary 978-1-4244-9280-0/10/$26.00 ©2010 IEEE - 113 -