Rank Based Evolution of Real Parameters on Noisy Fitness Functions Evolving a Robot Neurocontroller Daniel Flores Departamento de Matemáticas Aplicadas y Sistemas Universidad Autónoma Metropolitana - Cuajimalpa Distrito Federal, Mexico daniel.flores108@gmail.com Jorge Cervantes Departamento de Matemáticas Aplicadas y Sistemas Universidad Autónoma Metropolitana - Cuajimalpa Distrito Federal, Mexico jcervantes@correo.cua.uam.mx Abstract— We present a Rank Based Evolutionary Algorithm for representations in the real numbers. We introduce a new Rank Based Selection operator and a new variation of a Rank Based Mutation that act in a representation using real numbers. The problem in which we tested the algorithm was to evolve a fixed topology feed forward artificial neural network that is used as a controller for a robot. In order to be successful, the robot must be able to use both proximity sensors and video input but there is some level of noise in them. The test results show how the proposed operators are suitable for this kind of problems where the fitness landscape is noisy and where little else is known about it. Keywords- Rank Based Evolution; Representation in Reals; Neurocontroller for Robot I. INTRODUCTION The balance between exploration and exploitation in evolutionary computation has always been an interesting topic because it is not easy to understand the effect on the evolutionary process of changes in the values of some of the many parameters that are normally experimentally hand refined. The main problems are that either the population converges too soon, limiting the search to a small subspace of the search space and stagnating in a local optimum, or it does not converge sufficiently, delaying the process because search is performed in a region that is too big to be of practical use. A proposed solution to this problem is the use of genetic operators that can perform genetic search locally and globally. In [1] and [2] a set of Rank Based operators are defined for a genetic algorithm that is designed to do both local and global search at the same time. In [7] it is shown theoretically that an algorithm using only a Rank Based mutation operator without recombination is efficient for some fitness landscapes. Later in [3] a study on the Rank Based mutation operator showed that previously existing heuristics to determine the mutation rate are not sufficiently general and that the optimal mutation rate depends on several factors including the stage of evolution algorithm, the shape of the fitness landscape, among others. Also in [3] a comparative analysis was made of the efficiency of an algorithm using Rank Based Mutation and recombination operators against an algorithm with the usual operators. The results indicate that the Rank Based algorithm improves efficiency particularly in cases where it requires both exploitation and exploration as is the case of a fitness landscape featuring Building Blocks that require high levels of mutation rate to be solved efficiently (Deceptive Trap). The algorithm is able to find these blocks by its ability to explore, keep them in the population and join them by recombination. Two more examples of the benefits of Rank Based operators are [4] and [6] in which they were applied to bigger problem instances than in the more theoretical ones mentioned above, showing an improvement on performance, especially in multimodal fitness landscapes. All of the above mentioned studies were done on discrete search spaces, i.e., with binary representations. In this work we extend the experimentation with Rank Based operators to a representation in the reals domain which implies certain considerations. We also introduce a new form of Rank Based mutation operator in a bid to reduce the effects of noise in the fitness landscape. We define a new Rank Based selection operator in order to have a better control on selective pressure in genetic algorithms. Our experimental results were obtained from the application of this algorithm to a problem with long genotypes and noise in the fitness landscape. We show how the genetic operators contribute to the efficiency of the algorithm. In selction II we describe the basic existing definitions of Rank Based mutation and recombination operators. In section III the new Rank Based operators for mutation and selection are defined. Section IV describes all the experimental setup including the problem we used for tests. In section V we discuss the results and in section VI we report our conclusions. II. RANK BASED EVOLUTION Evolutionary algorithms that use any form of Rank Based operators are designed to provide a better balance between exploration and exploitation in the search process. The idea is to be able to escape local optima without losing the signal that the basin of attraction in the fitness landscape that is currently present in the algorithm’s population. There have been proposals of a Rank Based mutation operator and a Rank Based recombination operator. We describe them now here. A. Mutation The most straightforward form of Rank Based operators is for mutation as in [1], [2], [3], [4] and [7]. In this case, 2011 10th Mexican International Conference on Artificial Intelligence 978-0-7695-4605-6/11 $26.00 © 2011 IEEE DOI 10.1109/MICAI.2011.40 72