´ A AAAAAAAAAAAAAAAAAAA ´ A AAAAAAAAAAAAAAAAAAA ART ´ ICULO Performance Evaluation of the Parallel Polytree Approximation Distribution Algorithm on Three Network Technologies * Julio Madera Department of Computing, University of Camag¨ uey, Camag¨ uey, Cuba jmadera@inf.reduc.edu.cu Enrique Alba, Gabriel Luque Departamento de Lenguajes y Ciencias de la Computaci´ on E.T.S.I. Infom´ atica, University of M´ alaga M´ alaga, Spain {eat, gabriel}@lcc.uma.es Abstract This paper proposes two parallel versions of an Estimation of Distribution Algorithm (EDA) that represents the pro- bability distribution by means of a single connected graphical model based on a polytree structure (PADA). The main goal is to design a new and more efficient EDA. Our algorithm (pPADA) is based on the master/slave model which allows to perform the estimation of the probability distribution (the most time-consuming phase in EDAs) in a parallel way. The aim of our experimental studies is manifold. Firstly, we show that our parallel versions achieve a notable reduction of the total execution time with respect to existing algorithms. Secondly, we study the behavior of the algo- rithm from the numerical point of view, analyzing the different versions. Finally, our methods are evaluated over three interconnection networks (Fast Ethernet, Gigabit Ethernet, and Myrinet) and a study on the influence of the parallel platform in the communication is performed. Keywords: Parallel EDAs, Bayesian Networks, Polytree Approximation Distribution Algorithm. 1. Introduction Evolutionary Algorithms (EAs) are non determinis- tic search techniques designed as an attempt to sol- ve adaptive and hard optimization tasks on compu- ters [2]. In fact, it is possible to find this kind of algo- rithms applied for solving complex problems in eco- nomy, telecommunications, bioinformatics, etc. The landscape of these problems often shows multiple op- tima, noisy regions, and a large dimensionality. The- se algorithms work over a set (population) of poten- tial solutions (individuals) by applying some stochas- tic operators on them, called variation operators (e.g., natural selection, recombination, or mutation), in or- der to search for the best solutions. In the last years a new family of EAs known as Estimation of Distribution Algorithms (EDAs) [3, 8] has deserved a large attention in the scientific com- munity related to optimization, evolutionary compu- tation, and probabilistic models. These algorithms ha- ve arisen as an alternative to other methods where it is necessary to fit a high number of parameters. EDAs have been motivated by the need to identify the inter- relations between the variables, a key issue to solve complex problems. In EDAs, a different kind of va- riation operators is used. The successive generations of individuals are created by using estimations of the probability distributions observed in the current popu- lation, instead of evolving the population with the ty- * The two last authors are partially supported by the Spanish Ministry of Education and Science, by European FEDER under contract TIN2005- 08818-C04-01 (the OPLINK project, http://oplink.lcc.uma.es), and by the European Union under contract CP3-005 (the CARLINK project). Inteligencia Artificial, Revista Iberoamericana de Inteligencia Artificial. No 35 (2007), pp. 67-76. ISSN: 1137-3601. c AEPIA (http://www.aepia.org/revista)