Multikulti Algorithm: using genotypic differences in adaptive distributed evolutionary algorithm migration policies Lourdes Araujo, Juan J. Merelo Guerv´ os Abstract— Migration policies in distributed evolutionary al- gorithms are bound to have, as much as any other evolutionary operator, an impact on the overall performance. However, they have not been an active area of research until recently, and this research has concentrated on the migration rate. In this paper we compare different migration policies, including our proposed multikulti methods, which choose the individuals that are going to be sent to other nodes based on the principle of multiculturalism: the individual sent should be as different as possible to the receiving population (represented in several possible ways). We have checked this policy on two discrete optimization problems for different number of nodes, and found that, in average or in median, multikulti policies outperform others like sending the best or a random individual; however, their advantage changes with the number of nodes involved and the difficulty of the problem. The success of these kind of policies is explained via the measurement of entropies, which are known to have an impact in the performance of the evolutionary algorithm. I. I NTRODUCTION AND STATE OF THE ART The fact that parallel evolutionary algorithms can obtain better results than sequential ones for the same computational effort [1] has been sometimes attributed to the fact that evolution proceeds differently in each node, and the effect that the immigrants from one node to another have on its diversity. The mating restriction that is inherent to the isolation of the population in several islands avoids premature convergence of the whole population, while the increased diversity attained with the incoming member of the other populations takes it closer to finding a solution. However, according to the intermediate disturbance hypothesis [2], the closer the immigrant is the current state of the population, the smaller effect it will have on the overall performance. Diversity in the subpopulation is so important that it leads to improvement in quality and efficiency at the same time; and there are several mechanisms to preserve it: Herrera et al. [3], for instance, proposed a hierarchical configuration of subpopulations, each one of them running an evolutionary algorithm with different parameters, and connected so that there is a small variation from one subpopulation to the others connected to it. However, the migration mechanism itself can also be studied, since the selection of immigrants and the other aspects of migration will obviously have an effect on the overall performance. Here are some of these aspects: 1) the number of individuals undergoing migration, Lourdes Araujo is with Dpto. Lenguajes y Sistemas Inform´ aticos. UNED, Madrid, Spain (email lurdes@lsi.uned.es) Juan J. Merelo Guerv´ os is with Departamento de Arquitectura y Tecnolog´ ıa de Computadores, Universidad de Granada, Spain (email jmerelo@geneura.ugr.es) 2) the frequency of migration, i.e. the number of genera- tions or evaluations between migrations, 3) the policy for selecting immigrants, 4) the immigrant replacement policy, 5) the topology of the communication among subpopula- tions, 6) the synchronous or asynchronous nature of the the connection among subpopulations. Some of them have been studied in the literature: for instance, Alba et al. [4] look at the last one, concluding that asynchrony does not have a negative effect on performance, and can even outperform synchronous ones; Merelo et al. [2] looked at what would be the degree of asynchrony that would achieve the best algorithmic performance, applying also the above mentioned theory of intermediate disturbances. Papers such as the ones by Cant´ u-Paz [5], [6], Alba and Troya [7], and Noda et al. [8] are more comprehensive in the study of different migration policies. Several results presented in these mentioned works indicate that diversity is a fundamental key in the success of the island model. Par- ticularly, Cant´ u-Paz studied the four possible combinations of random and fitness-based emigration and replacement of existing individuals. He found that the migration policy that causes the greatest reduction in work (takeover time 1 ) is to choose both the immigrants and the replacements according to their fitness, because this policy increases the selection pressure and may cause the algorithm to converge significantly faster. However, if convergence is too fast it can lead to algorithm failure, as Cant´ u-Paz [6] states referring to parallel EAs: Rapid convergence is desirable, but an ex- cessively fast convergence may cause the EA to converge prematurely to a suboptimal solution. So, other policies must also be considered. Some authors [9] have proposed a model different to the island one, which follows an approach of segregation and reunification. In this case subpopulations evolve independently until detect- ing local premature convergence, which is indicated by a selection pressure value computed in each subpopulation. If stagnation is detected the calculations for this subpopulation are stopped until the next reunification phase is reached. Such a reunification phase is initiated, if all subpopulations have converged prematurely. Other authors Alba and Troya [7] found that in the island model migration of a random string prevents the “conquest” 1 Number of generations required to converge to the best individual from the initial population, by applying selection only 2858 978-1-4244-2959-2/09/$25.00 c  2009 IEEE Authorized licensed use limited to: Univ Nacional Edu Distancia. Downloaded on October 7, 2009 at 09:48 from IEEE Xplore. Restrictions apply.