A multilevel evolutionary algorithm for optimizing numerical functions

This is a study on the effects of multilevel selection (MLS) theory in optimizing numerical functions. Based on this theory, a Multilevel Evolutionary Optimization algorithm (MLEO) is presented. In MLEO, a species is subdivided in cooperative populations and then each population is subdivided in groups, and evolution occurs at two levels so called individual and group levels. A fast population dynamics occurs at individual level. At this level, selection occurs among individuals of the same group. The popular genetic operators such as mutation and crossover are applied within groups. A slow population dynamics occurs at group level. At this level, selection happens among groups of a population. The group level operators such as regrouping, migration, and extinction-colonization are applied among groups. In regrouping process, all the groups are mixed together and then new groups are formed. The migration process encourages an individual to leave its own group and move to one of its neighbour groups. In extinction-colonization process, a group is selected as extinct, and replaced by offspring of a colonist group. In order to evaluate MLEO, the proposed algorithms were used for optimizing a set of well known numerical functions. The preliminary results indicate that the MLEO theory has positive effect on the evolutionary process and provide an efficient way for numerical optimization.