Self-adaptive differential evolution based on best and mean schemes

Abstract

Differential evolution (DE), one of the evolutionary algorithms (EAs), is well-known for its quality solutions and speed convergence. Just like any EA, the execution of DE depends on the selection of its control parameters consisting of population size, crossover rate and scale factor. DE is operated by two different kinds of search mechanisms, i.e., exploration and exploitation. The selection of control parameters affects these search mechanisms, and thus, the performance of DE. Ranges on setting DE's control parameters are suggested in most studies but it still depends heavily on a user's knowledge and experiences, as well as the types of problems. The common approach adopted by users is the trial-and-error method but this approach consumes time. Since adaptation has been responsible for the search optimal solutions in DE, the adaptability should be further utilized to determine DE's optimal control parameters. Therefore, we proposed a self-adaptive DE which is able to self-determine its control parameters based on an ensemble. An ensemble is operated based on two different parameter selection schemes, i.e., BEST and MEAN. The performances of DEs based on the selection schemes in 20 benchmarks problems are compared based on best-fitness, mean-fitness, crossover rate and scale factor. The experimental results showed that the proposed self-adaptive DEs are able to perform adequately well in the benchmark problems. Besides that, the results have shown an interesting pattern between crossover rate and scale factor when the DE is given freedom to determine its control parameters.