Relaxed Differential Evolution Algorithm

This article presents a new variant of the Differential Evolution Algorithm (DEA) without the sequential condition of the individuals' selections in the Mutation process. Unlike other variants, where researchers focus on changes: in the formulation of the Mutation equation; the Crossover process; and/or Control parameters, this variant focuses on relaxing the selection conditions of the individuals involved in the creation of the mutation vector. Therefore, the main motivation of this proposal is to eliminate the condition that dictates that the selected individuals are different from each other. By relaxing this constraint, on the one hand, it can be expected that the execution time of the algorithm is lower, and on the other hand, the algorithm convergence could be slower, when the relaxed and original versions are compared at the same number of iterations at sequential computational processing. To analyze the performance, a comparative analysis of the proposed algorithm versus simple DEA is present by using as a case study a set of mathematical functions.