In this paper, we present an empirical comparison of some Differential Evolution variants to solve global optimization problems. The aim is to identify which one of them is more suitable to solve an optimization problem, depending on the problem's features and also to identify the variant with the best performance, regardless of the features of the problem to be solved. Eight variants were implemented and tested on 13 benchmark problems taken from the specialized literature. These variants vary in the type of recombination operator used and also in the way in which the mutation is computed. A set of statistical tests were performed in order to obtain more confidence on the validity of the results and to reinforce our discussion. The main aim is that this study can help both researchers and practitioners interested in using differential evolution as a global optimizer, since we expect that our conclusions can provide some insights regarding the advantages or limitations of each of the variants studied.

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In this paper, we incorporate a diversity mechanism to the differential evolution algorithm to solve constrained optimization problems without using a penalty function. The aim is twofold: (1) to allow infeasible solutions with a promising value of the objective function to remain in the population and also (2) to increase the probabilities of an individual to generate a better offspring while promoting collaboration of all the population to generate better solutions. These goals are achieved by allowing each parent to generate more than one offspring. The best offspring is selected using a comparison mechanism based on feasibility and this child is compared against its parent. To maintain diversity, the proposed approach uses a mechanism successfully adopted with other evolutionary algorithms where, based on a parameter Sr a solution (between the best offspring and the current parent) with a better value of the objective function can remain in the population, regardless of its feasibility. The proposed approach is validated using test functions from a well-known benchmark commonly adopted to validate constrainthandling techniques used with evolutionary algorithms. The statistical results obtained by the proposed approach are highly competitive (based on quality, robustness and number of evaluations of the objective function) with respect to other constraint-handling techniques, either based on differential evolution or on other evolutionary algorithms, that are representative of the state-of-the-art in the area. Finally, a small set of experiments were made to detect sensitivity of the approach to its parameters.

This article presents a modified version of the differential evolution algorithm to solve engineering design problems. The aim is to allow each parent vector in the population to generate more than one trial (child) vector at each generation and therefore to increase its probability of generating a better one. To deal with constraints, some criteria based on feasibility and a diversity mechanism to maintain infeasible solutions in the population are used. The approach is tested on a set of well-known benchmark problems. After that, it is used to solve engineering design problems and its performance is compared with those provided by typical penalty function approaches and also against state-of-the-art techniques.