Bernstain-search differential evolution algorithm for numerical function optimization

Abstract

The standard Differential Evolution Algorithm (sDE) is a stochactic search method commonly used in evolutionary computing. The problem solving success of sDE is highly sensitive to the genetic operators used and the initial values of the parameters of these operators. Since a universal Differential Evolution Algorithm (uDE) is not sensitive to the structure and parameter values of the genetic operators used, it is parameter-free in practice and easier to control than sDE. uDE does not need a trial-and-error process when selecting the genetic operators and initial values of intrinsic parameter of related genetic operators to solve the problem, unlike the sDE. Therefore, the use and adaptation of a uDE to solve different types of numerical engineering problems is easy and time-consuming compared to sDE. In this paper, a new uDE, Bernstain-Search Differential Evolution Algorithm (BSD), is introduced. BSD is new and easily controllable, simple structured, non-recursive, highly efficient, fast and practically parameter-free uDE. BSD have a too feasible random crossover and mutation process and does not have a control-parameter setting process, contrary to sDE and its improved variants. In this paper, 30 benchmark problems of CEC’2014, 60 classic benchmark problems, image evolution problems for 12 test images and one Triangulated Irregular Network (TIN) refinement problem were used in the experiments performed to investigate the problem solving success of BSD, statistically. Four tested methods (i.e., ABC, JADE, CUCKOO, WDE) were used in the conducted experiments. Problem solving successes of BSD and tested methods were statistically compared by using Wilcoxon Signed Rank Test piecewisely. Results obtained from the performed tests showed that in general, problem solving success of BSD is statistically better than the tested methods that have been used in this paper.