Bezier Search Differential Evolution Algorithm for numerical function optimization

Differential Evolution Algorithm (DE) is a commonly used stochastic search method for solving real-valued numerical optimization problems. Unfortunately, DE's problem solving success is very sensitive to the internal parameters of the artificial numerical genetic operators (i.e., mutation and crossover operators) used. Although several mutation and crossover methods have been developed for DE, there is not still an analytical method that can be used to select the most efficient mutation and crossover method while solving a problem with DE. Therefore, selection and parameter tuning processes of artificial numerical genetic operators used by DE are based on a trial-and-error process which is time consuming. The development of modern DE versions has been focused on developing fast, structurally simple and efficient genetic operators that are not sensitive to the initial values of their internal parameters. Problem solving successes of the Universal Differential Algorithms (uDE) are not sensitive to the structure and internal parameters of the related artificial numerical genetic operators used, unlike DE. In this paper a new uDE, Bezier Search Differential Evolution Algorithm, BeSD, has been proposed. BeSD's mutation and crossover operators are structurally simple, fast, unique and produce highly efficient trial patterns. BeSD utilizes a partially elitist unique mutation operator and a unique crossover operator. In this paper, the experiments were performed by using the 30 benchmark problems of CEC2014 with Dim=30, and one 3D viewshed problem as a real world application. The problem solving success of BeSD was statistically compared with five top-methods of CEC2014, i.e., CRMLSP, MVO, WA, SHADE and LSHADE by using Wilcoxon Signed Rank test. Statistical results exposed that BeSD's problem solving success is better than those of the comparison methods in general.