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Differential evolutionary (DE) algorithm is one of the most frequently used evolutionary computation method for the solution of non-differentiable, complex and discontinuous real value numerical problems. The analytical structure of the mutation and crossover operators used by DE and the initial values of the parameters of the relevant operators affect the problem-solving ability of DE. Unfortunately, there is no analytical method for selecting and initializing the best artificial genetic operators that DE can use to solve a problem. Therefore, there is a need to develop new evolutionary search methods that are parameter-free and insensitive to the artificial genetic operators they use. In this paper, the Bernstein–Levy differential evolution (BDE) algorithm, which has a unique elitist-mutation operator and a Bernstein polynomials-based stochastic parameter-free crossover operator, is introduced. The numerical problem-solving success of BDE is statistically evaluated by using 30 benchmark problems of CEC2014 in the numerical experiments presented. BDE's success in solving the related benchmark problems is statistically compared with six state-of-the-art comparison algorithms. In this paper, three real-world optimization problems are also solved by using the proposed algorithm, BDE. According to statistics generated from the experimental results, BDE is statistically better than comparison methods in solving the related real-world problems. [ABSTRACT FROM AUTHOR]

In this paper, weighted differential evolution algorithm (WDE) has been proposed for solving real-valued numerical optimization problems. When all parameters of WDE are determined randomly, in practice, WDE has no control parameter but the pattern size. WDE can solve unimodal, multimodal, separable, scalable, and hybrid problems. WDE has a very fast and quite simple structure, in addition, it can be parallelized due to its non-recursive nature. WDE has a strong exploration and exploitation capability. In this paper, WDE's success in solving CEC' 2013 problems was compared to 4 different EAs (i.e., CS, ABC, JADE, and BSA) statistically. One 3D geometric optimization problem (i.e., GPS network adjustment problem) and 4 constrained engineering design problems were used to examine the WDE's ability to solve real-world problems. Results obtained from the performed tests showed that, in general, problem-solving success of WDE is statistically better than the comparison algorithms that have been used in this paper. [ABSTRACT FROM AUTHOR]

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. • A new parameter-free crossover operator. • A new multi-component mutation operator. • A new Universal Differential Evolution Algorithm. • Real-valued evolutionary search for numerical function optimization. • Evolutionary 3D viewshed analysis. [ABSTRACT FROM AUTHOR]

• Bernstein polynomials based parameter-free crossover. • A new universal/parameter-free Differential Evolution. • Real-valued numerical function optimization. • Evolutionary Image Vectorization. • Evolutionary Digital Terrain Model Simplification. 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. [ABSTRACT FROM AUTHOR]