Bernstein-Levy differential evolution algorithm for numerical function optimization

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.