Abstract
Differential evolution (DE) algorithm is a global optimization algorithm over continuous search space. DE also has been applied in many fields, such as artificial neural networks, chemical engineering, mechanical design, robotics, signal processing, biological information, and economics. At the same time, as a powerful evolutionary algorithm for solving global numerical optimization problems, the DE algorithm has drawn more and more attention. However, how to make a proper balance between the global and local search is a burning question and to limit the optimization performance of DE. In this paper, an improved algorithm η_CODE with a new η_Cauchy operator is proposed to enhance the global and local search ability of a well-known DE variant JADE. In order to guarantee the effective performance of the proposed operator, all the fitness values are ranked through a ranking scheme based on increasing order before a new η_Cauchy operator is conducted. The pNP individuals that have better fitness are selected and carried out Cauchy disturbance operation considering the complexity of the algorithm. The Dynamic parameter mechanism is utilized to select pNP individuals that number is also adjusted dynamically in each generation. The scale factor F and crossover probability CR are obtained with Lehmer mean without using determined parameter c in JADE, which aims to balance the exploration and exploitation of the algorithm during the running time. A total of sixty benchmark functions from CEC2014 and CEC2017 on real parameter optimization are employed to prove the validity of η_CODE for solving complex high-dimensional problems. The experiments indicate that η_CODE is better than or at least comparable with several state-of-the-art DE variants, including JADE, SinDE, TSDE, AGDE, and EFADE in the global numerical optimization problems. In order to further analyze the performance of η_CODE, we also select extra two high-powered modified algorithms called EBLSHADE and LSHADESPACMA based on LSHADE to discuss advantages and disadvantages of the proposed algorithm.
Highlights
Evolutionary algorithms (EAs) [1]–[3], which are based on the principles of natural biological evolution, are a number of stochastic search and optimization methods
Where indices r1, r2, r3 ∈ 1, 2, · · ·, NP; F, which is called the scale factor, is a random constant between 0 and 1 to control the amplification of the difference vector XrG2 − XrG3 according to Storn and Price [4]; The conventional method for naming the mutation strategy is DEx/y/z, where Differential evolution (DE) stands for differential evolution, x represents the base vector to be perturbed, y is the number of difference vector, and z denotes crossover operation types including exponential and binomial crossover
In CEC2017 test, SinDE shows better performance with 4 minimum mean error values while η_CODE is ordinary with one among all algorithms in 30-D. η_CODE outperforms JADE, SinDE, TSDE, AGDE and EFADE on all hybrid functions as well as its performance is best among 6 algorithms for 50-D
Summary
Evolutionary algorithms (EAs) [1]–[3], which are based on the principles of natural biological evolution, are a number of stochastic search and optimization methods. The ability of DE to solve a specific problem depends on the choice of strategies [11] and the setting of control parameters [12]. We put forward a new operator called η_Cauchy. The whole individuals are ranked according to corresponding fitness whose selected pNP individuals with better fitness are executed Cauchy disturbance mechanism to get better information using greedy selected method like selection operator between these individuals and the perturbed individuals. The emergence for the new operator is better coordinated with global and local search ability.
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