Abstract
The Differential Evolution (DE) algorithm is arguably one of the most powerful stochastic optimization algorithms, which has been widely applied in various fields. Global numerical optimization is a very important and extremely dif-ficult task in optimization domain, and it is also a great need for many practical applications. This paper proposes an opposition-based DE algorithm for global numerical optimization, which is called GNO2DE. In GNO2DE, firstly, the opposite point method is employed to utilize the existing search space to improve the convergence speed. Secondly, two candidate DE strategies “DE/rand/1/bin” and “DE/current to best/2/bin” are randomly chosen to make the most of their respective advantages to enhance the search ability. In order to reduce the number of control parameters, this algorithm uses an adaptive crossover rate dynamically tuned during the evolutionary process. Finally, it is validated on a set of benchmark test functions for global numerical optimization. Compared with several existing algorithms, the performance of GNO2DE is superior to or not worse than that of these algorithms in terms of final accuracy, convergence speed, and robustness. In addition, we also especially compare the opposition-based DE algorithm with the DE algorithm without using the opposite point method, and the DE algorithm using “DE/rand/1/bin” or “DE/current to best/2/bin”, respectively.
Highlights
Global numerical optimization problems arise in almost every field such as industry and engineering design, applied and social science, and statistics and business, etc
This paper proposes an opposition-based Differential Evolution (DE) algorithm for global numerical optimization, which is called GNO2DE
This paper proposes an opposition-based DE algorithm for global numerical optimization (GNO2DE)
Summary
Global numerical optimization problems arise in almost every field such as industry and engineering design, applied and social science, and statistics and business, etc. The major challenge of the global numerical optimization is that the problems to be optimized have many local optima and multiple dimensions. Come the limitations of traditional global numerical optimization methods, mainly in terms of unknown system parameters, multiple local minima, non-differentiability, or multiple dimensions, etc. PSO has been a member of the wide category of Swarm Intelligence methods for solving global numerical optimization problems [13,14,15]. This paper proposes an opposition-based DE algorithm for global numerical optimization (GNO2DE). This algorithm employs the opposite point method to utilize the existing search spaces to speed the convergence [21,22,23,24].
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