Differential Evolution Using Opposite Point for Global Numerical Optimization

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 difficult 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.