Differential evolution algorithm with wavelet basis function and optimal mutation strategy for complex optimization problem

Abstract

The optimization performance of differential evolution(DE) algorithm significantly depends on control parameters and mutation strategy. However, it is difficult to set suitable control parameters and select reasonable mutation strategy for DE in solving an actual engineering optimization problem. To solve these problems, a new optimal mutation strategy based on the complementary advantages of five mutation strategies is designed to develop a novel improved DE algorithm with the wavelet basis function, named WMSDE, which can improve the search quality, accelerate convergence and avoid fall into local optimum and stagnation. In the proposed WMSDE, the initial population is divided into several subpopulations to exchange search information between the different subpopulations and improve the population diversity to a certain extent. The wavelet basis function and normal distribution function are used to control the scaling factor and the crossover rate respectively in order to ensure the diversity of solutions and accelerate convergence. The new optimal mutation strategy is used to improve the local search ability and ensure the global search ability. Finally, the proposed WMSDE is compared with five state-of-the-art DE variants by 11 benchmark functions. The experiment results indicate that the proposed WMSDE can avoid premature convergence, balance local search ability and global search ability, accelerate convergence, improve the population diversity and the search quality. Additionally, a real-world airport gate assignment problem is employed to further prove the effectiveness of the proposed WMSDE. The results show that it can effectively solve the complex airport gate assignment problem, and obtain airport gate assignment rate of 97.6%.