A novel hybrid PSO based on levy flight and wavelet mutation for global optimization.

The concise concept and good optimization performance are the advantages of particle swarm optimization algorithm (PSO), which makes it widely used in many fields. However, when solving complex multimodal optimization problems, it is easy to fall into early convergence. The rapid loss of population diversity is one of the important reasons why the PSO algorithm falls into early convergence. For this reason, this paper attempts to combine the PSO algorithm with wavelet theory and levy flight theory to propose a new hybrid algorithm called PSOLFWM. It applies the random wandering of levy flight and the mutation operation of wavelet theory to enhance the population diversity and seeking performance of the PSO to make it search more efficiently in the solution space to obtain higher quality solutions. A series of classical test functions and 19 optimization algorithms proposed in recent years are used to evaluate the optimization performance accuracy of the proposed method. The experimental results show that the proposed algorithm is superior to the comparison method in terms of convergence speed and convergence accuracy. The success of the high-dimensional function test and dynamic shift performance test further verifies that the proposed algorithm has higher search stability and anti-interference performance than the comparison algorithm. More importantly, both t-Test and Wilcoxon's rank sum test statistical analyses were carried out. The results show that there are significant differences between the proposed algorithm and other comparison algorithms at the significance level α = 0.05, and the performance is better than other comparison algorithms.