Similarity between existing position updating formulas and a unified and simplified formula in Particle Swarm Optimization

Particle Swarm Optimization (PSO) has become a hot topic in the field of artificial intelligence technology, wherein the two issues including theoretical analysis and premature convergence have attracted lots of attention. However, due to complex dynamics in particle swarm, the former research has been conducted only in simplified systems. The latter has been dealt with only through application of some additional operations, which inevitably increases the complexity of PSO and makes the theoretical analysis more difficult. To handle the above problems, a unified and simplified formula for position updating in the existing PSOs has been proposed in one reference, but the similarity between those original position updating formulas and this unified and simplified formula is still not completely clarified. In this paper, we took the similarity as a Jarque-Bera test of a null hypothesis, wherein a large amount of data samples were derived from ten classical or novel PSOs. Research results show that, in the statistical sense, there is a lack of similarity. This is helpful to guide the future research for the unified and simplified position updating formula.