A new PSO algorithm with Random C/D Switchings

This paper investigates the overall convergence analysis and proposes a novel Random C/D Switchings PSO algorithm with random switchings between convergence operator and divergence operator. With respect to the standard PSO algorithm, its convergence analysis provides a fundamental theory of selecting convergence operator and divergence operator. During the process of finding the suboptimal or global solution, the random switchings between two typical operators, namely Operator C and Operator D, which are two different ways to update velocities of all particles, are conducted by a so-called convergence ratio parameter, which can determine the tradeoff between exploration ability and exploitation ability from the quantitative perspective. Numerical results on several benchmark functions demonstrate the following observations: (1) The proper convergence ratio is closely related to the landscape of objective function, the dimension of solution space and the number of local optimums. (2) Small convergence ratio, setting to 0.60 or 0.65, may benefit the optimization problem which has many local optimums in the high dimensional space; while large convergence ratio, setting to 0.85 or 0.9, is probably helpful for the optimization problem with few local optimums or flat landscape.