Markov Chain Models of Bare-Bones Particle Swarm Optimizers

We apply a novel theoretical approach we recently developed to better understand the behaviour of different types of bare-bones PSO. It avoids many common but unrealistic assumptions often used in analyses of PSOs. Using finite element grid techniques, it builds a discrete Markov chain model of the BB-PSO which can approximate it on arbitrary continuous problems to any precision. Iterating the chain’s transition matrix gives precise information about the behaviour of the BB-PSO at each generation, including the probability of it finding the global optimum or being deceived. The predictions of the model are remarkably accurate and explain the features of Cauchy, Gaussian and other sampling distributions