Analysis of standard particle swarm optimization algorithm based on Markov chain

According to the proposed particle swarm optimization (PSO) difference model in this paper, the state sequence of a single particle and swarm state sequence are defined first, and their Markov property are analyzed, after that, it is demonstrated that the set of optimal states are closed set. Moreover, the one-step transition probability of a particle is calculated. Considering the complete probability formula and the Markov properties, the transition probability to the optimal set is deduced. According to the derived conclusion, the inertia weight ! and accelerate factor c of PSO are discussed. Finally, the premature convergence and divergent problem are explained, furthermore, it is proved that the standard PSO algorithm reaches the global optimum in probability.