Premature convergence of standard particle swarm optimisation algorithm based on Markov chain analysis

Particle Swarm Optimisation PSO is a population-based stochastic optimisation algorithm. The most important advantages of the PSO are that PSO is easy to implement and there are few parameters to adjust, but PSO is easy to get trapped in local optimum. In this paper, the premature convergence of standard PSO is investigated based on Markov chain. First, according to the difference model of standard PSO algorithm, the particle state sequence and swarm state sequence are defined and the one-step transition probability of state is introduced; it is shown that the particle state sequence and swarm state sequence are all Markov chains and their Markov properties are analysed. Second, for premature convergence of standard PSO, its analysis is given based on Markov chain. Last, it is proved that standard PSO is convergent to premature convergent state in probability.

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