To deal with the premature convergence of the bare-bone particle swarm optimization (BBPSO) algorithm

we make the analysis of the motion behavior of the particles and point out the reasons leading to the premature convergence.According to the analysis results

a parallel-cooperative BBPSO (PCBBPSO) algorithm is proposed in which the parallel-cooperative learning of a master swarm and a slave swarm balances between exploration and exploitation abilities.In order to improve the exploration ability of the master swarm

a dynamic learning exemplar strategy is presented to preserve the swarm diversity.Meanwhile

a stochastic opposition-based learning mechanism is developed to achieve the abilities of the slave swarm from the global search to the local search.The proposed algorithm was evaluated on 14 benchmark functions with different characteristics.The experimental results and statistic analysis show that the proposed method significantly outperforms six state-of-the-art BBPSO variants in terms of convergence speed and solution accuracy.