Hybrid non-parametric particle swarm optimization and its stability analysis

As a population-based random search optimization technique, particle swarm optimization (PSO) has become an important branch of swarm intelligence (SI). The tuning of parameters in PSO has attracted the attention of many researchers. This study proposes an alternative technology called hybrid non-parametric PSO (HNPPSO) algorithm. Other SI operations, including a multi-crossover operation, a vertical crossover, and an exemplar-based learning strategy, are combined with the proposed algorithm to balance the global and local search capabilities. The first- and second-order stability analyses conducted for the present study showed that the particle positions are expected to converge at a fixed point in the search space and that the variance of the particle positions converges to zero. In the experiments, the proposed algorithm was compared with 10 other advanced PSO techniques using 40 widely used benchmark functions. The experimental results indicated that the proposed algorithm yields better solution accuracy and convergence speed than the other PSO techniques. The proposed algorithm significantly outperformed the other PSO approaches in terms of convergence speed.