Unification and simplification for position updating formulas in particle swarm optimization

Abstract

Particle swarm optimization (PSO) has been a popular research area in artificial intelligence technology, where the two issues of theoretical analysis and premature convergence have been the focus of attention. However, due to the complex dynamics of a particle swarm, the former was conducted only for simplified systems. The latter has only been addressed by introducing some additional operations, which inevitably increases the complexity of PSO and complicates the theoretical analysis. This paper proposes a unified and simplified rule for position updating in the existing algorithms as an attempt to solve the above-mentioned problems. This rule simplifies the multiple-order stochastic difference equation to a first-order stochastic difference equation, and facilitates the analysis of the convergence and control of the search behavior of particles. Experiments were conducted on some representative algorithms, and the results verified the correctness of the unification and simplification of position updating formulas, which also performed more competitively.