Distributed Particle Swarm Optimization with Dimension-Level Interactions for Large-Scale Separable Optimization Problems

Optimization problems for large-scale distributed systems are challenging due to their complexities. In an attempt to solve these problems, centralized intelligence algorithms suffer from large computational costs and slow convergence rates. Therefore, in this paper, a distributed particle swarm optimization (MDPSO) algorithm is proposed. To reduce computational costs, a dimension-level interaction is introduced, and an average consensus operator is incorporated for accelerating convergence rates. In the distributed method, each agent is assigned only a single particle, rather than a subpopulation in traditional PSO. Furthermore, every particle position is decomposed into two sub-vectors that are processed separately, significantly improving convergence rate and solution accuracy. Moreover, a theorem and a corollary are presented, which guarantee the consensus convergence of the proposed method. Finally, three cases are designed. The results show that our method requires only half the number of iterations compared to other methods. Additionally, it finds optima with higher accuracy. More importantly, compared to the variants of PSO, only 1/N of the total particle population is used, which reduces the computational costs significantly.