Improving Particle Swarm Optimization Analysis Using Differential Models

Abstract

This paper employs the approach of the differential model to effectively improve the analysis of particle swarm optimization. This research uses a unified model to analyze four typical particle swarm optimization (PSO) algorithms. On this basis, the proposed approach further starts from the conversion between the differential equation model and the difference equation model and proposes a differential evolution PSO model. The simulation results of high-dimensional numerical optimization problems show that the algorithm’s performance can be greatly improved by increasing the step size parameter and using different transformation methods. This analytical method improves the performance of the PSO algorithm, and it is a feasible idea. This paper uses simple analysis to find that many algorithms are improved by using the difference model. Through simple analysis, this paper finds that many AI-related algorithms have been improved by using differential models. The PSO algorithm can be regarded as the social behavior of biological groups such as birds foraging and fish swimming. Therefore, these behaviors described above are an ongoing process and are more suitable for using differential models to improve the analysis of PSO. The simulation results of the experiment show that the differential evolution PSO algorithm based on the Runge–Kutta method can effectively avoid premature results and improve the computational efficiency of the algorithm. This research analyzes the influence of the differential model on the performance of PSO under different differenced conditions. Finally, the analytical results of the differential equation model of this paper also provide a new analytical solution.