Particle swarm cooperative optimization algorithm based on geometric algebra

Abstract

In order to overcome the demerits that the basic particle swarm optimization (hereinafter referred to as bPSO for short) algorithm is prone to fall into local extremum, slow convergence velocity and low convergence precision in the later stage of evolution, two strategies of Raman geometric relation particle swarm optimization equation and the addition of geometric rotation operator are adopted for the improvement, and Raman geometric relation particle swarm optimization (hereinafter referred to as Raman GPSO for short), geometric rotation particle swarm optimization (hereinafter referred to as grPSO) and the Raman geometric relation particle swarm optimization based on the geometric rotation of both (hereinafter referred to as Raman GPSO based on grPSO) algorithm are proposed. Raman GPSO has eliminated the particle velocity terms of the PSO evolution equation and simplified the original second-order geometric equation to the first-order geometry equation, with the evolutionary process controlled only by the particle position, which can avoid the problem of the slow convergence velocity and low precision in the later stage due to the particle divergence caused by the particle velocity term. grPSO can increase the geometric rotation operator which will accelerate the particle out of the local extreme point and continue the optimization. The experimental results of several classical test functions show that, Raman GPSO can greatly improve the convergence velocity and precision; grPSO can effectively get rid of the local extreme points; the combination of the aforementioned two strategies, Raman GPSO based on geometric rotation of Raman GPSO and grPSO have obtained very excellent optimization effect with smaller population size and evolutionary generations, so as to make the PSO algorithm more optimized.

Keywords:

• Geometric Algebra Calculation
• Raman Geometric Relation
• Particle Swarm Optimization
• Geometric Rotation