Improved Particle Swarm Optimization Based on the Geometric Analysis of Single Particle

To enhance the ability of the standard Particle Swarm Optimization (PSO) on solving the complex nonlinear problems, an improved algorithm with independent inertia weight for each particle was proposed in this paper. Firstly, a single particle of the particle swarm was studied. The law of the instantaneous movement of single particle at each iteration was analyzed in a novel geometric view. Two importance conclusions were drawn: 1) The introduction of the two random numbers makes the particle search in a broad parallelogram area, while the product of the inertia weight and the particles present speed is the parallel shift of the aforementioned parallelogram area; 2) The search ability will be greatly reduced as soon as a particle becomes the Global Optimal Particle (GOP). Then, on the ground of the significant conclusions, the improvement plan of the standard PSO was put forward. Experiments show that the proposed algorithm has obvious superiority on the convergence ratio, the convergence speed and the convergence stability.