Particle Swarm Optimization And Its Improvement

With the increasing difficulty on the optimization problems and calculation on the traditional methods, we are thirsty for a class of algorithms, which need less information of the problems, less calculation and has faster speed on solving these problems. Population-based intelligent optimization emerges, as the times require. PIO is basically proposed by simulation of swarm behavior for the swarm intelligence and evolutionary theory. These algorithms require less information of the issues, and through the iteration of group collaboration, self-adaption of the individual and competition of swarm to achieve the optimal. As a representative of PIO, particle swarm optimization is proposed by simulation of bird foraging behavior, by Kennedy and Eberhart in 1995. The algorithm has the advantages of simple structure, few parameters and fast convergence. In the next years, many scholars do a lot of improvement on the algorithm itself and take a further study on its application. In order to improve the precision of the optimal and the application of solving the eigenvalues of a matrix with the algorithm, on the basis of predecessors'work, two improvements in this paper are listed as follows:1 At the last period of the hybrid optimization, a new population will be produced around the best position found by the PSO, and differential evolution is carried out with this population. The search result of these new particles will take an effect on the global best position. The simulation experiment results show the higher precision and more probability to find the best solution.2 When we solve the eigenvalue of a matrix with pso, we propose to change the fitness function dynamically to gain the all eigenvalues of the matrix with only one execution of the PSO, eliminating the drawback of obtaining only one eigenvalue in an implementation.