The Research And Application Of PSO For Multimodal Function

Since the1980s, intelligent optimization algorithms (such as neural network, GA) havebeen developed through the simulation of nature and social process and present a newapproach for optimization problems. Particle Swarm Optimization (PSO) algorithm isproposed by Kennedy and Eberhart in1995after they researched the movement behavior ofthe flock of birds group. It is favored by a lot of scholars due to its good performance inoptimization and easy manipulation. Particle Swarm Optimization algorithm has been widelyused in function optimization, neural network trainings, pattern classification, fuzzy controlsystem, and some other engineering field.This paper firstly introduces the basic knowledge of the intelligent optimizationalgorithms including ACO, AFSA and PSO, and then analyze the theory, the usualimprovements of PSO. Since PSO is easy to fall into the local optimum, three improvementsfor PSO are proposed in this paper.1. Improve the distribution of initial population. Firstly generate an initial populationrandomly in the solution space. Secondly stretch the population along the dimensiondirection.2. Optimize the particles in the direction of gradient. Let the initial population’s positionmove to the drop direction. In this way we can keep the particles uniform to some extent andimprove the quality of the population which lay a good foundation for the iteration.3. Optimize the evolution of the particles. The speed of traditional PSO is only relative tothe particle’s speed, its best position in history and the best position of the population. SincePSO didn’t make good use of the function, DFP is used in the paper to modify the speed s ofthe swarm.At last the improved PSO is tested with some multi-model functions and used to getroot(s) of equation(s) and Multi-objective optimization.