| Now more and more importance has been attached to swarm intelligence optimization algorithm. Particle swarm optimization algorithm (PSO) is a typical swarm intelligence optimization algorithm. PSO has a simple structure, a strong ability to find best solution and can been realized easily. It has more evident advantage when comparing with traditional optimization methods. There are only two simple evolution formulas in PSO, and parameters needed to be adjusted are less. However, in the complicated optimization problems with multi-dimensions and many extrema, the standard PSO behaves with pool ability and is easy to find a local best solution. PSO has been applied broad, but it is significant to develop more application of PSO. The improvement and application of PSO are researched in this thesis.An improved PSO based on the forgetting character and the average information of swarm is advanced. It can be observed that the individual best position and the global best position have important effect on piloting every particle moving to optimal position. The individual in swarm intelligence optimization algorithm possess simple behavior. So we let the memory of particle finite in the improved PSO, and the best position in former phase is forgotten. The global best position is chosen from the all individual best positions, and then the swarm has forgetting character. The global best position has too strong attraction to every particle, so the standard PSO is easy to find local best solution. The individual has mind to follow the center of swarm (here it is the center of all individual best position). Namely, the individual will follow the excellent particle and also want to follow the center of all individual best positions. So, in the evolution process the global best position is displaced randomly by the center of all individual best positions, and both virtues are taken full advantage of. At the same time, we notice that the complexity of improved PSO is not added evidently. The good performance is validated by complicated optimization functions.The theory research for PSO is difficult currently. A mature theory system doesn't come into being. We think that PSO is similar to genetic algorithm in many ways. The genetic algorithm has mature Markov process theory system, so in this thesis PSO is researched by Markov process theory. The stochastic process variable is constituted by the vectors of all velocity and positions, and the proof that it is a homogeneous Markov process is given.A current research hotspot on PSO is to develop its broad application. At the same time, topology optimization is difficult in engineering. The application of PSO is developed in this thesis by applying PSO to truss structural topology optimization and continuum structural topology optimization. So a new measure is pioneered for structural topology optimization. The algorithm is realized and programmed by using MATLAB language and data transfer from ANSYS to MATLAB.The multi-objective optimization problems are often encountered in life and engineering. In the multi-objective optimization, more than one objective is needed to be optimized. So it is difficult to evaluate individual good or bad. The multi-objective optimization aims to find the Pareto solution set. We notice that the solution is impracticable which makes one objective very small but others very big. So the practicability criterion is defined by calculating the difference of objectives. Inspired by the idea that the global best position is chosen from the swarm elitism set, the individual elitism set is advanced, in order to get a solution set with good spacing and good practicability. Then the individual best position is chosen from the individual elitism set. The individual fitness is evaluated by calculating the difference of objectives. A good non-dominated solution set with good spacing and practicability can be gotten by the improved PSO seen from the examples.Finally, the outlook about further research directions is given briefly.
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