On Particle Swarm Optimization In Dynamic Environments

Particle Swarm Optimization (PSO) is an optimization method based on swarm intelligence, by Kennedy and Eberhart in 1995. Because of its fast convergence and easy to realize, PSO is widely used in many fields such as computational intelligence, task schedule, traffic optimization, telecommunications routing, circuit design. Now it has become a hot topic in field of computational intelligence research.Although PSO and its variants have been successfully applied to static optimization problem, in many real-world optimization problems, the objective function, the problem instance, or constraints may change over time, and thus, the optimum of that problem might change as well. This brings new challenges to PSO even to evolutionary computation as a whole.In this paper, theory, method and application of PSO are studied. Paper mainly includes the following three parts:The first part is mainly on the theory of PSO. First, by the Lyapunov time-varying model, the movement of single particle is analyzed, and stability condition is given, and then using stochastic processes theory to prove that the particle's position sequences converge in mean square. Furthermore, the movement of the whole swarm is analyzed. Finally according to the convergence criterion of stochastic optimization algorithm, a guaranteed global convergence PSO is proposed, which is tested on a few benchmark functions, the simulation shows the effectiveness of the improved algorithm.The second part is on the improved PSO in dynamic environments, mainly including dynamic single-objective PSO, dynamic multi-objective PSO, and dynamic high-dimensional PSO.This paper first represents the model of dynamic environment, makes an analysis of the difficulty to solve the dynamic optimization problems by PSO, and then propose a improved multi-swarm PSO based on Cauchy mutation and the repulsion potential field, the new algorithm is tested on CEC09 benchmark functions and the DF1, the simulation shows that the improved algorithm can track the changing extreme points effectively.For the dynamic multi-objective problem, the definition is given and performance evaluation criteria is analyzed in detail, then a collaborative multi-swarm PSO is proposed, which adaptively switching from competitive model to cooperative model to track for the Pareto front and Pareto solution set. The purpose of competition is to explore in the search space, on the contrary, the purpose of cooperation is to exploit in the search space. The improved algorithm is compared with the other two algorithms and performs well in tracking performance by tested on moving peaks benchmark and dynamic functions.As the dimension of the search space rise, almost all the evolutionary computation suffers "the curse of dimensionality". This paper first makes an analysis of reasons and put forward a dimensional adaptive learning PSO for the local extreme points. The simulation verifies the excellent tracking performance of the improved algorithm.The third part is the application of PSO in dynamic environment. This paper proposes an improved PSO to optimize the parameters of PID controller for the dynamic system. First the fitness function is defined by the rising time, overshoot and steady state error with appropriate weighting according to actual control system. Improved PSO is proposed to optimize the parametres of PID controller. Then based on Pareto optimization theory, the improved multi-objective PSO is proposed to provided a complete Pareto nondominated solutions, which could satisfy decision-makers to choose corresponding the parameters of PID controller according to their preference to the overshoot and rise time.Finally, the full text of this article is summarized, the deficiencies are explained and the future of PSO is prospected.