Mathematicle Modelling and Applications of Particle Swarm Optimization

Optimization is a mathematical technique that concerns the finding of maxima or minima of functions in some feasible region. There is no business or industry which is not involved in solving optimization problems. A variety of optimization techniques compete for the best solution. Particle Swarm Optimization (PSO) is a relatively new, modern, and powerful method of optimization that has been empirically shown to perform well on many of these optimization problems. It is widely used to find the global optimum solution in a complex search space. This thesis aims at providing a review and discussion of the most established results on PSO algorithm as well as exposing the most active research topics that can give initiative for future work and help the practitioner improve better result with little effort. This paper introduces a theoretical idea and detailed explanation of the PSO algorithm, the advantages and disadvantages, the effects and judicious selection of the various parameters. Moreover, this thesis discusses a study of boundary conditions with the invisible wall technique, controlling the convergence behaviors of PSO, discrete-valued problems, multi-objective PSO, and applications of PSO. Finally, this paper presents some kinds of improved versions as well as recent progress in the development of the PSO, and the future research issues are also given