Abstract: A mathematical technique or methodology that deals with the finding of maximal or minimal of functions in some feasible searching space or region is called as Optimization. Every business or industry is involved in solving optimization problems. Some different varieties of optimization processes compete for the best minima solution. Particle Swarm Optimization (PSO) is a relatively new, advanced, and powerful method for optimization that has been empirically tested on many optimization problems and it perform well in solving those optimization problems. PSO is widely used to find the global optimum solution in a complex searching space. This work is focused on providing a review and discussion of the most established results on PSO algorithm as well as exposing the most active research topics that can encourage the practitioner for future work with improved results by applying little effort .This work introduces a theoretical concepts and some detailed explaining of the PSO algorithm, its advantages and disadvantages, judiciary selection of the various parameters with their effects. Moreover, this dissertation discusses a study of boundary conditions with the invisible wall technique, controlling the convergence behaviours of PSO, discrete-valued problems, multi-objective PSO, and applications of PSO. Finally, this work presents some kinds of improved versions as well as recent progress in the development of the PSO, and the future research issues are also discussed.

Keywords: Optimization, Swarm Intelligence, Social network, convergence, stagnation, multi-objective.