This chapter will introduce the particle swarm optimization (PSO) algorithm giving an overview of it. In order to formally present the mathematical formulation of PSO algorithm, the classical version will be used, that is, the inertial version; meanwhile, PSO variants will be summarized. Besides that, hybrid methods representing a combination of heuristic and deterministic optimization methods are going to be presented as well. Before the presentation of these algorithms, the reader will be introduced to the main challenges when approaching PSO algorithm. Two study cases of diverse nature, one regarding the PSO in its classical version and another one regarding the hybrid version, are provided in this chapter showing how handful and versatile it is to work with PSO. The former case is the optimization of a mechanical structure in the nuclear fuel bundle and the last case is the optimization of the cost function of a cogeneration system using PSO in a hybrid optimization. Finally, a conclusion is presented.

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