This paper shows optimization results for a group of standard functions. When the optimization algorithm PSO is hybridized with the simplex traditional algorithm (SX, Nelder-Mead) in two different ways, i. e. thealternating interaction hybrid (PSOSX(AIH)) and the parametric evolution hybrid (PSOSX(PEH)), markedly noticeable effects are observed in both the computing time and the accuracy and precision of their results during the optimization process.