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This paper presents a few new competitive approaches to particle swarm optimization (PSO) algorithm in terms of the global and local best values (GLbest-PSO) and the standard PSO along with three set of variants namely, inertia weight (IW), acceleration co-efficient (AC) and mutation operators in this paper. Standard PSO is designed with time varying inertia weight (TVIW) and either time varying AC (TVAC) or fixed AC (FAC) while GLbest-PSO comprises of global-average local best IW (GaLbestIW) with either global-local best AC (GLbestAC) or FAC. The performances of these two algorithms are improved considerably in solving an optimal control problem, by introducing the concept of mutation variants between particles in each generation. The presence of mutation operator sharpens the convergence and tunes to the best solution. In order to compare and verify the validity and effectiveness of the new approaches for PSO, several statistical analyses are carried out. The results clearly demonstrate the improved performances of the proposed PSOs over the standard PSOs.