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A family of position mutated hierarchical particle swarm optimization algorithms with time varying acceleration coefficients (viz. PM_nHPSO-TVAC, n = 1, 2, 3, 4) is introduced in this paper. The proposed position mutation schemes help the swarm to get out of local optima traps and the hierarchical nature of the swarm prevents premature convergence. One distinct advantage of the proposed algorithms over the existing mutated PSO algorithms is that PM_nHPSO-TVAC do not involve any controlling parameter. Performance of the proposed algorithms is evaluated on standard benchmark functions. Comparative study shows that PM_4HPSO-TVAC performs better than the other PM_n HPSO-TVAC, HPSO-TVAC, comprehensive learning PSO (CLPSO), adaptive-CLPSO (A-CLSPO), PSO with time-varying inertia weight (PSO-TVIW), and constriction factor PSO (CFPSO) for the benchmark functions considered. We apply the proposed algorithm to the synthesis of uniformly excited, unequally dpaced linear array to minimize sidelobe level (SLL) and to control first-null-beamwidth (FNBW) and null locations. Further, we apply the proposed algorithm to the synthesis of unequally spaced sparse planar array to minimize SLL.