Nature inspired optimization algorithms, namely artificial bee colony (ABC) optimization and firefly algorithm (FA), have been applied to synthesize beam patterns of a hexagonal planar array of isotropic elements. Two different cases, comprising two different beam patterns of a pencil beam and a square footprint pattern over a bounded region with lower peak sidelobe levels are presented. The pencil beam is generated by thinning the uniformly excited array and the square footprint pattern is generated by imposing optimum amplitudes, phases, and their corresponding states (“on”/“off”) to the array elements. The optimum values of the parameters for both the cases are computed using ABC and FA individually, and the superiority of FA over ABC for the proposed problem in terms of computing solutions for both the cases is established.