This paper proposes a generalized Firefly Algorithm (FA) to solve an optimization framework having objective function and constraints as multivariate functions of independent optimization variables. Four representative examples of how the proposed generalized FA can be adopted to solve downlink beamforming problems are shown for a classic transmit beamforming, cognitive beamforming, reconfigurable-intelligent-surfaces-aided (RIS-aided) transmit beamforming, and RIS-aided wireless power transfer (WPT). Complexity analyzes indicate that in large-antenna regimes the proposed FA approaches require less computational complexity than their corresponding interior point methods (IPMs) do, yet demand a higher complexity than the iterative and the successive convex approximation (SCA) approaches do. Simulation results reveal that the proposed FA attains the same global optimal solution as that of the IPM for an optimization problem in cognitive beamforming. On the other hand, the proposed FA approaches outperform the iterative, IPM and SCA in terms of obtaining better solution for optimization problems, respectively, for a classic transmit beamforming, RIS-aided transmit beamforming and RIS-aided WPT.