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.

翻译：本文提出了一种广义萤火虫算法（FA），用于求解目标函数和约束条件均为独立优化变量多元函数的优化框架。通过四个代表性实例展示了所提出的广义FA如何应用于解决下行链路波束成形问题，包括经典发射波束成形、认知波束成形、可重构智能表面辅助（RIS辅助）发射波束成形以及RIS辅助无线功率传输（WPT）。复杂度分析表明，在大天线阵列场景下，所提出的FA方法相比对应的内点法（IPM）具有更低的计算复杂度，但比迭代法和逐次凸近似（SCA）法需要更高的复杂度。仿真结果显示，在认知波束成形的优化问题中，所提出的FA能够达到与IPM相同的全局最优解。另一方面，在经典发射波束成形、RIS辅助发射波束成形和RIS辅助WPT的优化问题中，所提出的FA方法分别在获取更优解方面优于迭代法、IPM和SCA法。