Firefly Algorithm for Beamforming Design in RIS-aided Communication Systems

This paper studies a non-convex power minimization problem for reconfigurable-intelligent-surfaces-aided communication systems whose constraints are multivariate functions of two independent optimization variables, i.e., active and passive beamforming vectors. A widely adopted alternative optimization (AO) approach approximates the originally non-convex problem by two convex sub-optimization problems where each sub-optimization problem deals with one variable considering the other variable as a constant. The solution for the original problem is obtained by iteratively solving these sub-optimization problems. Although the AO approach converts the original NP-hard optimization problem to two convex sub-problems, the solutions attained by this method may not be the global optimal solution due to the approximation process as well as the inherent non-convexity of the original problem. To overcome the issue, this paper adopts a nature-inspired optimization approach and introduces a novel Firefly algorithm (FA) to simultaneously solve for two independent optimization variables of the originally non-convex optimization problem. Computational complexity analyses are provided for the proposed FA and the AO approaches. Simulation results reveal that the proposed FA approach prevails its AO counterpart in obtaining a better solution for the understudied optimization problem with the same order of computational complexity.