Movable Antenna-Enhanced Beamforming via an Improved Osprey Optimization Algorithm

This letter proposes an improved osprey optimization algorithm (IOOA) to solve the joint optimization challenge of the antenna position vector (APV) and antenna weight vector (AWV) in movable antenna (MA) arrays. The proposed method introduces a two-stage cooperative framework integrating Lévy-flight-based global exploration and Gaussian-perturbation-based local exploitation. In addition, an adaptive probability mechanism is designed to dynamically guide the search for update target in each iteration, thereby enhancing exploration diversity and preventing premature convergence. Simulation results demonstrate that IOOA achieves superior beamforming gains and requires less computation time under interference null constraints, with its beamforming gain improved by 59.9% over fixed-position antenna (FPA) arrays. In addition, discrete phase-only multi-beam and shaped-beam simulations confirm its effectiveness in practical engineering applications for MA array pattern synthesis.