Abstract: The inherent trade-off between mainlobe width and sidelobe level exists in frequency diverse array(FDA) beamforming. To achieve effective mainlobe narrowing under constraints on low sidelobe levels, a single-objective optimization model was formulated based on the ε constraint method. Within this framework, simulations were performed on a full-array FDA using a particle swarm optimization(PSO) algorithm to validate the effectiveness of the proposed model for beam pattern optimization. Furthermore, a hybrid optimization algorithm(GA-IHSO), integrating an improved hive-based swarm optimization(IHSO) with a genetic algorithm(GA), was developed. Under the same optimization framework, a sparse FDA configuration was obtained through the joint optimization of element frequency offsets and inter-element spacing. Simulation results indicate that the proposed approach can achieve narrower mainlobe widths under low sidelobe level constraints, demonstrating its comprehensive advantages in both mainlobe narrowing and sidelobe suppression.