This research aims to design hybrid analog and digital beamforming to improve the signal-to-noise ratio (SNR) and spectral efficiency (SE) of communication links. Considering the complexity and cost associated with fully connected multiple-input multiple-output (MIMO) communication models, a partially connected system model is adopted for the downlink millimeter-wave (mmWave) communication model. The analog beamforming utilizes the adaptive search (AdaLS) algorithm to minimize interference and enhance user power, whereas digital beamforming is optimized using the proposed Chaotic Chebyshev Aquila Optimization (CCAO) algorithm. The CCAO algorithm integrates chaotic Chebyshev–based solution mapping with the conventional Aquila Optimization Algorithm to enhance exploration capability. The system model is illustrated, and the problem is formulated to maximize the signal-to-interference-plus-noise ratio (SINR) through the selection of the required signal at the receiver. The digital beamformer is designed using Lagrange's multiplier, and the analog beamformer is optimized using AdaLS. The proposed CCAO algorithm is detailed, incorporating chaotic dynamics to explore the solution space effectively. The research evaluates the performance of the proposed method against conventional approaches, showcasing improved normalized beam gain and SINR.