Gantry cranes are widely employed to handle heavy loads in construction projects and critical industries such as petrochemical and nuclear power stations. Achieving precise trolley positioning and minimizing sway oscillations are crucial for ensuring safety and operational efficiency. This paper presents an optimal control strategy based on a Linear Quadratic Regulator (LQR), where controller performance is highly sensitive to the selection of its weighting matrices, Q and R. Determining these matrices is often a challenging and time-consuming task. To address this issue, an Adaptive Genetic Algorithm (AGA) is applied to automatically compute the LQR parameters for a nonlinear double pendulum crane model implemented in MATLAB. Simulation results reveal that the proposed AGA-based LQR controller outperforms a conventional LQR tuned with a standard Genetic Algorithm (GA), delivering robust performance across a range of payload masses.