High-sensitivity operation of a radio-frequency atomic magnetometer (RF-AM) requires careful setting of the system parameters, including the lasers intensity and detuning, and the vapour cell temperature. The identification of the optimal operating parameters, which ensures high sensitivity, is typically performed empirically and is often a lengthy process, which is especially labour intensive if frequent retuning of the magnetometer is required to perform different tasks. This paper demonstrates an efficient approach to RF-AM performance optimisation which relies on an open-loop optimisation technique based on Uniform Design (UD). This paper specifically describes the optimisation of an unshielded RF-AM based on a 4-factor-12-level UD of the experimental parameters space. The proposed procedure is shown to lead to the efficient optimisation of the atomic magnetometer at different frequencies, and is applicable to both AC and DC sensitivity optimisation. The procedure does not require any detailed knowledge of the model underlying the operation of the RF-AM and is effective in reducing the number of experimental runs required for the optimisation. It is ideally suited to self-calibration of devices without human supervision.