Radiation Hardened by Design (RHBD) is one of the main measures for solving the soft error issue in digital circuits. However, a multi-objective optimization (MOO) problem obviously appears when utilizing the hardened counterparts to replace the original unreliable cells. This paper proposes a MOO framework based on Bayesian Optimization (BO) for balancing design metrics like area, Longest Path Delay (LPD)/power, and Soft Error Rate (SER) while hardening digital circuits, including combinational and sequential circuits. This framework comprises two phases: 1) data preprocessing and 2) multi-objective Bayesian optimization. The first phase makes this framework much more applicable for large-scale circuits through data dimensionality reduction. The second phase is characterized by utilizing a black-box approach to greatly promote the efficiency and accuracy of MOO. Experimental results on benchmark circuits demonstrate that the framework achieves a 1.34x improvement in accuracy, an 11.47x enhancement in efficiency, and a 0.77x reduction in SER, while exhibiting a 4.27x and 0.72x increase in area for combinational and sequential benchmark circuits, respectively, along with a 0.54x increase in LPD and a 1.25x increase in power for Triple Modular Redundancy (TMR) techniques.