Liquefied natural gas (LNG) technology, particularly the propane precooled mixed refrigerant (C3MR) process, has demonstrated efficiency and emerged as a distinctive dual-refrigerant technology widely used in LNG production. However, the liquefaction process is the highest energy-intensive stage within its supply chain as it consumes about 8 % of the LNG energy content. Thus, for the first time, this study proposes systematic knowledge-based and constrained Bayesian optimization approaches to identify the optimal operation of the C3MR process. These approaches optimize both the operational parameters (pressures and flow rates) and the composition of the mixed refrigerant with practical equipment specifications and rigorous constraints. The results show that the specific energy consumption (SEC) is reduced to 0.264 kWh/kgLNG, which is 14.6 %, and 26 % lower than the basic C3MR process (unoptimized case) and typical industrial C3MR processes, respectively. In addition, the optimized SEC in this study is 14.5 % to 38.6 % lower than those reported in the literature. At large-scale LNG production (10,000 tons per day), the reduction in the SEC is translated into an 18 MW decrease in compression power, saving approximately 4.7 million $ per year for each C3MR train. Moreover, the coefficient of performance (COP) of the C3MR process was improved by about 15 %, and the CO2 emissions were reduced by 17 % (7 tons per year) compared to the basic C3MR process, indicating potential advancements in large-scale LNG liquefaction processes.