In an effort to provide stable and affordable city gas, the open rack vaporizer (ORV), a heat exchanger that vaporizes Liquefied Natural Gas (LNG) using seawater, is receiving significant attention. In this study, a physics-based surrogate model for the ORV system with high fidelity and low computational load compared to a computational fluid dynamics (CFD) model is developed based on two-dimensional (2D) first principle equations of energy and mass balances for heat transfer. Partial key parameters are estimated using the mean squared error based parameter subset selection method with global sensitivity analysis to address the overfitting issue. The resulting physics-based surrogate model shows robust performance and approximates the temperature profile with an error of less than 5% compared to the CFD data. Using the surrogate model, operating conditions are optimized with both multi-objective and single-objective functions. The results indicate that the two objectives, profit and LNG outlet temperature, are incompatible and that two operating conditions, LNG and seawater flowrates, are inversely proportional.