About 8% of the natural gas feed to a Liquefied Natural Gas (LNG) plant is consumed for liquefaction. A significant challenge in optimizing engineering systems, including LNG plants, is the issue of uncertainty. To exemplify, each natural gas field has a different gas composition, which imposes an important uncertainty in LNG plant design. One class of optimization techniques that can handle uncertainty is robust optimization. A robust optimum is one that is both optimum and relatively insensitive to the uncertainty. For instance, a mobile LNG plant should be both energy efficient and its performance be insensitive to the natural gas composition.

In this dissertation to enhance the energy efficiency of the LNG plants, first, several new options are investigated. These options involve both liquefaction cycle enhancements and driver cycle (i.e., power plant) enhancements. Two new liquefaction cycle enhancement options are proposed and studied. For enhancing the diver cycle performance, ten novel driver cycle configurations for propane pre-cooled mixed refrigerant cycles are proposed, explored and compared with five different conventional driver cycle options. Also, two novel robust optimization techniques applicable to black-box engineering problems are developed. The first method is called gradient assisted robust optimization (GARO) that has a built-in numerical verification scheme. The other method is called quasi-concave gradient assisted robust optimization (QC-GARO). QC-GARO has a built-in robustness verification that is tailored for problems with quasi-concave functions with respect to uncertain variables. The performance of GARO and QC-GARO methods is evaluated by using seventeen numerical and engineering test problems and comparing their results against three previous methods from the literature. Based on the results it was found that, compared to the previous considered methods, GARO was the only one that could solve all test problems but with a higher computational effort compared to QC-GARO. QC-GARO's computational cost was in the same order of magnitude as the fastest previous method from the literature though it was not able to solve all the test problems. Lastly the GARO robust optimization method is used to devise a refrigerant for LNG plants that is relatively insensitive to the uncertainty from natural gas mixture composition.