The nitrogen (N2) expander and single mixed refrigerant (SMR) liquefaction processes are recognized as the most favorable options to produce liquefied natural gas (LNG) at small-scale and offshore sites. These processes have a simple and compact design that make them efficient with respect to their capital costs. Nevertheless, huge operating costs, mainly due to their lower energy efficiency, remains an ongoing issue. Utilization of design variables having non-optimal values is the primary cause for the lower energy efficiency; which, in turn, leads to exergy destruction (i.e., entropy generation), and ultimately the overall energy consumption is increased. The optimal execution of the design variables of LNG processes can be obtained through effective design optimization. However, the complex and highly non-linear interactions between design variables (refrigerant flowrates and operating pressures) and objective function (overall energy consumption) make the design optimization a difficult and challenging task. In this context, this study examines a new optimization algorithm, named “Jaya”, to reduce the operating costs of nitrogen dual expander and SMR LNG processes. The Jaya approach is an algorithm-specific parameter-less optimization methodology. It was found that by using the Jaya algorithm, the energy efficiency of the SMR process and nitrogen dual expander natural gas (NG) liquefaction process can be enhanced up to 14.3% and 11.6%, respectively, as compared to their respective base cases. Using the Jaya approach, significant improved results were observed even compared to other previously used optimization approaches for design optimization. Results of conventional exergy analysis revealed that the exergy destruction of SMR and N2 dual expander process can be reduced by 17.4% and 14%, respectively. Moreover, economic analysis identified the 13.3% and 11.6% relative operating costs savings for SMR and N2 dual expander LNG processes, respectively.