Refrigerant is one of the most important parts in a refrigeration cycle. In many refrigeration cycles, especially in the natural gas processing industry, propane is used as refrigerant due to its desirable thermodynamic properties. There are two ways for transferring propane and butane gases from extraction point to the consumption site: a) Pipeline and b) liquefaction and transport in liquid form. The most profitable method for transporting large quantities of propane and butane gases is liquefaction and transport in liquid form using storage tanks. Liquefaction at atmospheric pressure is the most common method for transporting large quantities of gases using specifically designed refrigerated ships. In this paper, a gas refinery butane and propane liquefaction cycle is described first and then simulated in HYSYS software. Afterwards, Genetic Algorithm is used to minimize the total power consumption of the liquefaction cycle, through connecting HYSYS and MATLAB softwares. There are 13 variables and 13 constraints for compressors and heat exchangers in the formulation of the optimization problem. The results of this constrained optimization problem show that the power consumption can be reduced by 12.49% compared to the base case.