Despite the wide applications of multi-effect vapor absorption systems, their energy requirement is relatively higher. Also, their exergy analyses found in the literature reveal that the exergy destruction rate at the absorber is quite significant and has the potential for improvement in its energy efficiency. In this work, the exergy destruction rate at the absorber is minimized using the penalty factor method against the optimized generator temperature of the double-effect vapor absorption system by considering absorber, evaporator, and condenser temperatures into consideration. Modeling of the double-effect vapor absorption system was performed using a thermodynamic toolbox in SIMULINK. The present model employed a refrigerant heat exchanger to enhance the system cooling capacity. The liquid-vapor ejector valve at the absorber also improved the mixing of the solution and refrigerant vapor resulting in lower irreversibility of the system. Results show that the coefficient of a performance increase by 2.4% with refrigerant heat exchanger and exergy loss at absorber decrease by 9.4% with ejector. The optimum performance was seen at the condenser and evaporator temperatures of 308.8 K and 278.1 K, respectively with an 8.2% improvement in exergetic efficiency. Finally, it is concluded that the multi-effect absorption system shows better performance by minimizing the irreversibility.