In this study, the compatibility of exergy destruction minimization (EDM) as the main objective is checked by plotting coefficient of performance (COP), exergy coefficient of performance (ECOP), and overall exergy destruction rate by simultaneously varying input operating temperatures for a 28 TR cooling load absorption system. The component-wise variation in exergy destruction is also considered and it is found that the maxima of COP and ECOP, and the minima of overall exergy destruction lies on a common point, and when the variation of operating temperatures is further extended, the exergy destruction in one of the component becomes negative, which marks the upper bound of the present analysis. At highest valid generator temperature (155 °C), the minimum possible overall exergy destruction rate is 53.50 kW and maximum COP is 0.523. Through inverse optimization (IO) using dragonfly algorithm (DA), the same overall exergy destruction rate is achieved for a wide range of generator temperatures much below than 155 °C, and as low as 127.34 °C. The above variation is explained in terms of flow ratio, mass flowrate of steam, and mass flowrate of cooling water.