The current study focuses on addressing the main weakness of the conventional Goswami cycle, namely that its cooling output is rather low in comparison to its ability to produce power. The suggested scheme incorporates a distillation unit assisted absorption chiller setup to the Goswami cycle, whose primary goal is to produce auxiliary cooling without any pressure losses and extra work input. The present modification has increased the conventional Goswami cycle’s power and cooling output from 25.25 kW to 29.83 kW and 6.03 kW to 55.52 kW, respectively. Further, based on the assembly’s thermal response and single objective optimization, it is found that its outputs from the Goswami cycle side, the absorption chiller side, and its exergy efficiency are in conflict with one other. After that, a multi-objective dragonfly algorithm and entropy-weighted TOPSIS methods are used to determine the optimal outputs for each side of the assembly at best possible exergy efficiency.