The study introduces an innovative three-stage nested power generation system that enables the cascading utilization of LNG cold energy. It makes the most of wasted energy by using ship jacket cooling water (JCW) and exhaust gas (EG) as heat sources, a trans-critical carbon dioxide cycle as internal circulation, and utilizing the pressure exergy of LNG. We choose two azeotrope mixing fluids that match the requirements and create four cases for the outer and middle cycle working fluids in the three-stage nested system. To discover the ideal system performance from the perspectives of exergy (E), economy (E), and environment (E), four cases were subjected to multi-objective optimization using the multi-objective particle swarm optimization technique (MOPSO). Finally, the optimal solution was found by applying the TOPSIS decision-making method. Through comparative analysis, the optimal system is selected among the four optimization results. R170 (22.66%) and R1150 (77.34%) are used as the outer circulating working medium, while R170 (90.86%) and R1270 (9.14%) are utilized as the inter-cycle working fluid. The net output work is 575.75 kW, the optimal exergy efficiency is 46.09%, the optimal electricity production cost is $0.04009 per kWh, the carbon dioxide emissions can be reduced by 36,910 tons, and the payback period is 2.548 years. After optimization, a more energy-efficient and environmentally friendly power generation system is obtained.