In recent years, growing concerns have arisen due to the tight energy supply and escalating demand have driven the research on energy-efficient polygeneration systems. Liquefied natural gas (LNG) is highly regarded as a clean fossil fuel, capable of both cooling and serving as a heat source. This makes it a favored choice for thermodynamic system design. LNG gasification at −162 °C under standard pressure releases substantial cold energy. To avoid its waste, a novel self-supplying thermodynamic system was devised to recover this energy, incorporating a specific cold storage module that combines power generation and heating systems. This approach offers insights into creating polygeneration systems using LNG as the sole energy source. In light of the intricate energy exchanges within the system, based on the energy parameters of each stream, a comprehensive evaluation of its engineering feasibility is conducted through the analysis of energy, exergy, exergoeconomic, and exergoenvironmental parameters. Additionally, key parameters like R1150 mass flow rate, pump 3 outlet pressure, compressor 2 outlet pressure, LNG pump outlet pressure, and R23 liquefaction temperature are examined. Finally, the non-dominated sorting genetic algorithm II (NSGA-II), particle swarm optimization (PSO) and the multi-objective artificial hummingbird algorithm (MOAHA) rooted in hummingbird foraging behavior, are applied to optimize the proposed system. The results show that the energy utilization efficiency, exergy efficiency, product unit exergoeconomic cost, and product unit exergoenvironmental impact are 72.08%, 45.45%, 98.04 $/GJ, and 1.478 × 10−2 mpt/kJ, respectively. These excellent performance indicators demonstrate that the system is developable in the field of LNG utilization, filling a gap in the joint research of cold storage, power generation and heating for LNG cold energy utilization. Enhancing system performance can be achieved by increasing the mass flow rate of R1150 and the output pressure of compressor 2, reducing the output pressure of pump 3 and the liquefaction temperature of R23. When increasing the output pressure of LNG pump, can only increase exergy efficiency, while the energy utilization efficiency, product unit exergoeconomic cost and product unit exergoenvironmental impact all go down. Compared with the initial condition, after the application of MOAHA optimization, the exergy efficiency increased by 2.8%, the product unit exergoeconomic cost decreased by 3.47 $/GJ and the product unit exergoenvironmental impact decreased by 0.047 × 10−2 mpt/kJ. These results outperform those of NSGA-II and PSO, indicating that MOAHA can lead to superior system performance by overcoming multi-objective conflicts. This study provides valuable insights for designing and optimizing LNG cold energy utilization systems in situations without nearby heat sources or when power generation, heating, and cold storage are required.