The present study aims to conduct multiobjective optimization investigations by using the genetic algorithm on the small scale and combined LNG cold utilized micro cogeneration system. The system combines the Stirling engine and the microturbine plant with the related heat exchanger for the hot water production. Before the optimization, thermodynamic and environmental analyses are performed in ranges of 288.15-313.15K with the constant relative humidity. Four different multiobjective optimization cases are considered which are: maximization of the generated net work/minimization of the CO2 emission rate, maximization of the exergetic efficiency/ minimization of the CO2 emission rate, maximization of the generated net work/ maximization of the thermal efficiency, and minimization of the overall exergy destruction/ minimization of the CO2 emission rate, respectively. Results show that the net generated power and exergetic efficiency decrease by 15% and 32%, respectively while the thermal efficiency and overall exergy destruction increase by 3.3% and 25% with 40K temperature increment. The CO2 emissions find their peak value at 298.15K. Due to different trends of the investigated parameters, multiobjective function studies infer that the best trade-off region is between 308.15 and 313.15K for the investigated 4 optimization cases.