The focus of this study is to optimize the exploration of biomass-driven multi-energy systems, which include combined heat, power, and gas generation. The objective is to enhance the thermal, environmental, and economic performance indicators of the system. The optimization objectives encompass the quantities of internal combustion engines and air source heat pumps, as well as the dimensions of tanks utilized for anaerobic fermentation. A mathematical model was developed to optimize multiple objectives for combined heat, power, and gas generation systems by employing multi-objective intelligent optimization algorithms. The validation and analysis were conducted using rural residences in Lanzhou, Gansu Province, China, as a case study. The sensitivity analysis of biomass gasification combined heat and power systems was conducted from both technical and cost perspectives, examining the dynamic impact characteristics on the outcomes of multi-objective optimization. The findings indicate that the annual energy-saving rate of the optimized combined generation system decreased from 3.62% to -6.78%, while the growth in carbon emissions reduction rate increased from 76.05 to 81.38%, and the annual cost-saving rate grew from 0.97 to 14.96%. The power generation efficiency of the cogeneration station and hydraulic retention time were found to have a significant impact on the multi-objective optimization results of the combined generation system among the technical parameters. The unit cost of anaerobic fermentation tanks had a more significant impact on the multi-objective optimization results in terms of cost parameters, compared to the price of biogas residue.