Abstract: Hydrogen-enriched combustion in gas-fired boilers represents a viable pathway for mitigating carbon emissions, yet the synergistic influence of multiple operating parameters on overall pollutant emission characteristics has not been systematically elucidated. A user-defined function was developed to implement the flue gas recirculation (FGR) function, and numerical simulations were conducted on the hydrogen-enriched combustion coupled with FGR process in a 49 MW natural gas boiler with an excess air coefficient of 1.2. Based on the Taguchi experimental method, 16 cases were designed with different hydrogen blending ratios (X_H2 = 0-0.3), flue gas recirculation rates (R_FGR = 0-0.15), and fuel preheating temperatures (T_p = 300 K-600 K) to investigate the effects of these variables on the emissions of different pollutants, namely NO_x, CO, and CO₂. The entropy weight method was used to propose a novel multi-objective comprehensive evaluation index (MEI) for pollutant emissions from hydrogen-enriched combustion. Further, signal-to-noise ratio analysis was performed to optimize the combustion boundary conditions with MEI as the objective. The results show that among the 16 cases, for single-pollutant objectives, the combination achieving the lowest NO_x emission is X_H2=0.2,、R_FGR=0.15、T_p=400 K; the lowest CO emission is achieved at X_H2=0.3、R_FGR=0.15、T_p=600 K; and the lowest CO₂ emission is achieved at X_H2=0.2、R_FGR=0.15、T_p=600 K. The mathematical expression of the multi-objective comprehensive evaluation index MEI is MEI=0.39E_NOx+ 0.32E_CO+ 0.29E_CO2. Under multi-objective optimization, the optimal MEI value is 1.102, which is 10.42% higher than the maximum value achieved under single-objective optimization. The corresponding optimal combination is X_H2=0.2、R_FGR=0.15、T_p=600 K, achieving the lowest emissions with a NO_x concentration of 12 mg/m³, CO concentration of 6 mg/m³, and CO₂ volume fraction of 5.31%. The results can provide new insights for the development of multi-pollutant control strategies in hydrogen-enriched combustion of gas-fired boilers.