There are two problems in the state-of-the-art Non-Intrusive Load Monitoring (NILM) method based on optimization. Firstly, using only one or two features for load disaggregation is ineffective. Secondly, it is difficult to utilize three or more features for NILM methods based on optimization as the objective function of equipment identification. A framework for non-intrusive load monitoring using multi-objective evolutionary algorithms is proposed, which solves the problems of traditional methods such as using fewer features and difficult to determine weighting coefficients. Active power, reactive power, apparent power, harmonic and current waveforms are taken as objective functions of electric appliances operation state, and a multi-objective load disaggregation model is established. The measured power consumption data for different electric appliances is disaggregated by MOEAs to obtain Pareto optimal solution set. Finally, multi-criteria decision-making method is used to select the recognition result. The experimental results show that the recognition accuracy rate of MOEAs for the case that multiple appliances operate simultaneously is increased with the increasing number of features. Compared with the state-of-the-art NILM methods, the proposed framework has higher recognition rate for household load disaggregation. This work is supported by National Natural Science Foundation of China (No. 61772255, No. 61866025 and No. 61866026) and Natural Science Foundation of Jiangxi Province (No. 20181BAB202025).