Correlation electromagnetic analysis (CEMA) is a method prevalent in side-channel analysis of cryptographic devices. Its success mostly depends on the quality of electromagnetic signals acquired from the devices. In the past, only one byte of the key was analyzed and other bytes were regarded as noise. Apparently, other bytes' useful information was wasted, which may increase the difficulty of recovering the key. Multi-objective optimization is a good way to solve the problem of a single byte of the key. In this work, we applied multi-objective optimization to correlation electromagnetic analysis taking all bytes of the key into consideration. Combining the advantages of multi-objective optimization and genetic algorithm, we put forward a novel multi-objective electromagnetic analysis based on a genetic algorithm to take full advantage of information when recovering the key. Experiments with an Advanced Encryption Standard (AES) cryptographic algorithm on a Sakura-G board demonstrate the efficiency of our method in practice. The experimental results show that our method reduces the number of traces required in correlation electromagnetic analysis. It achieved approximately 42.72% improvement for the corresponding case compared with CEMA.