The mayfly algorithm is a new type of swarm intelligence optimization algorithm inspired by mayfly flight and mating behavior. It has good optimization performance, but its efficiency is affected by failure mayflies when faced with high-dimensional and complex problems. In view of this, a migration evolutionary mayfly algorithm (MEMA) is proposed in this paper. First, the individual ability of the mayfly population is evaluated, and individuals with a long life-cycle but weaker evolutionary ability are eliminated from the population. At the same time, with those eliminated ones as strongholds, a global position shift is performed on the mayfly population to obtain new individuals. Then, directional dynamic evolution training is carried out on new individuals to improve the overall optimization ability of the population. Finally, in the Matlab environment, six benchmark test functions are randomly selected to design simulation experiments for the effectiveness verification of the MEMA algorithm. The experimental results show that compared with the other five comparison algorithms, the MEMA algorithm outperforms in both low-dimensional and high-dimensional function tests for the optimal solution search, and it has advantages in convergence accuracy, convergence speed, and robustness.