In view of the problems of poor global search ability and weak adaptive ability of mayfly algorithm, an enhance global search and adaptive mayfly algorithm (MIWMA) was proposed. Firstly, the non-uniform Gaussian mutation strategy was adopted to update the position of male mayfly and female mayfly, guide the global optimal position mutation to leading other individuals to approach the good position, and promote the population to have certain guidance, so as to improve the global search ability and enhance the diversity of the population. Secondly, the adaptive inertia weight of incomplete gamma function and beta cumulative distribution was introduced to establish a better balance between the global search and development ability, regulate the global search and local search ability of the population, and then improve the convergence accuracy of the algorithm, which is conducive to the potential of the global search of the population to find the optimal solution. The local stagnation countermeasure strategy was introduced. On the basis of the iterative stagnation, the inertia part and social part of mayfly speed update were adjusted to make it have the optimal search state and enhance the global search ability of the algorithm. The classic test function set and IEEE CEC2021 test competition set were used for test optimization comparison to verify the effectiveness and robustness of the algorithm. Results show that the proposed algorithm had better stability, robustness, and reliability by using Friedman and Wilcoxon rank sum test. Finally, two engineering problems were used for optimization. The results verified the applicability of the algorithm in engineering optimization problems and are suitable for solving optimization problems requiring high precision.