With the transformation of transmission and distribution grids into smart grids that are more dominated by renewable energy, power electronics-based inverters that can improve power quality are becoming more visible. In order to maximize the output voltage quality and reduce the total harmonic distortion (THD), efficient operation of inverters is required. Therefore, in this paper, the problem of harmonic elimination in multilevel inverters is solved by using an adaptive grey wolf optimizer with local search. We have performed a grid search-based landscape analysis of the seven-level inverter to understand the behaviour of the proposed algorithm. For verification, the numerical results of the proposed adaptive grey wolf optimizer are compared with those of the original grey wolf optimization algorithm, a modified version of the grey wolf optimization algorithm, the particle swarm optimization algorithm, multi-verse optimization algorithm, and salp swarm algorithm. In the simulations, we solved the optimization model for three different structures of multilevel inverters (7, 11, and 15 levels) by changing the modulation indexes. It is found that the adaptive grey wolf optimization provides lower total harmonic distortion for different modulation indexes.