The merits of decomposition-based many-objective evolutionary algorithms are known in solving many-objective optimization problem (MaOP). Device model extraction is one of MaOPs, in this work, we first time apply a decomposition-based many-objective evolutionary algorithm with two types of adjustments for the direction vectors (MaOEA/D-2ADV) to model auto extraction of MOSFETs. This approach can fast extract 65 nm devices and sub-5-nm gate-all-around (GAA) silicon (Si) nanowire (NW) MOSFETs. The results of this study indicate that the automatic extraction by using the MaOEA/D-2ADV converges accurately, rapidly, and stably. It can not only jump out local traps but optimize final results efficiently for various devices. Compared with measured results, the accuracy of extracted ID-VG, ID-VD, gm, and gds are less than 1% within a few minutes.