  It is still a challenge to experimentally realize shortcuts to adiabaticity
(STA) for a non-Hermitian quantum system since a non-Hermitian quantum system's
counterdiabatic driving Hamiltonian contains some unrealizable auxiliary
control fields. In this paper, we relax the strict condition in constructing
STA and propose a method to redesign a realizable supplementary Hamiltonian to
construct non-Hermitian STA. The redesigned supplementary Hamiltonian can be
eithersymmetric or asymmetric. For the sake of clearness, we apply this method
to an Allen-Eberly model as an example to verify the validity of the optimized
non-Hermitian STA. The numerical simulation demonstrates that a ultrafast
population inversion could be realized in a two-level non-Hermitian system.
