In our recent work we showed,by investigating the initialization of some unusual forms of assisted driving Hamiltonians,that the addition of an assisted driving Hamiltonian is not always useful in quantum adiabatic evolution.These unusual forms are those that are not the relatively fixed ones that are widely used in the literature.In this paper,we continue this study,providing further evidence for the validity of the conclusion above by researching some relatively more complex forms of assisted driving scheme,which generalize the ones studied in our previous work.