For solving dynamic optimization problems with fixed boundary

a novel strategy named as graded optimization was developed. It had two alternative schemes

of which the one was to deal with the constraint of fixed boundary prior to objective optimization

while the other one was to treat them in the reversed procedure. By using this strategy a fixed boundary problem was reduced to a series of free boundary problems that could be solved by using existing

sophisticated optimization methods. For boxing constraint of control

trigonometric function transformation was developed to achieve an unconstrained problem. Graded optimization had the abilities to avoid the demerits of penalty function strategy. Case studies showed that graded optimization could meet fixed boundary requirements with reasonable accuracy and trigonometric function transformation was feasible.