In using penalty functions to handle final state equality constraints,
we propose a systematic scheme for adjusting the penalty function fac
tors, so that all the constraints are satisfied within a specified tol
erance, and so that the performance index is minimized. Two typical en
gineering problems, which are used to test the procedure, show that th
e proposed method of adjusting the penalty function factors can be use
d for reasonably complex systems to yield reliable results.