7.19 Penalty Function Method for Parametric Constraints 457
Figure 7.17 Output angles generated and desired.
Figure 7.18 Rectangular plate under arbitrary load.
be stated as a parametric constraint as
|σ (x, y)| −σmax≤ 0 , 0 ≤x≤a, 0 ≤y≤b (7.233)
Thus this constraint has to be satisfied at all the values of parametersxandy.
7.19.2 Handling Parametric Constraints
One method of handling a parametric constraint is to replace it by a number of ordinary
constraints as
gj (X,θi) ≤ 0 , i= 1 , 2 ,... , r (7.234)
whereθ 1 ,θ 2 ,... , θr are discrete values taken in the range ofθ.This method is not
efficient, for the following reasons:
1.It results in a very large number of constraints in the optimization problem.
2.Even if all therconstraints stated in Eq. (7.234) are satisfied, the constraint may
still be violated at some other value ofθ[i.e.,gj( X,θ )>0 whereθk< θ < θk+ 1
for some k].
