In industrial design, synthesizing a guide for a given cut-off frequen
cy or attenuation limit is a challenging problem. In this paper, an al
gorithm is applied for the quick computation of the gradients of the o
bject function, without using the solution of two finite-element eigen
value problems to compute the gradient of the object function with res
pect to every parameter of description. It is shown that because of th
e presence of deep valleys in the object function, the traditionally i
nferior zeroth-order pattern search method performs better than the fi
rst order conjugate gradient method.