The optimization of electromagnetic devices governed by the Poisson eq
uation is now well established. This paper extends the methodology to
scattering problems. In particular, the permittivity and permeability
of the coating on an aircraft fuselage and its thickness are computed
so as to minimize the scattered signature. It is shown that the reflec
tion coefficient has multiple minima and maxima as the thickness of th
e coating is varied, thereby making search techniques superior to the
usually efficient gradient methods. On the other hand, as the permeabi
lity and permittivity are varied, the reflection coefficient varies gr
adually to its one minimum, except for a few local minima, thereby mak
ing gradient techniques very powerful.