  A multilayered particle is illuminated by plane acoustic or electromagnetic
waves of one or several frequencies. We consider the inverse scattering problem
for the identification of the layers and of the refraction coefficients of the
scatterer in a non-Born region of scattering. Local deterministic and global
probabilistic minimization methods are studied. A special Reduction Procedure
is introduced to reduce the dimensionality of the minimization space. Deep's
and the Multilevel
  Single-Linkage methods for global minimization are used for the solution of
the inverse problem. Their performance is analyzed for various multilayer
configurations.
