  Inverse problems associated with designing cylindrical thermal cloaking
shells are studied. Using the optimization method these inverse problems are
reduced to corresponding control problems in which the diagonal components of
diagonal in polar coordinates tensor of thermal conductivities play the role of
passive controls. A numerical algorithm based on the particle swarm
optimization is proposed and the results of numerical experiments are
discussed. Rigorous optimization analysis shows that high cloaking efficiency
of the shell can be achieved either using a highly anisotropic single-layer
shell or using a multilayer shell composed of only three isotropic natural
materials with optimally selected thermal conductivities.
