Inverse problems associated with designing cylindrical thermal layered shielding and cloaking shells are studied. Using the optimization method these inverse problems are reduced to corresponding control problems. Thermal conductivities of the shell layers 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. Important properties of optimal solutions are established. Based on these properties simple design rules are formulated allowing to design cloaking and shielding shells which possess the best cloaking or shielding performance in addition to easy manufacturability. (C) 2019 Elsevier Ltd. All rights reserved.