A generalized Benders decomposition-based algorithm for heat conduction optimization and inverse design

Heat conduction optimization benefits many important applications and attracts researchers' interest unceasingly. Here we present an alternative heat conduction optimization algorithm on the basis of generalized Benders decomposition technique. In this algorithm, the heat conduction optimization problem is first decomposed to a subproblem and a master problem. The subproblem calculates the temperature field with the given thermal conductivity distribution, updates the upper boundary of objective, and constructs an optimality cut at the current point. The master problem updates the lower boundary of objective from solving the programming problem formed by all optimality cuts generated. The subproblem and master problem are solved alternately, the two boundaries approach mutually, and the optimal solution can be reached. The proposed algorithm is validated by applying it on the classic "volume-to-point" problem. Results show that the average and maximum temperature in the domain can be effectively reduced. It is further extended to the topology optimization to obtain discrete material distribution, and numerical studies are also conducted for validation. Finally, the inverse design of thermal cloak is studied by using the proposed algorithm, and square and circular thermal cloaks are numerically designed and verified. All cases studied demonstrate the efficacy and flexibility of the proposed algorithm. & COPY; 2023 Elsevier Ltd. All rights reserved.