FGM optimization in complex domains using Gaussian process regression based profile generation algorithm

This manuscript addresses the challenge of designing functionally graded materials (FGMs) for arbitrary-shaped domains. Towards this goal, the present work proposes a generic volume fraction profile generation algorithm based on Gaussian Process Regression (GPR). The proposed algorithm can handle complex-shaped domains and generate smooth FGM profiles while adhering to the specified volume fraction values at boundaries/part of boundaries. The resulting design space from GPR comprises diverse profiles, enhancing the potential for discovering optimal configurations. Further, the algorithm allows the user to control the smoothness of the underlying profiles and the size of the design space through a length scale parameter. Further, the proposed profile generation scheme is coupled with the genetic algorithm to find the optimum FGM profiles for a given application. To make the genetic algorithm consistent with the GPR profile generation scheme, the standard simulated binary crossover operator in the genetic algorithm has been modified with a projection operator. We present numerous thermoelastic optimization examples to demonstrate the efficacy of the proposed profile generation algorithm and optimization framework.