Xu, H., Chuang, C., and Yang, R., "Towards Optimization of Multi-material Structure: Metamodeling of Mixed-Variable Problems," SAE Int. J. Mater. Manf. 9(2):400-409, 2016, doi:10.4271/2016-01-0302.
In structural design optimization, it is challenging to determine the optimal dimensions and material for each component simultaneously. Material selection of each part is always formulated as a categorical design variable in structural optimization problems. However, it is difficult to solve such mixed-variable problems using the metamodelbased strategy, because the prediction accuracy of metamodels deteriorates significantly when categorical variables exist. This paper investigates two different strategies of mixed-variable metamodeling: the “feature separating” strategy and the “all-in-one” strategy. A supervised learning-enhanced cokriging method is proposed, which fuses multi-fidelity information to predict new designs’ responses. The proposed method is compared with several existing mixed-variable metamodeling methods to understand their pros and cons. These methods include Neural Network (NN) regression, Classification and Regression Tree (CART) and Gaussian Process (GP). This study provides insights and guidance on the establishment of proper metamodels for multi-material structural design problems.