Augmented D-optimal design for effective response surface modeling and optimization
For effective response surface modeling during sequential approximate optimization (SAO), thenormalized and the augmented D-optimality criteria are presented. Thenormalized D-optimality criterion uses the normalized Fisher information matrix by its diagonal terms in order to obtain a balance among the linear-order and higher-order terms. Then, it is augmented to directly include other experimental designs or the pre-sampled designs. This augmentation enables the trust region managed sequential approximate optimization to directly use the pre-sampled designs in the overlapped trust regions in constructing the new response surface models. In order to show the effectiveness of the normalized and theaugmented D-optimality criteria, following two comparisons are performed. First, the information surface of thenormalized D-optimal design is compared with those of the original D-optimal design. Second, a trust-region managed sequential approximate optimizer having three D-optimal designs is developed and three design problems are solved. These comparisons show that thenormalized D-optimal design gives more rotatable designs than the original D-optimal design, and theaugmented D-optimal design can reduce the number of analyses by 30 % –40 % than the original D-optimal design.
Key WordsSequential Approximate Optimization RSM D-Optimality
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