Multiresponse and multistage metamodeling approach for design optimization

A new multiresponse and multistage metamodeling approach is developed for design optimization. Distinct from the existing objective-oriented sequential sampling methods, where the design objective and constraints have to be combined into a single response of interest, our method offers the flexibility of building metamodels for multiple responses (objective/constraints) simultaneously. Uncertainty quantification is introduced for each metamodel to represent the confidence interval due to the lack of sufficient sample points. Based on the extreme values of the optimal solution identified within the confidence interval, the level set representation, together with a series of Boolean operations, is used to synthesize the region(s) of interest with arbitrary topologies. Introducing the level set representation into the metamodeling process facilitates manipulations of regions formed by different responses, the representation of disconnected regions of interest, and the visualization for design exploration. Through mathematical benchmark examples and an engineering design problem, we demonstrate that the proposed method possesses superior efficiency in design exploration and allows multiple sample points at each sampling stage. As the metamodeling process moves on, the region of interest is progressively reduced, and the optimal design is asymptotically approached. Our results are compared with those from one-stage metamodeling using the optimal Latin hypercube experiments and from the sequential metamodeling using the efficient global optimization algorithm to demonstrate the efficiency and effectiveness of our method.