In recent years, researchers have made great efforts in tackling the High-dimensional, Expensive (computationally), Black box (HEB) design problems. The high dimensionality and lack of knowledge of the problem usually demand a large number of samples for optimization, which is often impractical due to the total time required to compute the required number of expensive simulations. In this thesis, Correspondence Analysis (CA) is introduced to discover as much information as possible about the black box to minimize the number of samples. The discovered information such as the promising subdomains, important variables, and symmetric variables is used to assist the resampling in an existing optimization algorithm. While being independent from the optimization algorithm, the approached method is applied to the Trust Region based Mode Pursuing Sampling (TRMPS2), a global optimization method developed for HEB problems. The CA based TRMPS2 method (CA_TRMPS) is shown to yield better optima with higher efficiency than TRMPS2. Tests on mathematical benchmark functions and application to a real-world engineering problem show the promise of the proposed approach.
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Thesis advisor: Wang, Gary
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