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COLLABORATIVE RESEARCH: SHORT CYCLE SURROGATE BASED DESIGN OPTIMIZATION PROJECT SUMMARY This proposal involves two engineers and a mathematician, and should also be considered under Section 2.(a) of the NSF 04-538 Mathematical Sciences solicitation. Surrogate-based optimization methods (SBO) for engineering design have become popu- lar because they allow the optimization of engineering systems requiring expensive com- puter simulations. SBO proceed in design cycles, each cycle consisting of gathering in- put/output data using computer simulations, construction of a surrogate based on these data, estimation of the optimum using the surrogate, and a simulation at that optimum. SBO are popular in industry as they are easily parallelized to meet the time constraints typical of such environments, with the surrogates being also used for visualization and sensitivity analysis. However, due to time and cost constraints, the design optimization is limited to a small number of cycles (short cycle SBO) and rarely allowed to proceed to convergence. Engineers must decide whether to invest in one additional optimization cy- cle or to accept the best design found so far. The objective of the proposed research is to help engineers using currently popular SBO to make that decision rationally. The intent is to make use of currently underutilized information available through the use of multiple surrogates and their corresponding appraisal prediction components. Intellectual merits: The current frontier of surrogate-based engineering design lacks sta- tistically rigorous procedures for assessing the merit of investing in another cycle of analysis versus accepting the present best solution (PBS). There is, however, the under- utilized machinery of model appraisal, which predicts the uncertainty in the surrogate es- timate at different points in design space. The proposed research will devise a procedure based on model appraisal information for providing the designer with a probability distri- bution for the expected improvement in the PBS with one additional design cycle. Fur- thermore, given the sparseness of the data used to construct the surrogates, alternative surrogates can provide reasonable approximations while giving different uncertainty es- timates throughout the design space. Therefore, the proposed research will make use of multiple surrogates in order to improve the quality of the probability information pro- vided to the designer. Broader impacts: The use of computer-assisted methods to facilitate design decisions is becoming pervasive in many fields, including automotive, aerospace, and enhanced oil recovery. SBO potentially provide more efficient ways to exploit computer simulations when making such decisions. With high-technology products, the design process can be a large portion of their costs. The proposed research will provide engineers with a more rigorous basis for involving SBO in the design process, and enable rational decisions on when to terminate the design phase. This will lead to a more efficient design phase with
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