Type of Document Dissertation Author Croicu, Ana-Maria Author's Email Address firstname.lastname@example.org URN etd-11142005-102344 Title Single- and Multiple-objective Stochastic Programming Models with Applications to Aerodynamics Degree Doctor of Philosophy Department Mathematics, Department of Advisory Committee
Advisor Name Title M. Yousuff Hussaini Committee Chair Anuj Srivastava Committee Member David A. Kopriva Committee Member Qi Wang Committee Member Keywords
- Stochastic Programming
- Optimization Under Uncertainty
- Nash Equilibrium
Date of Defense 2005-10-28 Availability unrestricted AbstractDeterministic design assumes that there is no uncertainty in the modeling parameters, and as a consequence, there is no variability in the simulation outputs. Therefore, deterministic optimal designs that are obtained without
taking into account uncertainty are usually unreliable. This is the case with transonic shape optimization, where the randomness in the cruise Mach number might have significant impact on the optimal geometric design. In this context, a stochastic search turns out to be more appropriate.
Approaches to stochastic optimization have followed a variety of modeling philosophies, but little has been done to systematically compare different models. The goal of this thesis is to present a comparison between two stochastic optimization algorithms, with the emphasis on applications, especially on the airfoil shape optimization. Single-objective and multi-objective optimization programs are analyzed as well.
The relationship between the expected minimum value (EMV) criterion and the minimum expected value (MEV) criterion is explored, and it is shown that, under favorable conditions, a better optimal point could be obtained via the EMV approach. Unfortunately, the advantages of using the EMV approach are far outweighed by the prohibitive exorbitant computational cost.
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