[CCoE Notice] Dissertation Defense: A Novel Approach to Robust Design Using Recent Advances in Robust and Multiobjective Optimization Methods

[Grayson, Audrey A]

A Novel Approach to Robust Design Using Recent Advances in Robust and Multiobjective Optimization Methods

Gregory Joseph Dissertation
Defense Date: Thursday, December 3rd 2015
Time: 12:00pm Location Room: Room 202, Engineering Building 1
Committee Members: Dr. Karolos Grigoriadis, Dr. Gangbing Song, Dr. Gino Lim, Dr. Qianmei Feng, Dr. Jagannatha Rao

              Parameter uncertainty is a fact of life for engineering design. Traditionally, uncertainty has been treated by several approaches, such as Factor of Safety, Worst Case Analysis, or Monte Carlo methods. More recently, the field of Robust Optimization has arisen to treat parameter uncertainty more precisely. These new methods seek to immunize the objective function against appropriate definitions of parametric uncertainty sets. A standard feature of current methods is that they require information about the uncertain parameters to be known before the method can be applied.

            In this dissertation, we study an alternate viewpoint to the treatment of uncertainty. Rather than begin with a known parameter distribution, we choose to let the problem itself resolve information regarding the inherent model flexibility that may already exist. Motivated by ideas from goal programming, we formulate a new multiobjective model which solves for a weighted balance of optimality and robustness metrics. This approach, which we call the Budget of Uncertainty (BoU) model, allows for an optimization method which (1) generates robust solutions feasible in the presence of problem uncertainty; (2) allows for design trades between fully optimal and fully robust solutions; (3) simultaneously solves design variables and allowed problem uncertainties; and (4) provides an opportunity for lexicographic adjustment of the uncertain parameters.

            We illustrate these ideas using the numerical solution of design case studies in which the budget of uncertainty is allocated across parameters in conjunction with the solution for the optimum design variables.
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