Robust optimization for engineering design

Abstract

Generally, robust optimization problems are trade-offs between expected performance (i.e., expected cost) and variability measures, resulting multiobjective problems. While various robustness measures have been proposed to account for robustness, efforts to theoretically analyze the properties of robustness measures have thus far rarely been carried out, despite that such work is important to obtain desirable robust solutions. This thesis aims at investigating the properties of robustness measures, namely, economic robustness measure and technical robustness measure, according to the characteristic of uncertainties and suggesting a proper robust optimization model for engineering design, finally. For economic robustness measures, monotonic functions are recommended because economic robustness should focus on reducing or increasing economic terms as much as possible for realization of any model uncertainty. On the contrary, even functions are utilized for technical robustness because technical robustness should focus on reducing variance among technical terms as small as possible. The range of robust model parameters is diagnosed for robustness measures and the graphical representation of meaningful parameter ranges is clearly defined with theoretical explanation. It was noted that the use of probability and a target value causes ill-conditioned natures of partial mean so that a modified formulation is proposed. The modified model is identified with the robust worst-case model for the proposed range of a model parameter in discrete domain. For technical robustness, half interval among several even functions is selected in this study because it is linear and consistent with worst-case robustness measure. Finally, the robust optimization model is proposed such that its objectives consist of expected cost, economic robustness measure, and technical robustness measures. Pareto optimal subset condition is redefined to consider technical robustness together. For an at...