Robust Optimization of System Design

摘要

The data of real-world optimization problems are usually uncertain, that is especially true for early stages of system design. Data uncertainty can significantly affect the quality of the nominal solution. Robust Optimization (RO) methodology uses chance and robust constraints to generate a robust solution immunized against the effect of data uncertainty. RO methodology can be applied to any generic optimization problem where one can separate uncertain numerical data from the problem's structure. Since 2000, the RO area is witnessing a burst of research activity in both theory and applications. However, RO could lead to over-conservative requirements, resulting in typical-case bad solutions or even empty solution spaces. This drawback of the classical RO methodology can be overcome by distinguishing between real decision variables and so-called state variables. While the first type should satisfy the chance or robust constraints and their value cannot depend on a specific realization of the uncertain data, the state variables are adjustable (i.e., their value can depend on the specific realization of the uncertain data), since most of the constraints defining state variables merely "calculate" their exact value, and hence are always satisfied. In this paper we summarize how adjustable RO approach can be applied to a general uncertain linear optimization problem. Then, using an allocation example we demonstrate how this approach can be integrated in the design optimization process and its impact on the optimal system design.