Local Approximation of the Efficient Frontier in Robust Design

ABSTRACT: The problem of robust design is treated as a bi-objective optimization problem in which the performance mean and variation are optimized and minimized, respectively. A method for deriving a utility function as a local approximation of the efficient frontier is presented and investigated at different locations of candidate solutions, with different ranges of interest, and for efficient frontiers with both convex and nonconvex behaviors. As an integral part of the interactive robust design procedure earlier proposed by the authors, the method assists designers in adjusting the preference structure and exploring alternative efficient robust design solutions. It eliminates the need of solving the bi-objective problem repeatedly using new preference structures, which is often computationally expensive. Though demonstrated for robust design problems, the principle is also applicable to any bi-objective optimization problem.