Local approximation of the efficient frontier in robust design

The problem of robust design is treated as a bi-objective optimization prob lem in which the performance mean and variation are optimized and minimized , respectively. A method for deriving a utility function as a local approxi mation of the efficient frontier is presented and investigated at different locations of candidate solutions, with different ranges of interest, and f or efficient frontiers with both convex and nonconvex behaviors. As an inte gral part of the interactive robust design procedure earlier proposed by th e authors, the method assists designers in adjusting the preference structu re and exploring alternative efficient robust design solutions. It eliminat es the need of solving the bi-objective problem repeatedly using new prefer ence structures, which is often computationally expensive. Though demonstra ted for robust design problems, the principle is also applicable to any bi- objective optimization problem. [S1050-0472(00)00702-9].