Abstract: A new robust design optimization method to automatically search multiple optimal solutions and to estimate robust objective variations is presented. The method does not require a presumed probability distribution for parameters, and is applicable even when the objective function is non-differentiable and/or discontinuous and when parameter variations are large. The method is developed based on the relationships between performance variation and their sensitivity regions using a worst-case scenario analysis. Three loops are included in the method. Inner loop optimizes objective function subject to the robustness constraints at a robust index; Middle loop conducts the search for the robust objective variation using a iterative approach; Outer loop performs the search for the multiple optimal solutions by means of adjusting the thresholds of robustness indexes. The method provides the objective values and their robust objective variations of multiple optimal solutions. By using analytical interpretations and providing a illustrative example, the method shows advantages that it does not require designers to cautiously determine the thresholds of robustness indexes and yields more information that enable designers to carry out a trade-offs analysis between objective values and their robustness.

Key words: Design optimization, Robust design, Robustness, Uncertainty analysis