On the formulation of optimization problems under uncertainty in mechanical design

This paper proposes a guide to help designer to formulate the optimization under uncertainty in mechanical design problem. An efficient tool based on the necessary conditions for each optimization under uncertainty type is introduced here. This tool is capable to guide the designer to choose between different types of optimization under uncertainty, the suitable method for a given problem. The problematic of the antagonism between the performance and its stability is studied. We also identify the importance of the evaluation of this antagonism before solving the design problem in robustness formulation. An efficient general method is developed for this evaluation. This method is very useful to save computational time and to give to the designer an early information about the stability of performance under uncertainties of his design.