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Robust optimization usually requires numerous functional evaluations, which is not feasible when the functional evaluation is time-consuming. Examples in automobile industry include crash worthiness/safety and fatigue life simulations. In practice, a response surface model (RSM) is often used as a surrogate to the CAE model, so that robust optimization can be carried out. However, if the error in the RSM is significant, the solution based on the RSM can be invalid. This paper proposes a method of finding multiple candidate solutions, all of which have similar predicted performances. This approach is effective in finding the close-to-optimum solutions when the model has error, and providing design alternatives. Examples are provided to illustrate the method.

In performing stochastic simulations using computer models, the method of sampling is important. It affects the quality and the convergence speed of the results. This paper discusses one special case: sampling of spot-weld locations from potentially thousands of spot welds on a vehicle body. This study is prompted by the need of evaluating the effect of missed spot welds on the structural integrity, identifying critical welds, and optimizing weld locations. A balanced random sampling algorithm based on the concept of Latin-Hypercube sampling is developed for this application. We also present a case study in which the efficiency of three different sampling methods is compared using a car joint stiffness example. The new method, called the Balanced Latin-Hypercube Sampling (BLHS), has shown significantly faster convergence over the other two.