Nearly all engineering design problems have multiple objectives with parameters that have uncontrollable variations due to noise or uncertainty. Such variations can significantly degrade performance of design solutions or can even make them infeasible. The variations can also adversely affect customer's preferences for a product design alternative and its success in the market.

This dissertation presents two multi-objective optimization approaches for obtaining robustly optimal design solutions. The two approaches use the same method to obtain a feasibly robust solution: one that does not violate any constraint due to uncontrollable variations. However, each approach uses a different method to obtain multi-objectively robust solutions. Approach 1 obtains a multi-objectively robust solution in which, with respect to a target point and under uncontrollable variations, the distance between worst case and target design points and the distance between worst and best case design points are minimized. Approach 2 obtains a multi-objectively robust solution which is optimal for nominal values of parameters and at the same time maintains an acceptable range of variability with respect to individual objective functions. Approach 2 is used within an integrated design and marketing framework to facilitate the generation of a robustly optimal set of single product design alternatives and a robustly optimal product line design alternative. By way of this framework, in the design domain, Approach 2 evaluates performance and robustness of design alternatives. While in the marketing domain, it considers designs that are robust with respect to customer preferences for variations propagated from the design domain as well as inherent variations due to the fit of a preference model to sampled marketing data.

The applicability and differences of the two robust optimization approaches are demonstrated and explored with a numerical and an engineering example. In particular, since Approach 2 is more flexible and less conservative than Approach 1, it has been applied and demonstrated with a real-word case study in single product and product line engineering of a power tool with both design and marketing considerations.