Multi-objective robust optimization using a sensitivity region concept

In multi-objective design optimization, it is quite desirable to obtain solutions that are "multi-objectively" optimum and insensitive to uncontrollable (noisy) parameter variations. We call such solutions robust Pareto solutions. In this paper we present a method to measure the multi-objective sensitivity of a design alternative, and an approach to use such a measure to obtain multi-objectively robust Pareto optimum solutions. Our sensitivity measure does not require a presumed probability distribution of uncontrollable parameters and does not utilize gradient information; therefore, it is applicable to multi-objective optimization problems that have non-differentiable and/or discontinuous objective functions, and also to problems with large parameter variations. As a demonstration, we apply our robust optimization method to an engineering example, the design of a vibrating platform. We show that the solutions obtained for this example are indeed robust.