Single/Multi-objective Inverse Robust Evolutionary Design Methodology in the Presence of Uncertainty

Many existing works for handling uncertainty in problem-solving rely on some form of a priori knowledge of the uncertainty structure. However, in reality, one may not always possess the necessary expertise or sufficient knowledge to identify suitable bounds of the uncertainty involved. Rather, it is more likely that specifications of the realistic performance desired are derived, which may be based on the maximum degradation tolerable or worst-case performance permissible in the final solution. In this paper, we present a Single/Multi-objective Inverse Robust Evolutionary (SMIRE) optimization methodology. In contrast to conventional forward robust optimization, an inverse approach based on non-probabilistic methods is introduced to avoid making possible erroneous assumptions about the uncertainty when insufficient field data exists for accurately estimating its structure. Further, since uncertainty is practically impossible to avoid, we consider the possible benefits as the uncertainty prevails by introducing an opportunity criterion in the inverse search scheme. Four inverse schemes are presented to include the different objectives possibly considered in robust evolutionary optimization. The inverse schemes are applied on synthetic test functions to illustrate their utility.