Distributionally robust optimization for Gaussian mixture model ambiguity under moment variations

Introduction:

Real-world uncertainty often comes from several different operating conditions, which can be naturally described by a Gaussian mixture model. In many cases, we may have a good idea of how frequently these conditions occur, while the behavior within each condition is still difficult to estimate accurately. This paper develops a distributionally robust optimization framework for this situation. Instead of changing the probabilities of different operating conditions, the method keeps these probabilities fixed and allows the characteristics of each condition, such as its average behavior and variability, to change. In this way, decisions are protected against errors in the estimated Gaussian components while still preserving the overall structure of the data. The method is evaluated through numerical examples and a chemical production planning case study, showing that it can provide a useful balance between robustness and conservatism when uncertainty mainly comes from inaccurate component estimates.