Multi-objective optimization under parametric uncertainty: A Pareto ellipsoids-based algorithm

Model-based multi-objective optimization is a useful tool to compute optimal trade-offs between multiple conflicting objectives such as minimizing energy consumption while maximizing productivity. However, the computational cost of solving such optimization problems is high. In addition, a model approximates the real process, meaning uncertainty is inherently present. To avoid erroneous predictions of process performance and unsafe operation conditions, this uncertainty should be accounted for. Adding uncertainty propagation techniques increases the computational cost even further. In this article, a novel algorithm is presented that efficiently computes relevant Pareto points based on a significance criterion using Pareto ellipsoids. These ellipsoids represent and visualize the uncertainty on the objective functions due to parametric uncertainty. This facilitates the selection of the Pareto points as it allows a decision-maker to easily consider the uncertainty of a solution. The algorithm is showcased using three case studies with different levels of complexity.