Pareto Analysis with Uncertainty

Pareto analysis is a broadly applicable method to model and analyze tradeoffs in multi-objective optimization problems. The set of Pareto optimal solutions is guaranteed to contain the best solution for any arbitrary cost function or selection procedure. This work introduces a method to explicitly take uncertainty into account during Pareto analysis. A solution is not modeled by a single point in the solution space, but rather by a set of such points. This is useful in settings with much uncertainty, such as during model-based design space exploration for embedded systems. A bounding-box abstraction is introduced as a finite representation of Pareto optimal solutions under uncertainty. It is shown that the set of Pareto optimal solutions in the proposed approach still captures exactly the potentially best solutions for any cost function as well as any way of reducing the amount of uncertainty. During model-based design space exploration, for instance, design and implementation choices that are made during the development process reduce the amount of uncertainty. Steps in such a refinement trajectory can render previously Pareto optimal solutions sub optimal. The presented results provide a way to ensure that early selections in the refinement process remain valid.