Pareto Solutions in Multicriteria Optimization Under Uncertainty

We present and analyze several definitions of Pareto optimality for multicriteria optimization or decision problems with uncertainty primarily in their objective function values. In comparison to related notions of Pareto robustness, we first provide a full characterization of an alternative efficient set hierarchy that is based on six different ordering relations both with respect to the multiple objectives and a possibly finite, countably infinite or uncountable number of scenarios. We then establish several scalarization results for the generation of the corresponding efficient points using generalized weighted-sum and epsilon-constraint techniques. Finally, we leverage these scalarization results to also derive more general conditions for the existence of efficient points in each of the corresponding optimality classes, under suitable assumptions.