Efficient solutions in uncertain multiobjective optimization with countably many scenarios

Abstract

We use a vector approach to address, from an efficient point of view, an uncertain unconstrained multiobjective optimization problem with countably many scenarios. Specifically, we introduce several efficient solution notions that work not only in the Pareto case, but also when the preferences in the image space depend on the scenario and they are defined by a convex cone in the usual way. We state basic properties of these notions and we relate the involved solution sets with other well-known solution sets of the literature. Particularly, it is shown that the so-called highly solutions are a particular case of efficient solutions. In addition, we obtain characterizations through solutions of associated scalar optimization problems and we derive existence theorems. Finally, two applications are provided to illustrate the main results.