Robust Multi-Objective Optimization: Analysis and Approaches

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This project deals with multi-objective optimization problems under uncertainty, i.e., it combines robust optimization with multi-objective optimization. Although uncertain data is common in most multi-objective real-world problems, research on robust multi-objective optimization started only recently. In the last six years, many concepts have been published which define what a "robust efficient" solution is, but not much theory on robust multi-objective optimization has been developed yet. More importantly, algorithms are scarce and if at all available then only for the simpler case of uncertain multi-objective problems whose robust counterparts are (deterministic) multi-objective problems. However, the robust counterpart of a multi-objective uncertain problem is usually a set-valued optimization problem. We propose to bring the theory on robust multi-objective optimization forward by working on aspects known from multi-objective optimization (such as scalarization or an efficient front) and from robust optimization (such as robust counterparts and the robustness gap). As we have to deal with set-valued optimization problems, a transfer of such aspects and results is not straightforward but needs suitable set order relations.The results obtained should be utilized in solution approaches for robust multi-objective problems which are to be tested with a focus on combinatorial robust multi-objective optimization problems.We furthermore will investigate which of our approaches are also suitable for more general set-valued optimization problems.