Robust Multiobjective Optimization: Analysis and Solution Methods
This project is funded by the DFG from 2019 to 2022.
This project combines the two areas of multi-objective and robust optimization: it deals with multi-objective optimization problems under uncertain data. Although uncertain data occur in most practical applications of multiobjective problems, the topic has only attracted attention in the literature very recently. Various concepts have been proposed to define a "robustly efficient" solution to multiobjective problems, but little research has been done on the theory. Likewise, there are hardly any solution methods. The few approaches mostly refer to the simple case in which robustly efficient solutions can be found by solving a deterministic multi-criteria problem. In most cases, however, the solution of a set-valued problem is necessary. The aim of the project is to advance the theory of multiobjective robust optimization. Therefore, aspects of multiobjective optimization (like scalarizations or the efficient front) as well as aspects of robust optimization (like the analysis of the resulting robust counterparts or the robustness gap) will be investigated. This is mathematically challenging, because as robust counterparts of multiobjective problems, set-valued optimization problems arise, for the treatment of which suitable set relations are required. The results obtained will be used to develop solution methods for multiobjective robust problems, which will be further developed and tested especially for combinatorial robust multiobjective problems. It will also be investigated whether the approaches developed can also be used for more general set-valued problems.