360. Multiobjective optimization, uncertainty, and a bit of set optimization
Invited abstract in session TE-1: Plenary III - Gabriele Eichfelder EUROPT Fellow, stream Plenaries.
Thursday, 16:20 - 17:20Room: M:A
Authors (first author is the speaker)
| 1. | Gabriele Eichfelder
|
| Institute of Mathematics, Technische Universität Ilmenau |
Abstract
In many applications one has to deal with various difficulties at the same time, like uncertain data or several competing objective functions. For instance, for the integration of neighborhood networks into overarching distributing energy networks, a pure optimization of the neighborhood networks under an externally defined weighting of the relevant targets does not adequately model the problem. Moreover, uncertainties in the form of fluctuations or other disturbances can appear and a found solution has to be robust against that. A robust approach to uncertain multiobjective optimization corresponds to solving a set-valued optimization problem. However, it is a very difficult task to solve these optimization problems even for specific cases.
In this talk, we give a short introduction and motivation for multiobjective optimization. In case of uncertainties, a family of parametrized multiobjective optimization problems has to be examined and we discuss approaches on how this is done in the literature. Thereby, basic concepts of set optimization are needed, i.e., of optimization with a set-valued objective function. For that reason, we also provide a short introduction to the main optimality concepts and to new solution approaches used in set optimization. We combine everything for obtaining a solvable reformulation of an uncertain multiobjective problem using a robust approach which extends the classical epigraphical reformulation from single-objective optimization to multiple objectives.
Keywords
- Multi- and many-objective optimization
Status: accepted
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