457. On Derivative-Free Methods for Solving Set-based Robust Counterparts to Uncertain Multiobjective Optimization Problems
Invited abstract in session MD-3: Variational Methods in Set and Vector Optimization, stream Multiobjective and Vector Optimization.
Monday, 16:30-18:30Room: B100/4011
Authors (first author is the speaker)
| 1. | Christian Günther
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| Institut für Angewandte Mathematik, Leibniz University Hannover |
Abstract
This talk is devoted to derivative-free methods for solving set-based robust counterparts to uncertain multiobjective optimization problems. The motivation comes from uncertain multiobjective engineering problems for damage localization and quantification in flexible mechanical structures, which are in fact nonsmooth nonlinear multiobjective parameter estimation problems. We focus on robustness concepts (e.g., set-based min-max robust efficiency, set-based optimistic robust efficiency) given by solution concepts for the set-based robust counterpart problems based on preorder set relations (e.g., upper set less relation, lower set less relation). We illustrate an algorithmic pattern search procedure for approximating solutions to the set-based robust counterpart problems (with special emphasis on the case with a finite number of uncertainties), which is based on set-based (first- and higher-level) non-dominated sorting for finite families of sets and an infinite penalty approach, together with some implementation details of the procedure to improve numerical efficiency.
Keywords
- Multi-objective optimization
- Derivative-free optimization
Status: accepted
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