Publikation: Set-Oriented Multiobjective Optimal Control of PDEs using Proper Orthogonal Decomposition
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2018
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KEIPER, Winfried, ed., Anja MILDE, ed., Stefan VOLKWEIN, ed.. Reduced-Order Modeling (ROM) for Simulation and Optimization : Powerful Algorithms as Key Enablers for Scientific Computing. Cham: Springer, 2018, pp. 47-72. ISBN 978-3-319-75318-8. Available under: doi: 10.1007/978-3-319-75319-5_3
Zusammenfassung
In this chapter, we combine a global, derivative-free subdivision algorithm for multiobjective optimization problems with a-posteriori error estimates for reduced-order models based on Proper Orthogonal Decomposition in order to efficiently solve multiobjective optimization problems governed by partial differential equations. An error bound for a semilinear heat equation is developed by which the errors in the conflicting objectives can be estimated individually. The resulting algorithm constructs a library of locally valid reduced-order models online using a Greedy (worst-first) search. Using this approach, the number of evaluations of the full-order model can be reduced by a factor of more than 1000.
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Fachgebiet (DDC)
510 Mathematik
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Multiobjective optimization, PDE-constrained optimization, reduced-order modeling, set-oriented methods
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Reduced-Order Modeling for Simulation and Optimization : Powerful Algorithms as Key Enablers for Scientific Computing ; KoMSO Challenge Workshop, 17. Nov. 2016 - 18. Nov. 2016, Renningen, Germany
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BEERMANN, Dennis, Michael DELLNITZ, Sebastian PEITZ, Stefan VOLKWEIN, 2018. Set-Oriented Multiobjective Optimal Control of PDEs using Proper Orthogonal Decomposition. Reduced-Order Modeling for Simulation and Optimization : Powerful Algorithms as Key Enablers for Scientific Computing ; KoMSO Challenge Workshop. Renningen, Germany, 17. Nov. 2016 - 18. Nov. 2016. In: KEIPER, Winfried, ed., Anja MILDE, ed., Stefan VOLKWEIN, ed.. Reduced-Order Modeling (ROM) for Simulation and Optimization : Powerful Algorithms as Key Enablers for Scientific Computing. Cham: Springer, 2018, pp. 47-72. ISBN 978-3-319-75318-8. Available under: doi: 10.1007/978-3-319-75319-5_3BibTex
@inproceedings{Beermann2018SetOr-38752,
year={2018},
doi={10.1007/978-3-319-75319-5_3},
title={Set-Oriented Multiobjective Optimal Control of PDEs using Proper Orthogonal Decomposition},
isbn={978-3-319-75318-8},
publisher={Springer},
address={Cham},
booktitle={Reduced-Order Modeling (ROM) for Simulation and Optimization : Powerful Algorithms as Key Enablers for Scientific Computing},
pages={47--72},
editor={Keiper, Winfried and Milde, Anja and Volkwein, Stefan},
author={Beermann, Dennis and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}
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