Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition
D. Beermann, M. Dellnitz, S. Peitz, S. Volkwein, in: Reduced-Order Modeling (ROM) for Simulation and Optimization, Cham, 2018, pp. 47–72.
Download
No fulltext has been uploaded.
Book Chapter
| Published
| English
Author
Beermann, Dennis;
Dellnitz, Michael;
Peitz, SebastianLibreCat 
;
Volkwein, Stefan
;
Volkwein, StefanDepartment
Abstract
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 in such a way that 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.
Publishing Year
Book Title
Reduced-Order Modeling (ROM) for Simulation and Optimization
Page
47-72
ISBN
LibreCat-ID
Cite this
Beermann D, Dellnitz M, Peitz S, Volkwein S. Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition. In: Reduced-Order Modeling (ROM) for Simulation and Optimization. Cham; 2018:47-72. doi:10.1007/978-3-319-75319-5_3
Beermann, D., Dellnitz, M., Peitz, S., & Volkwein, S. (2018). Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition. In Reduced-Order Modeling (ROM) for Simulation and Optimization (pp. 47–72). Cham. https://doi.org/10.1007/978-3-319-75319-5_3
@inbook{Beermann_Dellnitz_Peitz_Volkwein_2018, place={Cham}, title={Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition}, DOI={10.1007/978-3-319-75319-5_3}, booktitle={Reduced-Order Modeling (ROM) for Simulation and Optimization}, author={Beermann, Dennis and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}, year={2018}, pages={47–72} }
Beermann, Dennis, Michael Dellnitz, Sebastian Peitz, and Stefan Volkwein. “Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition.” In Reduced-Order Modeling (ROM) for Simulation and Optimization, 47–72. Cham, 2018. https://doi.org/10.1007/978-3-319-75319-5_3.
D. Beermann, M. Dellnitz, S. Peitz, and S. Volkwein, “Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition,” in Reduced-Order Modeling (ROM) for Simulation and Optimization, Cham, 2018, pp. 47–72.
Beermann, Dennis, et al. “Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition.” Reduced-Order Modeling (ROM) for Simulation and Optimization, 2018, pp. 47–72, doi:10.1007/978-3-319-75319-5_3.
Google Scholar
ISBN Search