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Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition

In: Reduced-Order Modeling (ROM) for Simulation and Optimization

Author

Listed:
  • Dennis Beermann

    (University of Konstanz, Department of Mathematics and Statistics)

  • Michael Dellnitz

    (Paderborn University, Department of Mathematics)

  • Sebastian Peitz

    (Paderborn University, Department of Mathematics)

  • Stefan Volkwein

    (University of Konstanz, Department of Mathematics and Statistics)

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.

Suggested Citation

  • Dennis Beermann & Michael Dellnitz & Sebastian Peitz & Stefan Volkwein, 2018. "Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition," Springer Books, in: Winfried Keiper & Anja Milde & Stefan Volkwein (ed.), Reduced-Order Modeling (ROM) for Simulation and Optimization, pages 47-72, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-75319-5_3
    DOI: 10.1007/978-3-319-75319-5_3
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