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

Dennis Beermann (), Michael Dellnitz (), Sebastian Peitz () and Stefan Volkwein ()
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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

A chapter in Reduced-Order Modeling (ROM) for Simulation and Optimization, 2018, pp 47-72 from Springer

Abstract: 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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-75319-5_3

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DOI: 10.1007/978-3-319-75319-5_3

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