Multiobjective PDE-constrained optimization using the reduced-basis method

Journal article (2017)

Authors

L. Iapichino Computational Design and Mechanics - Mechanical, Maritime and Materials Engineering
S. Ulbrich Technische Universität Darmstadt
S. Volkwein Universität Konstanz
Research Group
Computational Design and Mechanics (Mechanical, Maritime and Materials Engineering) (TU Delft)
Sensitivity analysis Reduced basis method A-posteriori error Multiobjective PDE-constrained optimization Weighted sum method
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Published Date

2017

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Precision and Microsystems Engineering

Research Group

Computational Design and Mechanics

Abstract

In this paper the reduced basis (RB) method is applied to solve quadratic multiobjective optimal control problems governed by linear parametrized variational equations. These problems often arise in applications, where the quality of the system behavior has to be measured by more than one criterium. The weighted sum method is exploited for defining scalar-valued linear-quadratic optimal control problems built by introducing additional optimization parameters. The optimal controls corresponding to specific choices of the optimization parameters are efficiently computed by the RB method. The accuracy is guaranteed by an a-posteriori error estimate. An effective sensitivity analysis allows to further reduce the computational times for identifying a suitable and representative set of optimal controls.