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

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 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.