ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation
Multiobjective optimization plays an increasingly important role in modern
applications, where several objectives are often of equal importance. The task
in multiobjective optimization and multiobjective optimal control is therefore
to compute the set of optimal compromises (the Pareto set) between the
conflicting objectives. Since the Pareto set generally consists of an infinite
number of solutions, the computational effort can quickly become challenging
which is particularly problematic when the objectives are costly to evaluate as
is the case for models governed by partial differential equations (PDEs). To
decrease the numerical effort to an affordable amount, surrogate models can be
used to replace the expensive PDE evaluations. Existing multiobjective
optimization methods using model reduction are limited either to low parameter
dimensions or to few (ideally two) objectives. In this article, we present a
combination of the reduced basis model reduction method with a continuation
approach using inexact gradients. The resulting approach can handle an
arbitrary number of objectives while yielding a significant reduction in
computing time.
43-76
43-76
Springer