---
_id: '8751'
abstract:
- lang: eng
  text: Multiobjective optimization plays an increasingly important role in modern
    applications, where several criteria 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. The advances in algorithms and the increasing interest in Pareto-optimal
    solutions have led to a wide range of new applications related to optimal and
    feedback control, which results in new challenges such as expensive models or
    real-time applicability. 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 or
    when a solution has to be presented very quickly. This article gives an overview
    of recent developments in accelerating multiobjective optimal control for complex
    problems where either PDE constraints are present or where a feedback behavior
    has to be achieved. In the first case, surrogate models yield significant speed-ups.
    Besides classical meta-modeling techniques for multiobjective optimization, a
    promising alternative for control problems is to introduce a surrogate model for
    the system dynamics. In the case of real-time requirements, various promising
    model predictive control approaches have been proposed, using either fast online
    solvers or offline-online decomposition. We also briefly comment on dimension
    reduction in many-objective optimization problems as another technique for reducing
    the numerical effort.
article_type: review
author:
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
citation:
  ama: Peitz S, Dellnitz M. A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate
    Models, Feedback Control and Objective Reduction. <i>Mathematical and Computational
    Applications</i>. 2018;23(2). doi:<a href="https://doi.org/10.3390/mca23020030">10.3390/mca23020030</a>
  apa: Peitz, S., &#38; Dellnitz, M. (2018). A Survey of Recent Trends in Multiobjective
    Optimal Control—Surrogate Models, Feedback Control and Objective Reduction. <i>Mathematical
    and Computational Applications</i>, <i>23</i>(2). <a href="https://doi.org/10.3390/mca23020030">https://doi.org/10.3390/mca23020030</a>
  bibtex: '@article{Peitz_Dellnitz_2018, title={A Survey of Recent Trends in Multiobjective
    Optimal Control—Surrogate Models, Feedback Control and Objective Reduction}, volume={23},
    DOI={<a href="https://doi.org/10.3390/mca23020030">10.3390/mca23020030</a>}, number={2},
    journal={Mathematical and Computational Applications}, author={Peitz, Sebastian
    and Dellnitz, Michael}, year={2018} }'
  chicago: Peitz, Sebastian, and Michael Dellnitz. “A Survey of Recent Trends in Multiobjective
    Optimal Control—Surrogate Models, Feedback Control and Objective Reduction.” <i>Mathematical
    and Computational Applications</i> 23, no. 2 (2018). <a href="https://doi.org/10.3390/mca23020030">https://doi.org/10.3390/mca23020030</a>.
  ieee: S. Peitz and M. Dellnitz, “A Survey of Recent Trends in Multiobjective Optimal
    Control—Surrogate Models, Feedback Control and Objective Reduction,” <i>Mathematical
    and Computational Applications</i>, vol. 23, no. 2, 2018.
  mla: Peitz, Sebastian, and Michael Dellnitz. “A Survey of Recent Trends in Multiobjective
    Optimal Control—Surrogate Models, Feedback Control and Objective Reduction.” <i>Mathematical
    and Computational Applications</i>, vol. 23, no. 2, 2018, doi:<a href="https://doi.org/10.3390/mca23020030">10.3390/mca23020030</a>.
  short: S. Peitz, M. Dellnitz, Mathematical and Computational Applications 23 (2018).
date_created: 2019-03-29T13:27:51Z
date_updated: 2022-01-06T07:04:00Z
department:
- _id: '101'
doi: 10.3390/mca23020030
intvolume: '        23'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://www.mdpi.com/2297-8747/23/2/30/pdf
oa: '1'
publication: Mathematical and Computational Applications
publication_identifier:
  issn:
  - 2297-8747
publication_status: published
status: public
title: A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models,
  Feedback Control and Objective Reduction
type: journal_article
user_id: '47427'
volume: 23
year: '2018'
...