A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction

S. Peitz, M. Dellnitz, Mathematical and Computational Applications 23 (2018).

Journal Article | Published | English
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Abstract
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.
Publishing Year
Journal Title
Mathematical and Computational Applications
Volume
23
Issue
2
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Peitz S, Dellnitz M. A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction. Mathematical and Computational Applications. 2018;23(2). doi:10.3390/mca23020030
Peitz, S., & Dellnitz, M. (2018). A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction. Mathematical and Computational Applications, 23(2). https://doi.org/10.3390/mca23020030
@article{Peitz_Dellnitz_2018, title={A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction}, volume={23}, DOI={10.3390/mca23020030}, number={2}, journal={Mathematical and Computational Applications}, author={Peitz, Sebastian and Dellnitz, Michael}, year={2018} }
Peitz, Sebastian, and Michael Dellnitz. “A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction.” Mathematical and Computational Applications 23, no. 2 (2018). https://doi.org/10.3390/mca23020030.
S. Peitz and M. Dellnitz, “A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction,” Mathematical and Computational Applications, vol. 23, no. 2, 2018.
Peitz, Sebastian, and Michael Dellnitz. “A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction.” Mathematical and Computational Applications, vol. 23, no. 2, 2018, doi:10.3390/mca23020030.

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