Special Issue "Recent Trends in Multiobjective Optimization and Optimal Control"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 29 February 2020.

Special Issue Editors

Prof. Dr. Michael Dellnitz
E-Mail Website
Guest Editor
Department of Mathematics, Paderborn University, D-33095 Paderborn, Germany
Interests: Multiobjective Optimization; Computational Dynamics; Dynamical Systems
Prof. Dr. Sina Ober-Bloebaum
E-Mail Website
Guest Editor
Department of Engineering Science, University of Oxford, Oxford, UK
Interests: Multiobjective Optimal Control; Geometric Integration; Computational Mechanics
Dr. Sebastian Peitz
E-Mail Website
Guest Editor
Department of Mathematics, Paderborn University, Paderborn, Germany
Interests: Multiobjective Optimization; Optimal Control; Model Order Reduction

Special Issue Information

Dear Colleagues,

In many applications in the natural sciences, in engineering or in industry one has to optimize several objectives at the same time. A topical paradigm is the simultaneous optimization of safety, energy efficiency and comfort in the area of autonomous driving. In mathematical terms this leads to multiobjective optimization problems whose solution—the “optimal compromise” between the different objectives—is provided by the set of so-called Pareto optimal points.

Due to the increasing complexity of current technical innovations, interest in the field of multiobjective optimization has recently increased significantly. The purpose of this Special Issue is to highlight recent trends and significant advances in this area. Of interest in this context are topics including but not limited to:

  • multiobjective optimal/model predictive/feedback control;
  • multiobjective optimization with PDE constraints;
  • many-objective optimization (i.e. the number of objectives is larger than 3);
  • multiobjective optimization based on data, or in combination with mathematical models (e.g. for the problems mentioned above).

Approaches to the solution of these problems are e.g. provided by classical mathematical optimization methods, modern control strategies, techniques from model order reduction, evolutionary algorithms, robust and data-driven optimization or from machine learning. Each submission should either directly address or elaborate on the relevance for an application. However, the wide spectrum of applications is not limited and it could range from real-time applications in autonomous driving to control problems in fluid mechanics.

Prof. Dr. Michael Dellnitz
Prof. Dr. Sina Ober-Bloebaum
Dr. Sebastian Peitz
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • multiobjective optimization
  • multiobjective optimal control
  • data based control
  • reduced order modelling
  • surrogate modelling

Published Papers (2 papers)

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Research

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Open AccessArticle
An Iterative Method Based on the Marginalized Particle Filter for Nonlinear B-Spline Data Approximation and Trajectory Optimization
Mathematics 2019, 7(4), 355; https://doi.org/10.3390/math7040355 - 16 Apr 2019
Cited by 1
Abstract
The B-spline function representation is commonly used for data approximation and trajectory definition, but filter-based methods for nonlinear weighted least squares (NWLS) approximation are restricted to a bounded definition range. We present an algorithm termed nonlinear recursive B-spline approximation (NRBA) for an iterative [...] Read more.
The B-spline function representation is commonly used for data approximation and trajectory definition, but filter-based methods for nonlinear weighted least squares (NWLS) approximation are restricted to a bounded definition range. We present an algorithm termed nonlinear recursive B-spline approximation (NRBA) for an iterative NWLS approximation of an unbounded set of data points by a B-spline function. NRBA is based on a marginalized particle filter (MPF), in which a Kalman filter (KF) solves the linear subproblem optimally while a particle filter (PF) deals with nonlinear approximation goals. NRBA can adjust the bounded definition range of the approximating B-spline function during run-time such that, regardless of the initially chosen definition range, all data points can be processed. In numerical experiments, NRBA achieves approximation results close to those of the Levenberg–Marquardt algorithm. An NWLS approximation problem is a nonlinear optimization problem. The direct trajectory optimization approach also leads to a nonlinear problem. The computational effort of most solution methods grows exponentially with the trajectory length. We demonstrate how NRBA can be applied for a multiobjective trajectory optimization for a battery electric vehicle in order to determine an energy-efficient velocity trajectory. With NRBA, the effort increases only linearly with the processed data points and the trajectory length. Full article
(This article belongs to the Special Issue Recent Trends in Multiobjective Optimization and Optimal Control)
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Review

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Open AccessReview
The Averaged Hausdorff Distances in Multi-Objective Optimization: A Review
Mathematics 2019, 7(10), 894; https://doi.org/10.3390/math7100894 - 24 Sep 2019
Abstract
A brief but comprehensive review of the averaged Hausdorff distances that have recently been introduced as quality indicators in multi-objective optimization problems (MOPs) is presented. First, we introduce all the necessary preliminaries, definitions, and known properties of these distances in order to provide [...] Read more.
A brief but comprehensive review of the averaged Hausdorff distances that have recently been introduced as quality indicators in multi-objective optimization problems (MOPs) is presented. First, we introduce all the necessary preliminaries, definitions, and known properties of these distances in order to provide a stat-of-the-art overview of their behavior from a theoretical point of view. The presentation treats separately the definitions of the ( p , q ) -distances GD p , q , IGD p , q , and Δ p , q for finite sets and their generalization for arbitrary measurable sets that covers as an important example the case of continuous sets. Among the presented results, we highlight the rigorous consideration of metric properties of these definitions, including a proof of the triangle inequality for distances between disjoint subsets when p , q 1 , and the study of the behavior of associated indicators with respect to the notion of compliance to Pareto optimality. Illustration of these results in particular situations are also provided. Finally, we discuss a collection of examples and numerical results obtained for the discrete and continuous incarnations of these distances that allow for an evaluation of their usefulness in concrete situations and for some interesting conclusions at the end, justifying their use and further study. Full article
(This article belongs to the Special Issue Recent Trends in Multiobjective Optimization and Optimal Control)
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