@inproceedings{8752, abstract = {{In this article we develop a gradient-based algorithm for the solution of multiobjective optimization problems with uncertainties. To this end, an additional condition is derived for the descent direction in order to account for inaccuracies in the gradients and then incorporated into a subdivision algorithm for the computation of global solutions to multiobjective optimization problems. Convergence to a superset of the Pareto set is proved and an upper bound for the maximal distance to the set of substationary points is given. Besides the applicability to problems with uncertainties, the algorithm is developed with the intention to use it in combination with model order reduction techniques in order to efficiently solve PDE-constrained multiobjective optimization problems.}}, author = {{Peitz, Sebastian and Dellnitz, Michael}}, booktitle = {{NEO 2016}}, isbn = {{9783319640624}}, issn = {{1860-949X}}, pages = {{159--182}}, title = {{{Gradient-Based Multiobjective Optimization with Uncertainties}}}, doi = {{10.1007/978-3-319-64063-1_7}}, year = {{2017}}, } @phdthesis{10594, 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. Since – in contrast to the solution of a single objective optimization problem – the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging. This is even more the case when many problems have to be solved, when the number of objectives is high, or when the objectives are costly to evaluate. Consequently, this thesis is devoted to the identification and exploitation of structure both in the Pareto set and the dynamics of the underlying model as well as to the development of efficient algorithms for solving problems with additional parameters, with a high number of objectives or with PDE-constraints. These three challenges are addressed in three respective parts. In the first part, predictor-corrector methods are extended to entire Pareto sets. When certain smoothness assumptions are satisfied, then the set of parameter dependent Pareto sets possesses additional structure, i.e. it is a manifold. The tangent space can be approximated numerically which yields a direction for the predictor step. In the corrector step, the predicted set converges to the Pareto set at a new parameter value. The resulting algorithm is applied to an example from autonomous driving. In the second part, the hierarchical structure of Pareto sets is investigated. When considering a subset of the objectives, the resulting solution is a subset of the Pareto set of the original problem. Under additional smoothness assumptions, the respective subsets are located on the boundary of the Pareto set of the full problem. This way, the “skeleton” of a Pareto set can be computed and due to the exponential increase in computing time with the number of objectives, the computations of these subsets are significantly faster which is demonstrated using an example from industrial laundries. In the third part, PDE-constrained multiobjective optimal control problems are addressed by reduced order modeling methods. Reduced order models exploit the structure in the system dynamics, for example by describing the dynamics of only the most energetic modes. The model reduction introduces an error in both the function values and their gradients, which has to be taken into account in the development of algorithms. Both scalarization and set-oriented approaches are coupled with reduced order modeling. Convergence results are presented and the numerical benefit is investigated. The algorithms are applied to semi-linear heat flow problems as well as to the Navier-Stokes equations. }}, author = {{Peitz, Sebastian}}, title = {{{ Exploiting structure in multiobjective optimization and optimal control}}}, doi = {{10.17619/UNIPB/1-176}}, year = {{2017}}, } @article{8756, abstract = {{We present a new algorithm for model predictive control of non-linear systems with respect to multiple, conflicting objectives. The idea is to provide a possibility to change the objective in real-time, e.g. as a reaction to changes in the environment or the system state itself. The algorithm utilises elements from various well-established concepts, namely multiobjective optimal control, economic as well as explicit model predictive control and motion planning with motion primitives. In order to realise real-time applicability, we split the computation into an online and an offline phase and we utilise symmetries in the open-loop optimal control problem to reduce the number of multiobjective optimal control problems that need to be solved in the offline phase. The results are illustrated using the example of an electric vehicle where the longitudinal dynamics are controlled with respect to the concurrent objectives arrival time and energy consumption.}}, author = {{Peitz, Sebastian and Schäfer, Kai and Ober-Blöbaum, Sina and Eckstein, Julian and Köhler, Ulrich and Dellnitz, Michael}}, issn = {{2405-8963}}, journal = {{Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)}}, number = {{1}}, pages = {{8674--8679}}, title = {{{A multiobjective MPC approach for autonomously driven electric vehicles}}}, doi = {{10.1016/j.ifacol.2017.08.1526}}, volume = {{50}}, year = {{2017}}, } @inproceedings{8759, abstract = {{In a wide range of applications, it is desirable to optimally control a system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a single optimal solution, the set of optimal compromises, the so-called Pareto set, has to be approximated. When it is not possible to compute the entire control trajectory in advance, for instance due to uncertainties or unforeseeable events, model predictive control methods can be applied to control the system during operation in real time. In this article, we present an algorithm for the solution of multiobjective model predictive control problems. In an offline scenario, it can be used to compute the entire set of optimal compromises whereas in a real time scenario, one optimal compromise is computed according to an operator's preference. The results are illustrated using the example of an industrial laundry. A logistics model of the laundry is developed and then utilized in the optimization routine. Results are presented for an offline as well as an online scenario.}}, author = {{Peitz, Sebastian and Gräler, Manuel and Henke, Christian and Molo, Mirko Hessel-von and Dellnitz, Michael and Trächtler, Ansgar}}, booktitle = {{Procedia Technology}}, issn = {{2212-0173}}, pages = {{483--490}}, title = {{{Multiobjective Model Predictive Control of an Industrial Laundry}}}, doi = {{10.1016/j.protcy.2016.08.061}}, year = {{2016}}, } @inproceedings{8758, abstract = {{In this contribution we compare two different approaches to the implementation of a Model Predictive Controller in an electric vehicle with respect to the quality of the solution and real-time applicability. The goal is to develop an intelligent cruise control in order to extend the vehicle range, i.e. to minimize energy consumption, by computing the optimal torque profile for a given track. On the one hand, a path-based linear model with strong simplifications regarding the vehicle dynamics is used. On the other hand, a nonlinear model is employed in which the dynamics of the mechanical and electrical subsystem are modeled.}}, author = {{Eckstein, Julian and Peitz, Sebastian and Schäfer, Kai and Friedel, Patrick and Köhler, Ulrich and Hessel von Molo, Mirko and Ober-Blöbaum, Sina and Dellnitz, Michael}}, booktitle = {{Procedia Technology, 3rd International Conference on System-Integrated Intelligence: New Challenges for Product and Production Engineering}}, issn = {{2212-0173}}, pages = {{465--472}}, title = {{{A comparison of two predictive approaches to control the longitudinal dynamics of electric vehicles}}}, doi = {{10.1016/j.protcy.2016.08.059}}, volume = {{26}}, year = {{2016}}, } @inproceedings{29433, author = {{Peitz, Sebastian and Ober-Blöbaum, Sina and Dellnitz, M.}}, booktitle = {{Proceedings of International Congress of Theoretical and Applied Mechanics}}, title = {{{Reduced order model based multiobjective optimal control of fluids}}}, year = {{2016}}, } @inproceedings{8760, abstract = {{n this article an efficient numerical method to solve multiobjective optimization problems for fluid flow governed by the Navier Stokes equations is presented. In order to decrease the computational effort, a reduced order model is introduced using Proper Orthogonal Decomposition and a corresponding Galerkin Projection. A global, derivative free multiobjective optimization algorithm is applied to compute the Pareto set (i.e. the set of optimal compromises) for the concurrent objectives minimization of flow field fluctuations and control cost. The method is illustrated for a 2D flow around a cylinder at Re = 100.}}, author = {{Peitz, Sebastian and Dellnitz, Michael}}, booktitle = {{PAMM}}, issn = {{1617-7061}}, pages = {{613--614}}, title = {{{Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction}}}, doi = {{10.1002/pamm.201510296}}, year = {{2015}}, }