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A trust region approach for multi-objective heterogeneous optimization
This thesis presents a trust region approach for multi-objective optimization problems with heterogeneous objective functions. One of the objective functions is an expensive black-box function, not given analytically, but for example by a simulation. Computing function values is assumed to be time-consuming and derivative information is not available with reasonable effort. The other objective functions are assumed to be given analytically and function evaluations and derivatives are easily available with low numerical effort. A basic algorithm for such optimization problems is presented. It is an iterative approach using local model functions and a search direction which is defined in the image space. The algorithm generates a sequence of iteration points. It is proved that the accumulation point of this sequence fulfills a necessary condition for local optimality. Moreover, several modifications of the basic algorithm are presented that make more use of the heterogeneity of the objective functions and partly produce several points as output. Numerical results for the basic algorithm and several modifications are presented and discussed. They confirm the theoretical findings and show the usefulness of the approaches. Moreover, an application-motivated optimization problem from fluid dynamics is considered and the results are presented and interpreted according to the application. ; In dieser Arbeit wird ein "Trust-Region" Algorithmus für multikriterielle Optimierungsprobleme mit heterogenen Zielfunktionen vorgestellt. Eine der Zielfunktionen ist eine teure Black-Box-Funktion. Sie ist nicht analytisch gegeben, sondern beispielsweise durch eine Simulation. Für diese Funktion wird angenommen, dass die Berechnung von Funktionswerten zeitaufwändig ist und die Ableitungen nicht mit vertretbarem numerischen Aufwand berechnet werden können. Des Weiteren wird vorausgesetzt, dass die anderen Zielfunktionen analytisch gegeben sind und die Berechnung von Funktionswerten und Ableitungen mit geringem numerischen Aufwand ...
A trust region approach for multi-objective heterogeneous optimization
This thesis presents a trust region approach for multi-objective optimization problems with heterogeneous objective functions. One of the objective functions is an expensive black-box function, not given analytically, but for example by a simulation. Computing function values is assumed to be time-consuming and derivative information is not available with reasonable effort. The other objective functions are assumed to be given analytically and function evaluations and derivatives are easily available with low numerical effort. A basic algorithm for such optimization problems is presented. It is an iterative approach using local model functions and a search direction which is defined in the image space. The algorithm generates a sequence of iteration points. It is proved that the accumulation point of this sequence fulfills a necessary condition for local optimality. Moreover, several modifications of the basic algorithm are presented that make more use of the heterogeneity of the objective functions and partly produce several points as output. Numerical results for the basic algorithm and several modifications are presented and discussed. They confirm the theoretical findings and show the usefulness of the approaches. Moreover, an application-motivated optimization problem from fluid dynamics is considered and the results are presented and interpreted according to the application. ; In dieser Arbeit wird ein "Trust-Region" Algorithmus für multikriterielle Optimierungsprobleme mit heterogenen Zielfunktionen vorgestellt. Eine der Zielfunktionen ist eine teure Black-Box-Funktion. Sie ist nicht analytisch gegeben, sondern beispielsweise durch eine Simulation. Für diese Funktion wird angenommen, dass die Berechnung von Funktionswerten zeitaufwändig ist und die Ableitungen nicht mit vertretbarem numerischen Aufwand berechnet werden können. Des Weiteren wird vorausgesetzt, dass die anderen Zielfunktionen analytisch gegeben sind und die Berechnung von Funktionswerten und Ableitungen mit geringem numerischen Aufwand ...
A trust region approach for multi-objective heterogeneous optimization
Thomann, Jana (author) / Eichfelder, Gabriele / Fliege, Jörg
2019-03-13
Theses
Electronic Resource
English
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