Doctoral Thesis
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- Doctoral Thesis (2) (remove)
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This thesis introduces so-called cone scalarising functions. They are by construction compatible with a partial order for the outcome space given by a cone. The quality of the parametrisations of the efficient set given by the cone scalarising functions are then investigated. Here, the focus lies on the (weak) efficiency of the generated solutions, the reachability of effiecient points and continuity of the solution set. Based on cone scalarising functions Pareto Navigation a novel, interactive, multiobjective optimisation method is proposed. It changes the ordering cone to realise bounds on partial tradeoffs. Besides, its use of an equality constraint for the changing component of the reference point is a new feature. The efficiency of its solutions, the reachability of efficient solutions and continuity is then analysed. Potential problems are demonstrated using a critical example. Furthermore, the use of Pareto Navigation in a two-phase approach and for nonconvex problems is discussed. Finally, its application for intensity-modulated radiotherapy planning is described. Thereby, its realisation in a graphical user interface is shown.
Robuste Optimierung wird zur Entscheidungsunterstützung eines komplexen Beschaffungs- und Transportmodells genutzt, um die Risikoeinstellung der Entscheidenden abzubilden und gleichzeitig ein robustes Ergebnis zu erzielen. Die Modellierung des Problems ist umfassend dargestellt und Ergebnisse der nicht-deterministischen Planung bei verschiedenen Parametern und Risikoeinstellungen gegenübergestellt. Die Datenunsicherheit wird an einem Praxisfall erläutert und Methoden und -empfehlungen zum Umgang mit dieser dargestellt.