Concepts of Robustness for Uncertain Multi-Objective Optimization

by Jonas Ide
Doctoral thesis
Date of Examination:2014-04-23
Date of issue:2014-04-30
Advisor:Prof. Dr. Anita Schöbel
Referee:Prof. Dr. Anita Schöbel
Referee:Prof. Dr. Matthias Ehrgott
Referee:Prof. Dr. Stephan Westphal
Persistent Address: http://dx.doi.org/10.53846/goediss-4482

 

 

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Abstract

English

In this thesis, several concepts of handling uncertainties in the formulation of mathematical optimization problems are presented. Some of these concepts are extensions of classical concepts of robustness for single objective optimization problems, others are newly introduced concepts particularly developed for the multi-objective setting. Properties of these concepts and algorithms for computing the respective solutions are analyzed. Connections between the concepts are investigated and the connection between multi-objective and set-valued optimization is pointed out and used to develop new concepts of robustness. Furthermore, the several concepts are extended to optimization problems using order relations induced by arbitrary cones. Finally, an application problem is presented analyzing the practical value of robust efficient solutions.
Keywords: Optimization; Multi-Objective; Robustness; Uncertainty; Scenarios; Set-Valued
 
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