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3810. Characterizations of supported efficiency
Invited abstract in session WC-37: Theory of Multiobjective Optimization, stream Multiobjective Optimization.
Wednesday, 12:30-14:00Room: 33 (building: 306)
Authors (first author is the speaker)
| 1. | Fabian Chlumsky-Harttmann
|
| Department of Mathematics, University of Kaiserslautern-Landau | |
| 2. | Anita Schöbel
|
| Department of Mathematics, University of Kaiserslautern-Landau |
Abstract
When given a multi-objective optimization problem, one usually aims to find efficient solutions. Yet, often this is hard. Solutions that are often easier to identify than efficient solutions are supported efficient solutions. Intuitively, the set of supported efficient solutions can be described as the set that contains all solutions to the weighted-sum scalarization for “reasonable” choices of weights. However, different authors work with different definitions of supported efficiency (and—if in the image space--supported nondominatedness, respectively).
We examine definitions found in the literature and show that there are in fact differences. We are able to categorize them into four layers with an implicit hierarchy: The characterization at the highest level being the most restrictive. Moreover, we show that these layers only coincide in special cases, such as discrete, linear or bi-objective problems, while counterexamples show that these characterizations are not equivalent for more general problems. We argue which characterizations are best suited to be used for different kinds of multi-objective optimization problems.
Last, we extend our results to concepts of extreme supported efficiency and extreme supported nondominatedness, respectively.
Keywords
- Multi-Objective Decision Making
Status: accepted
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