2046. On image space transformations in multiobjective optimization
Invited abstract in session MA-51: Recent advances in multiobjective optimization, stream Multiobjective and vector optimization.
Monday, 8:30-10:00Room: Parkinson B22
Authors (first author is the speaker)
| 1. | Felix Neussel
|
| Institute for Operations Research, KIT | |
| 2. | Oliver Stein
|
| Institute of Operations Research, Karlsruhe Institute of Technology |
Abstract
It is well known that one can apply a strictly increasing function to the objective function of any standard single-objective optimization problem without altering the set of optimal points. This can be helpful in generating properties like smoothness or convexity of the objective.
As a generalization to multiobjective optimization, we consider monotone transformations of the objective space that leave the set of efficient points invariant. Under mild assumptions, for the standard ordering cone, we show that such transformations must be component-wise transformations, which means that a univariate strictly increasing function is applied to each of the objectives.
The same class of transformations also leaves the sets of weakly and of Geoffrion properly efficient points invariant. In addition, our approach allows us to specify trade-off bounds of properly efficient points after the transformation. We apply our results to prove some previously unknown properties of the compromise approach.
Keywords
- Programming, Multi-Objective
- Multi-Objective Decision Making
Status: accepted
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