Preference Articulation by Means of the R2 Indicator

Wagner T, Trautmann H, Brockhoff D


Abstract
In multi-objective optimization, set-based performance indicators have become the state of the art for assessing the quality of Pareto front approximations. As a consequence, they are also more and more used within the design of multi-objective optimization algorithms. The R2 and the Hypervolume (HV) indicator represent two popular examples. In order to understand the behavior and the approximations preferred by these indicators and algorithms, a comprehensive knowledge of the indicator’s properties is required. Whereas this knowledge is available for the HV, we presented a first approach in this direction for the R2 indicator just recently. In this paper, we build upon this knowledge and enhance the considerations with respect to the integration of preferences into the R2 indicator. More specifically, we analyze the effect of the reference point, the domain of the weights, and the distribution of weight vectors on the optimization of μ solutions with respect to the R2 indicator. By means of theoretical findings and empirical evidence, we show the potentials of these three possibilities using the optimal distribution of µ solutions for exemplary setups.



Publication type
Conference Paper

Peer reviewed
Yes

Publication status
Published

Year
2013

Conference
7th International Conference EMO 2013, March 19-22

Venue
Sheffield, UK,

Volume
7811

Book title
Evolutionary Multi-Criterion Optimization - 7th International Conference, EMO 2013, Sheffield, UK, Proceedings

Editor
Purshouse R C, Fleming P J, Fonseca C M, Greco S, Shaw J

Pages range
81-95

Title of series
Lecture Notes in Computer Science

Publisher
Springer

Language
English