Preference Articulation by Means of the R2 Indicator

  • Tobias Wagner
  • Heike Trautmann
  • Dimo Brockhoff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7811)


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.


Weight Vector Pareto Front Target Direction Weight Space Target Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Tobias Wagner
    • 1
  • Heike Trautmann
    • 2
  • Dimo Brockhoff
    • 3
  1. 1.Institute of Machining Technology (ISF)TU Dortmund UniversityGermany
  2. 2.Statistics DepartmentTU Dortmund UniversityGermany
  3. 3.DOLPHIN TeamINRIA Lille - Nord EuropeVilleneuve d’AscqFrance

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