---
_id: '46397'
abstract:
- lang: eng
  text: In multiobjective optimization, set-based performance indicators are commonly
    used to assess the quality of a Pareto front approximation. Based on the scalarization
    obtained by these indicators, a performance comparison of multiobjective optimization
    algorithms becomes possible. The R2 and the Hypervolume (HV) indicator represent
    two recommended approaches which have shown a correlated behavior in recent empirical
    studies. Whereas the HV indicator has been comprehensively analyzed in the last
    years, almost no studies on the R2 indicator exist. In this paper, we thus perform
    a comprehensive investigation of the properties of the R2 indicator in a theoretical
    and empirical way. The influence of the number and distribution of the weight
    vectors on the optimal distribution of μ solutions is analyzed. Based on a comparative
    analysis, specific characteristics and differences of the R2 and HV indicator
    are presented.
author:
- first_name: Dimo
  full_name: Brockhoff, Dimo
  last_name: Brockhoff
- first_name: Tobias
  full_name: Wagner, Tobias
  last_name: Wagner
- first_name: Heike
  full_name: Trautmann, Heike
  id: '100740'
  last_name: Trautmann
  orcid: 0000-0002-9788-8282
citation:
  ama: 'Brockhoff D, Wagner T, Trautmann H. On the Properties of the R2 Indicator.
    In: <i>Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation</i>.
    GECCO ’12. Association for Computing Machinery; 2012:465–472. doi:<a href="https://doi.org/10.1145/2330163.2330230">10.1145/2330163.2330230</a>'
  apa: Brockhoff, D., Wagner, T., &#38; Trautmann, H. (2012). On the Properties of
    the R2 Indicator. <i>Proceedings of the 14th Annual Conference on Genetic and
    Evolutionary Computation</i>, 465–472. <a href="https://doi.org/10.1145/2330163.2330230">https://doi.org/10.1145/2330163.2330230</a>
  bibtex: '@inproceedings{Brockhoff_Wagner_Trautmann_2012, place={New York, NY, USA},
    series={GECCO ’12}, title={On the Properties of the R2 Indicator}, DOI={<a href="https://doi.org/10.1145/2330163.2330230">10.1145/2330163.2330230</a>},
    booktitle={Proceedings of the 14th Annual Conference on Genetic and Evolutionary
    Computation}, publisher={Association for Computing Machinery}, author={Brockhoff,
    Dimo and Wagner, Tobias and Trautmann, Heike}, year={2012}, pages={465–472}, collection={GECCO
    ’12} }'
  chicago: 'Brockhoff, Dimo, Tobias Wagner, and Heike Trautmann. “On the Properties
    of the R2 Indicator.” In <i>Proceedings of the 14th Annual Conference on Genetic
    and Evolutionary Computation</i>, 465–472. GECCO ’12. New York, NY, USA: Association
    for Computing Machinery, 2012. <a href="https://doi.org/10.1145/2330163.2330230">https://doi.org/10.1145/2330163.2330230</a>.'
  ieee: 'D. Brockhoff, T. Wagner, and H. Trautmann, “On the Properties of the R2 Indicator,”
    in <i>Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation</i>,
    2012, pp. 465–472, doi: <a href="https://doi.org/10.1145/2330163.2330230">10.1145/2330163.2330230</a>.'
  mla: Brockhoff, Dimo, et al. “On the Properties of the R2 Indicator.” <i>Proceedings
    of the 14th Annual Conference on Genetic and Evolutionary Computation</i>, Association
    for Computing Machinery, 2012, pp. 465–472, doi:<a href="https://doi.org/10.1145/2330163.2330230">10.1145/2330163.2330230</a>.
  short: 'D. Brockhoff, T. Wagner, H. Trautmann, in: Proceedings of the 14th Annual
    Conference on Genetic and Evolutionary Computation, Association for Computing
    Machinery, New York, NY, USA, 2012, pp. 465–472.'
date_created: 2023-08-04T15:52:42Z
date_updated: 2023-10-16T13:47:23Z
department:
- _id: '34'
- _id: '819'
doi: 10.1145/2330163.2330230
keyword:
- hypervolume indicator
- multiobjective optimization
- performance assessment
- r2 indicator
language:
- iso: eng
page: 465–472
place: New York, NY, USA
publication: Proceedings of the 14th Annual Conference on Genetic and Evolutionary
  Computation
publication_identifier:
  isbn:
  - '9781450311779'
publisher: Association for Computing Machinery
series_title: GECCO ’12
status: public
title: On the Properties of the R2 Indicator
type: conference
user_id: '15504'
year: '2012'
...