---
_id: '46379'
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 extended version of
    our previous conference 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. Furthermore, the R2
    indicator is integrated into an indicator-based steady-state evolutionary multiobjective
    optimization algorithm (EMOA). It is shown that the so-called R2-EMOA can accurately
    approximate the optimal distribution of µ solutions regarding R2.
author:
- first_name: D
  full_name: Brockhoff, D
  last_name: Brockhoff
- first_name: T
  full_name: Wagner, T
  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. R2 Indicator Based Multiobjective Search.
    <i>Evolutionary Computation Journal</i>. 2015;23(3):369–395. doi:<a href="https://doi.org/10.1162/EVCO_a_00135">10.1162/EVCO_a_00135</a>
  apa: Brockhoff, D., Wagner, T., &#38; Trautmann, H. (2015). R2 Indicator Based Multiobjective
    Search. <i>Evolutionary Computation Journal</i>, <i>23</i>(3), 369–395. <a href="https://doi.org/10.1162/EVCO_a_00135">https://doi.org/10.1162/EVCO_a_00135</a>
  bibtex: '@article{Brockhoff_Wagner_Trautmann_2015, title={R2 Indicator Based Multiobjective
    Search}, volume={23}, DOI={<a href="https://doi.org/10.1162/EVCO_a_00135">10.1162/EVCO_a_00135</a>},
    number={3}, journal={Evolutionary Computation Journal}, author={Brockhoff, D and
    Wagner, T and Trautmann, Heike}, year={2015}, pages={369–395} }'
  chicago: 'Brockhoff, D, T Wagner, and Heike Trautmann. “R2 Indicator Based Multiobjective
    Search.” <i>Evolutionary Computation Journal</i> 23, no. 3 (2015): 369–395. <a
    href="https://doi.org/10.1162/EVCO_a_00135">https://doi.org/10.1162/EVCO_a_00135</a>.'
  ieee: 'D. Brockhoff, T. Wagner, and H. Trautmann, “R2 Indicator Based Multiobjective
    Search,” <i>Evolutionary Computation Journal</i>, vol. 23, no. 3, pp. 369–395,
    2015, doi: <a href="https://doi.org/10.1162/EVCO_a_00135">10.1162/EVCO_a_00135</a>.'
  mla: Brockhoff, D., et al. “R2 Indicator Based Multiobjective Search.” <i>Evolutionary
    Computation Journal</i>, vol. 23, no. 3, 2015, pp. 369–395, doi:<a href="https://doi.org/10.1162/EVCO_a_00135">10.1162/EVCO_a_00135</a>.
  short: D. Brockhoff, T. Wagner, H. Trautmann, Evolutionary Computation Journal 23
    (2015) 369–395.
date_created: 2023-08-04T15:28:25Z
date_updated: 2023-10-16T13:42:47Z
department:
- _id: '34'
- _id: '819'
doi: 10.1162/EVCO_a_00135
intvolume: '        23'
issue: '3'
language:
- iso: eng
page: 369–395
publication: Evolutionary Computation Journal
status: public
title: R2 Indicator Based Multiobjective Search
type: journal_article
user_id: '15504'
volume: 23
year: '2015'
...