---
_id: '46363'
abstract:
- lang: eng
  text: "The averaged Hausdorff distance has been proposed as an indicator for assessing
    the quality of finitely sized approximations of the Pareto front of a multiobjective
    problem. Since many set-based, iterative optimization algorithms store their currently
    best approximation in an internal archive these approximations are also termed
    archives. In case of two objectives and continuous variables it is known that
    the best approximations in terms of averaged Hausdorff distance are subsets of
    the Pareto front if it is concave. If it is linear or circularly concave the points
    of the best approximation are equally spaced.\r\n\r\nHere, it is proven that the
    optimal averaged Hausdorff approximation and the Pareto front have an empty intersection
    if the Pareto front is circularly convex. But the points of the best approximation
    are equally spaced and they rapidly approach the Pareto front for increasing size
    of the approximation."
author:
- first_name: G
  full_name: Rudolph, G
  last_name: Rudolph
- first_name: O
  full_name: Schütze, O
  last_name: Schütze
- first_name: Heike
  full_name: Trautmann, Heike
  id: '100740'
  last_name: Trautmann
  orcid: 0000-0002-9788-8282
citation:
  ama: 'Rudolph G, Schütze O, Trautmann H. On the Closest Averaged Hausdorff Archive
    for a Circularly Convex Pareto Front. In: Squillero G, Burelli P, eds. <i>Applications
    of Evolutionary Computation: 19$^th$ European Conference, EvoApplications 2016,
    Porto, Portugal, March 30 — April 1, 2016, Proceedings, Part II</i>. Springer
    International Publishing; 2016:42–55. doi:<a href="https://doi.org/10.1007/978-3-319-31153-1_4">10.1007/978-3-319-31153-1_4</a>'
  apa: 'Rudolph, G., Schütze, O., &#38; Trautmann, H. (2016). On the Closest Averaged
    Hausdorff Archive for a Circularly Convex Pareto Front. In G. Squillero &#38;
    P. Burelli (Eds.), <i>Applications of Evolutionary Computation: 19$^th$ European
    Conference, EvoApplications 2016, Porto, Portugal, March 30 — April 1, 2016, Proceedings,
    Part II</i> (pp. 42–55). Springer International Publishing. <a href="https://doi.org/10.1007/978-3-319-31153-1_4">https://doi.org/10.1007/978-3-319-31153-1_4</a>'
  bibtex: '@inbook{Rudolph_Schütze_Trautmann_2016, place={Cham}, title={On the Closest
    Averaged Hausdorff Archive for a Circularly Convex Pareto Front}, DOI={<a href="https://doi.org/10.1007/978-3-319-31153-1_4">10.1007/978-3-319-31153-1_4</a>},
    booktitle={Applications of Evolutionary Computation: 19$^th$ European Conference,
    EvoApplications 2016, Porto, Portugal, March 30 — April 1, 2016, Proceedings,
    Part II}, publisher={Springer International Publishing}, author={Rudolph, G and
    Schütze, O and Trautmann, Heike}, editor={Squillero, G and Burelli, P}, year={2016},
    pages={42–55} }'
  chicago: 'Rudolph, G, O Schütze, and Heike Trautmann. “On the Closest Averaged Hausdorff
    Archive for a Circularly Convex Pareto Front.” In <i>Applications of Evolutionary
    Computation: 19$^th$ European Conference, EvoApplications 2016, Porto, Portugal,
    March 30 — April 1, 2016, Proceedings, Part II</i>, edited by G Squillero and
    P Burelli, 42–55. Cham: Springer International Publishing, 2016. <a href="https://doi.org/10.1007/978-3-319-31153-1_4">https://doi.org/10.1007/978-3-319-31153-1_4</a>.'
  ieee: 'G. Rudolph, O. Schütze, and H. Trautmann, “On the Closest Averaged Hausdorff
    Archive for a Circularly Convex Pareto Front,” in <i>Applications of Evolutionary
    Computation: 19$^th$ European Conference, EvoApplications 2016, Porto, Portugal,
    March 30 — April 1, 2016, Proceedings, Part II</i>, G. Squillero and P. Burelli,
    Eds. Cham: Springer International Publishing, 2016, pp. 42–55.'
  mla: 'Rudolph, G., et al. “On the Closest Averaged Hausdorff Archive for a Circularly
    Convex Pareto Front.” <i>Applications of Evolutionary Computation: 19$^th$ European
    Conference, EvoApplications 2016, Porto, Portugal, March 30 — April 1, 2016, Proceedings,
    Part II</i>, edited by G Squillero and P Burelli, Springer International Publishing,
    2016, pp. 42–55, doi:<a href="https://doi.org/10.1007/978-3-319-31153-1_4">10.1007/978-3-319-31153-1_4</a>.'
  short: 'G. Rudolph, O. Schütze, H. Trautmann, in: G. Squillero, P. Burelli (Eds.),
    Applications of Evolutionary Computation: 19$^th$ European Conference, EvoApplications
    2016, Porto, Portugal, March 30 — April 1, 2016, Proceedings, Part II, Springer
    International Publishing, Cham, 2016, pp. 42–55.'
date_created: 2023-08-04T15:09:14Z
date_updated: 2023-10-16T13:37:33Z
department:
- _id: '34'
- _id: '819'
doi: 10.1007/978-3-319-31153-1_4
editor:
- first_name: G
  full_name: Squillero, G
  last_name: Squillero
- first_name: P
  full_name: Burelli, P
  last_name: Burelli
language:
- iso: eng
page: 42–55
place: Cham
publication: 'Applications of Evolutionary Computation: 19$^th$ European Conference,
  EvoApplications 2016, Porto, Portugal, March 30 — April 1, 2016, Proceedings, Part
  II'
publication_identifier:
  isbn:
  - 978-3-319-31153-1
publisher: Springer International Publishing
status: public
title: On the Closest Averaged Hausdorff Archive for a Circularly Convex Pareto Front
type: book_chapter
user_id: '15504'
year: '2016'
...