---
_id: '46420'
abstract:
- lang: eng
  text: A systematic approach for determining the generation number at which a specific
    Multi-Objective Evolutionary Algorithm (MOEA) has converged for a given optimization
    problem is introduced. Convergence is measured by the performance indicators Generational
    Distance, Spread and Hypervolume. The stochastic nature of the MOEA is taken into
    account by repeated runs per generation number which results in a highly robust
    procedure. For each generation number the MOEA is repeated a fixed number of times,
    and the Kolmogorow-Smirnov-Test is used in order to decide if a significant change
    in performance is gained in comparison to preceding generations. A comparison
    of different MOEAs on a problem with respect to necessary generation numbers becomes
    possible, and the understanding of the algorithm’s behaviour is supported by analysing
    the development of the indicator values. The procedure is illustrated by means
    of standard test problems.
author:
- first_name: Heike
  full_name: Trautmann, Heike
  id: '100740'
  last_name: Trautmann
  orcid: 0000-0002-9788-8282
- first_name: Uwe
  full_name: Ligges, Uwe
  last_name: Ligges
- first_name: Jörn
  full_name: Mehnen, Jörn
  last_name: Mehnen
- first_name: Mike
  full_name: Preuss, Mike
  last_name: Preuss
citation:
  ama: 'Trautmann H, Ligges U, Mehnen J, Preuss M. A Convergence Criterion for Multiobjective
    Evolutionary Algorithms Based on Systematic Statistical Testing. In: Rudolph G,
    Jansen T, Beume N, Lucas S, Poloni C, eds. <i>Parallel Problem Solving from Nature
    – PPSN X</i>. Springer Berlin Heidelberg; 2008:825–836.'
  apa: Trautmann, H., Ligges, U., Mehnen, J., &#38; Preuss, M. (2008). A Convergence
    Criterion for Multiobjective Evolutionary Algorithms Based on Systematic Statistical
    Testing. In G. Rudolph, T. Jansen, N. Beume, S. Lucas, &#38; C. Poloni (Eds.),
    <i>Parallel Problem Solving from Nature – PPSN X</i> (pp. 825–836). Springer Berlin
    Heidelberg.
  bibtex: '@inproceedings{Trautmann_Ligges_Mehnen_Preuss_2008, place={Berlin, Heidelberg},
    title={A Convergence Criterion for Multiobjective Evolutionary Algorithms Based
    on Systematic Statistical Testing}, booktitle={Parallel Problem Solving from Nature
    – PPSN X}, publisher={Springer Berlin Heidelberg}, author={Trautmann, Heike and
    Ligges, Uwe and Mehnen, Jörn and Preuss, Mike}, editor={Rudolph, Günter and Jansen,
    Thomas and Beume, Nicola and Lucas, Simon and Poloni, Carlo}, year={2008}, pages={825–836}
    }'
  chicago: 'Trautmann, Heike, Uwe Ligges, Jörn Mehnen, and Mike Preuss. “A Convergence
    Criterion for Multiobjective Evolutionary Algorithms Based on Systematic Statistical
    Testing.” In <i>Parallel Problem Solving from Nature – PPSN X</i>, edited by Günter
    Rudolph, Thomas Jansen, Nicola Beume, Simon Lucas, and Carlo Poloni, 825–836.
    Berlin, Heidelberg: Springer Berlin Heidelberg, 2008.'
  ieee: H. Trautmann, U. Ligges, J. Mehnen, and M. Preuss, “A Convergence Criterion
    for Multiobjective Evolutionary Algorithms Based on Systematic Statistical Testing,”
    in <i>Parallel Problem Solving from Nature – PPSN X</i>, 2008, pp. 825–836.
  mla: Trautmann, Heike, et al. “A Convergence Criterion for Multiobjective Evolutionary
    Algorithms Based on Systematic Statistical Testing.” <i>Parallel Problem Solving
    from Nature – PPSN X</i>, edited by Günter Rudolph et al., Springer Berlin Heidelberg,
    2008, pp. 825–836.
  short: 'H. Trautmann, U. Ligges, J. Mehnen, M. Preuss, in: G. Rudolph, T. Jansen,
    N. Beume, S. Lucas, C. Poloni (Eds.), Parallel Problem Solving from Nature – PPSN
    X, Springer Berlin Heidelberg, Berlin, Heidelberg, 2008, pp. 825–836.'
date_created: 2023-08-04T16:20:35Z
date_updated: 2024-06-10T11:55:46Z
department:
- _id: '34'
- _id: '819'
editor:
- first_name: Günter
  full_name: Rudolph, Günter
  last_name: Rudolph
- first_name: Thomas
  full_name: Jansen, Thomas
  last_name: Jansen
- first_name: Nicola
  full_name: Beume, Nicola
  last_name: Beume
- first_name: Simon
  full_name: Lucas, Simon
  last_name: Lucas
- first_name: Carlo
  full_name: Poloni, Carlo
  last_name: Poloni
language:
- iso: eng
page: 825–836
place: Berlin, Heidelberg
publication: Parallel Problem Solving from Nature – PPSN X
publication_identifier:
  isbn:
  - 978-3-540-87700-4
publisher: Springer Berlin Heidelberg
status: public
title: A Convergence Criterion for Multiobjective Evolutionary Algorithms Based on
  Systematic Statistical Testing
type: conference
user_id: '15504'
year: '2008'
...