A Convergence Criterion for Multiobjective Evolutionary Algorithms Based on Systematic Statistical Testing
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.
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Conference Paper
| English
Author
Trautmann, HeikeLibreCat 
;
Ligges, Uwe;
Mehnen, Jörn;
Preuss, Mike
;
Ligges, Uwe;
Mehnen, Jörn;
Preuss, MikeEditor
Rudolph, Günter;
Jansen, Thomas;
Beume, Nicola;
Lucas, Simon;
Poloni, Carlo
Abstract
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.
Publishing Year
Proceedings Title
Parallel Problem Solving from Nature – PPSN X
Page
825–836
ISBN
LibreCat-ID
Cite this
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. Parallel Problem Solving from Nature – PPSN X. Springer Berlin Heidelberg; 2008:825–836.
Trautmann, H., Ligges, U., Mehnen, J., & Preuss, M. (2008). A Convergence Criterion for Multiobjective Evolutionary Algorithms Based on Systematic Statistical Testing. In G. Rudolph, T. Jansen, N. Beume, S. Lucas, & C. Poloni (Eds.), Parallel Problem Solving from Nature – PPSN X (pp. 825–836). Springer Berlin Heidelberg.
@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} }
Trautmann, Heike, Uwe Ligges, Jörn Mehnen, and Mike Preuss. “A Convergence Criterion for Multiobjective Evolutionary Algorithms Based on Systematic Statistical Testing.” In Parallel Problem Solving from Nature – PPSN X, edited by Günter Rudolph, Thomas Jansen, Nicola Beume, Simon Lucas, and Carlo Poloni, 825–836. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008.
H. Trautmann, U. Ligges, J. Mehnen, and M. Preuss, “A Convergence Criterion for Multiobjective Evolutionary Algorithms Based on Systematic Statistical Testing,” in Parallel Problem Solving from Nature – PPSN X, 2008, pp. 825–836.
Trautmann, Heike, et al. “A Convergence Criterion for Multiobjective Evolutionary Algorithms Based on Systematic Statistical Testing.” Parallel Problem Solving from Nature – PPSN X, edited by Günter Rudolph et al., Springer Berlin Heidelberg, 2008, pp. 825–836.
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