A Convergence Criterion for Multiobjective Evolutionary Algorithms Based on Systematic Statistical Testing

  • Heike Trautmann
  • Uwe Ligges
  • Jörn Mehnen
  • Mike Preuss
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)


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.


Performance Indicator Generation Number Pareto Front Multiobjective Optimization Step Width 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Heike Trautmann
    • 1
  • Uwe Ligges
    • 1
  • Jörn Mehnen
    • 2
  • Mike Preuss
    • 3
  1. 1.Department of StatisticsTechnische Universität DortmundGermany
  2. 2.Decision Engineering CentreCranfield UniversityUK
  3. 3.Chair of Algorithm EngineeringTechnische Universität DortmundGermany

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