An EMO Algorithm Using the Hypervolume Measure as Selection Criterion

  • Michael Emmerich
  • Nicola Beume
  • Boris Naujoks
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3410)


The hypervolume measure is one of the most frequently applied measures for comparing the results of evolutionary multiobjective optimization algorithms (EMOA). The idea to use this measure for selection is self-evident. A steady-state EMOA will be devised, that combines concepts of non-dominated sorting with a selection operator based on the hypervolume measure. The algorithm computes a well distributed set of solutions with bounded size thereby focussing on interesting regions of the Pareto front(s). By means of standard benchmark problems the algorithm will be compared to other well established EMOA. The results show that our new algorithm achieves good convergence to the Pareto front and outperforms standard methods in the hypervolume covered. We also studied the applicability of the new approach in the important field of design optimization. In order to reduce the number of time consuming precise function evaluations, the algorithm will be supported by approximate function evaluations based on Kriging metamodels. First results on an airfoil redesign problem indicate a good performance of this approach, especially if the computation of a small, bounded number of well-distributed solutions is desired.


Pareto Front Extremal Solution True Pareto Front Convergence Measure Kriging Metamodels 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Michael Emmerich
    • 2
  • Nicola Beume
    • 1
  • Boris Naujoks
    • 1
  1. 1.Chair of Systems AnalysisUniversity of DortmundDortmundGermany
  2. 2.Leiden Institute for Advanced Computer ScienceUniversity of LeidenLeidenNL

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