An EMO algorithm using the hypervolume measure as selection criterion

  • Authors:

  • Michael Emmerich;Nicola Beume;Boris Naujoks

  • Affiliations:

  • Leiden Institute for Advanced Computer Science, University of Leiden, Leiden, NL;Chair of Systems Analysis, University of Dortmund, Dortmund, Germany;Chair of Systems Analysis, University of Dortmund, Dortmund, Germany

  • Venue:
  • EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
  • Year:
  • 2005

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Abstract

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.