A Generalization of the Averaged Hausdorff Distance

Authors

  • Andrés Vargas Pontificia Universidad Javeriana, Bogotá D.C.
  • Johan Bogoya Pontificia Universidad Javeriana, Bogotá D.C.

DOI:

https://doi.org/10.13053/cys-22-2-2950

Keywords:

averaged Hausdorff distance, generational distance, inverted generational distance, multiobjective optimization, performance indicator, power means

Abstract

The averaged Hausdorff distance p is aninframetric which has been recently used in evolutionary multiobjective optimization (EMO). In this paper we introduce a new two-parameter performance indicator p,q which generalizes p as well as the standard Hausdorff distance. For p, q > 1 the indicator p,q (that we call the (p, q)-averaged distance) turns out to be aproper metric and preserves some of the p advantages. We proof several properties of p,q, and provide acomparison with p and the standard Hausdorff distance. For simplicity we restrict our selves to finite sets, which is the most common case, but our results can be extended to the continuous case.

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Published

2018-06-29

Issue

Vol. 22 No. 2 (2018): Thematic Issue on Numerical and Evolutionary Optimization (Guest editors: L. Trujillo, Y. Maldonado, O. Schuetze)

Section

Articles of the Thematic Issue

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