Resumo

VARGAS, Andrés  e  BOGOYA, Johan. A Generalization of the Averaged Hausdorff Distance. Comp. y Sist. [online]. 2018, vol.22, n.2, pp.331-345.  Epub 21-Jan-2021. ISSN 2007-9737.  https://doi.org/10.13053/cys-22-2-2950.

The averaged Hausdorff distance ${\Delta }_p$ is an inframetric which has been recently used in evolutionary multiobjective optimization (EMO). In this paper we introduce a new two-parameter performance indicator ${\Delta }_{p,q}$ which generalizes ${\Delta }_p$ as well as the standard Hausdorff distance. For $p,q\ge 1$ the indicator ${\Delta }_{p,q}$ (that we call the $(p,q)$-averaged distance) turns out to be a proper metric and preserves some of the ${\Delta }_p$ advantages. We proof several properties of ${\Delta }_{p,q}$, and provide a comparison with ${\Delta }_p$ and the standard Hausdorff distance. For simplicity we restrict ourselves to finite sets, which is the most common case, but our results can be extended to the continuous case.

Palavras-chave : Averaged Hausdorff distance; generational distance; inverted generational distance; multiobjective optimization; performance indicator; power means.