A Generalization of the Averaged Hausdorff Distance

Andrés Vargas, Johan Bogoya


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.


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

Full Text: PDF