A Generalization of the Averaged Hausdorff Distance

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.