Study of a generalization of the averaged Hausdorff distance

The averaged Hausdorff distance is an inframetric that has been recently used in evolutionary multiobjective optimization (EMO). The aim of this project is to introduce a new two-parameter performance indicator that we call the (p,q)-averaged Hausdorff distance. Our purpose is to study and provide rigorous mathematical proofs of the metric properties of and study its behavior in standard Multiobjective Optimization Problems (MOPs), providing in this way a comparison with behaviour and properties of the averaged Hausdorff distance as well as the usual Hausdorff distance between sets.