Some comments on GD and IGD and relations to the Hausdorff distance

When measuring distances between different objects such as different sets the use of metrics has been well established in literature. We investigate here two widely used indicators for the evaluation of Multi-objective Evolutionary Algorithms, the Generational Distance (GD) and the Inverted Generational Distance (IGD), with respect to the properties of a metric. Since the outcome is quite poor, we propose further on a new indicator which is made up of GD and IGD. The novel indicator can be viewed as an `averaged version' of the Hausdorff distance and forms a pseudo-metric under certain assumptions.