Using the Averaged Hausdorff Distance as a Performance Measure in Evolutionary Multiobjective Optimization


The Hausdorff distance dH could be a widely used tool to live the distance between different objects in many analysis fields. Attainable reasons for this would possibly be that it is a natural extension of the well-known and intuitive distance between points and/or the very fact that dH defines in sure cases a metric within the mathematical sense. In evolutionary multiobjective optimization (EMO) the task is usually to compute the entire solution set-the therefore-known as Pareto set-respectively its image, the Pareto front. Hence, dH ought to, at least at initial sight, be a natural alternative to measure the performance of the result set in explicit since it's related to the terms spread and convergence as utilized in EMO literature. But, thus far, dH does not notice the general approval in the EMO community. The main reason for this is often that dH penalizes single outliers of the candidate set which will not adjust to the use of stochastic search algorithms like evolutionary ways. In this paper, we tend to outline a replacement performance indicator, Δp, which can be viewed as an “averaged Hausdorff distance” between the outcome set and the Pareto front and that is composed of (slight modifications of) the well-known indicators generational distance (GD) and inverted generational distance (IGD). We have a tendency to will discuss theoretical properties of Δp (plus for GD and IGD) like the metric properties and also the compliance with state-of-theart multiobjective evolutionary algorithms (MOEAs), and can additional on demonstrate by empirical results the potential of Δp as a replacement performance indicator for the evaluation of MOEAs.

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