El problema de medir la diversidad en conjuntos no dominados y una propuesta de solución

Abstract

Diversity is a very important property for non-dominated sets. The diversity is a measure of how much information is contained in a non-dominated set. Evaluating diversity has been a diffcult issue in multi-objective evolutionary computation. Many diversity performance measures fail in simple cases. In this work, we describe the most common problems in diversity performance measures and we propose a more robust approach. The problem with most performance measures is that they consist on evaluating the standard deviation of the distances between the elements of the non-dominated sets, or a similar calculation. This dependence on a standard deviation produces a high sensibility to small changes in the non-dominated sets. Our approach is based on an hype-volume associated to the non-dominated set. The behavior of this hyper-volume is exactly what we expect from a diversity performance measure. We tested our approach using a benchmark published in bibliography, showing an exceptional performance.

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