Misleading Pareto optimal front diversity metrics: Spacing and distribution
Christiaan Scheepers, Andries Petrus Engelbrecht · 2016
The spacing metric by Schott and the distribution metric by Goh and Tan are often used to quantify the quality of the Pareto optimal front (POF) solution diversity. This paper presents a hypothesis that both the spacing and distribution metrics suffer from a pairwise grouping problem. This pairwise grouping problem leads to inaccurate measurement results that give a false indication of the POF solution diversity. In order to verify the hypothesis, a new diversity metric based on crowding distance is introduced. The vector evaluated particle swarm optimization (VEPSO) algorithm is used to evaluate the three POF solution diversity metrics. Results from the new diversity metric verify the presented hypothesis.