One MOEA Uniformity Measurement Based on Generalized Spherical Transformation

So far there are a number of evolutionary algorithms (EAs) applied in solving multi-objective optimization problems (MOPs), but it is very hard to evaluate the performance of a multi-objective optimization evolutionary algorithm (MOEA) especially to equably evaluate the Pareto Front (PF) when the dimension of the objective space is greater than 2. This paper has made a corresponding analysis on the existed MOEA and proposed a MOEA uniformity measurement based on generalized spherical transformation, which mapped the space points onto a spherical space by transforming the coordinate to get the corresponding polar angle. And then find out the points distributing in different quadrant around according to the polar angle. Finally, measure the uniformity of the points in the space distribution by calculating the space Euclidean distance. The experiments show that this algorithm can well evaluate the distributing of the PF.