What metric should be minimized when searching from a subset of points that are as uniformly distributed across the space as possible? Given a set of n points, I have to find a subset of given size m<n, so that the m points are as uniformly distributed as possible across the volume enclosed by the convex hull of set n. See example figure:

Here we have a toy 2D example of the problem with n=600 and m=100. I am solving this problem using Evolutionary Algorithm and I do not know what the fitness (objective function) to minimize should be. I tried minimizing electrostatic potential $$E=\frac{1}{2}\sum_i\sum_j\frac{1}{|r_i-r_j|}$$ following the idea of the Thomson problem, however the resulting output is clearly incorrect (see figure below, red points denote solution found by the evolutionary algorithm) as the density of the selected points is higher at the edges. I tried squaring values in denominator of given equation for E, but the solutions are still clearly suboptimal.
What is the objective function I should minimize to get what I want? Note that I want to solve this problem in high dimension space for arbitrary set of points with unknown distribution.


As per comment by @ttnphns, Hopkin's statistic answered my question. In the genetic algorithm optimization process, minimazing the Hopkin's statistic would converge to finding the solutions with more uniform distribution.
