Maximising the distance between $n$ points in a 2d region

Question

I've been looking into the problem of computing the problem of placing $n$ points on a finite rectangular region of size $w \times h$ in a 2d plane so as to minimise the function $\sum_{i,j} \frac{1}{d_{i,j}} $, where $d_{i,j}$ is the euclidean distance between point $i$ and $j$. So far I've not had any success in working out the complexity of this problem, so I was hoping to look at the problem of placing the points such that the average distance is maximised between each pair of points.