This optimization problem is very similar to that of minimizing the diagonal bandwidth of a matrix, a common problem in large numerical computations [1]. It is also related to cluster finding in graphs and graph layouts by considering the adjacency matrix.

The difference is that in both those cases the values are boolean, but in this post the cost function is weighted.

[1] https://en.wikipedia.org/wiki/Cuthill%E2%80%93McKee_algorith...