Intact group assignment problem

[1] Solves a problem of mapping volunteer groups to sites. The question is brought up whether we should minimize the number of links between groups and sites, or something else.

If we assume that the sites accept more than the demanded number of volunteers, we do not have to split any groups at all. This can be modeled by introducing variables that count split groups. The new objective will be the number of split groups. 

Furthermore, we can augment this objective with a small float times the number of workers, to make it as tight as possible. Result:

                  

[1] A variant of the transportation problem  http://yetanothermathprogrammingconsultant.blogspot.com/2019/01/a-variant-of-transportation-problem.html

Sampling fractal boxes, N-dimensional

Can we get more interesting clusters by sampling from boxes in higher dimensions?

For N=3 dimensions, we can still plot. The result is not very remarkable.

For higher dimensions, we have to project onto a subplane. I use sklearn's PCA to find the subplane with the highest variation. The result is that we get more noise points, so it's not more useful than the standard 2-dimensional box sampling. 

Sampling points in box-shaped clusters

We want to generate a set of random points with a lot of features, using minimal coding effort. We should use fractal sampling.

In this solution, I split the area randomly into smaller and smaller boxes. The only computation that is being done is to select a box at random, and then either split it vertically or horizontally. In the end, a uniform random point is sampled from each box.

The result is raw, but may be useful to test algorithms on.