This is an example to illustrate the problem. Imagine you have to make two groups of 5 students each from a classroom of 50 students. Students differ on three grades: math, physics, and language (all have the same unit of measure). The goal is to make the two groups as similar as possible considering these three dimensions. That is, simultaneously minimize the average difference for each dimension between groups.
I solved this numerically by randomly sampling the students and computing each group's mean on each dimension and comparing these means between groups as to minimize them. As you can imagine this solution is far from ideal.
Is there an analytical way to solve this problem? Is there a general solution for D dimensions, n students per groups, and a pool of N students from which to pick?
