[ngruhn]

The details are pretty math heavy but what these solvers are doing is they try to find an optimal assignment to a bunch of variables x,y,z,etc while respecting a bunch of constraints like

3x + 2y <= 10

4z >= 3.5

Additionally, there is an “objective function” that defines what optimal means. Something like:

maximize (3x + 10y - 2z)

It’s not obvious but all kinds of problems can be modeled in this framework, like scheduling-, graph-, routing- problems. A big application is logistics: maximize profit / minimize costs under certain constraints.

So the solvers are just dealing with this inequality solving business. And this is where a lot of theoretical advances have happened. It’s a large field and I barely scratch the surface but it’s very interesting. Some keywords are: Operations Research, Mixed Integer Programming, Simplex Method.