Energy markets used to use Lagrangian Relaxation and Dynamic Programming to find the least cost dispatch. Some still do, but the larger ones (all the ones in the US) use Mixed-Integer Linear Programming and Linear Programming as the engines can handle a lot more and still solve.

The problem is that you'd need to get your hands on a large dataset and none of the true ones are public. I think some of the national labs have synthetic models of various sizes to play with. Seriously cool field.