Comment by sigbottle

> Your best bet using them is when you have a large collection of smaller unstructured problems, most of which align with the heuristics.

Agreed. An algorithm right now in our company turns a directed graph problem, which to most people would seem crazy, into roughly ~m - n (m edges, n nodes) SAT checks that are relatively small. Stuffing all the constraints into an ILP solver would be super inefficient (and honestly undefined). Instead, by defining the problem statement properly and carving out the right invariants, you can decompose the problem to smaller NP-complete problems.

Definitely a balancing act of design.