Branch-and-bound, cutting planes, implicit enumeration… they’re all ways of admitting “brute force, but try to be clever about it.”

That said, the irony is half the problems that matter in the real world, like capital budgeting, scheduling, routing, warehouse placement, are integer problems.

LP relaxations are nice, but you can’t run an airline with fractional pilots or build 2.3 hospitals. So you either lean on heuristics, or you call CPLEX/Gurobi and pray.

The fact that modern solvers still do as well as they do is, honestly, one of the underappreciated miracles of applied cs.

Okay, maybe I was a bit harsh, but it definitely doesn't pop up as often as deep learning and statistical machine learning. For those who wish to get deeper into this, I highly recommend Optimization over Integers by Bertsimas and Weismantel.