What I find interesting about the knapsack problem, and the traveling salesman problem as well, is that they're fast to satisfy, but incredibly time-consuming to solve.

Once upon a time, I had a 4x8 sheet of small plastic parts to route out on a ShopBot. The naive layout from the vector drawing program was incredibly inefficient, and we ended up downloading a general-purpose traveling-salesman-solver written in Java.

It converged upon a dramatically better solution in a few seconds, and didn't really improve it in the next few minutes. So we just stopped it and ran the good-enough route, while leaving the solver running for two days out of pure curiosity.

Now, it was visibly not perfect, there were a couple skips where we could see a shorter way to do it. And it did eventually find those routes.

So if all you need is a reasonable route for your traveling salespersons, or an acceptably efficient packing arrangement for your shipping container, this is achievable and easy, if you're willing to leave that last 1-2% sitting on the table.