Well, not really, because as I was saying below, in a lot of cases you know that on average a certain solution is (just as an example) 10% off the best possible solution (on average, avoiding Mawell's devils). Once you know that, it's not the TSP all over again. Because you can control the first number and you expect the second to stay within 10% (on average).

An easy example is computing an integral of any function (assuming the integral exists, makes sense, blah blah blah). I can write a solution Monte Carlo style in something like 10 lines of code. It takes me 2 minutes to code and it solves most integrals. Of course, the solution isn't exact, but I can go as far as I want in precision (using a little more code if I want to use optimization methods instead of just brute force). Still, it's pretty fast to write.

Now you can write a program that actually solves the integral exactly, but that takes more time.

Or you can write a program that makes bins and calculates the hight of each bin and computes the integral (not as good, not as fast).

So, if I know I need a solution where I don't care about the forth digit precision, why wouldn't just write the Monte Carlo solution that is superfast?

Although you can try to go back to some academic problems in most cases I don't need an academic solution, so...