There are also a lot of approximation on the TSP problem.
Auto routing is basically the TSP as we want the shortest path, but we have
- multiple path to look at the same time
- there are most of the time constrain on the path you have to choose because some sellers have to travel at the same time going to different borough of the same town (basically routing a bus)
- path MUST NOT cross in most conditions, where in the normal TSP it doesn't matter
- Highly parallelisable? Maybe by doing a lot of approximations, but there are some rules that would ultimately prevent parallelisations, like the fact that two track which does not belong to the same net must not ever cross, and that have a huge impact on parallelisation as each thread need to know what the other are doing, so basically they are not running asynchronously.
- Giving a solution "fast" does not mean that it's the best! It's also possible to give really fast a solution for the TSP, but it will never be the best solution.
There are way more constrain on routing than on the TSP, that's why it's more difficult.
Current approach of auto routing are approximations and not the "best results", as current TSP solvers.