I am interested in ways to improve or come up with algorithms that are able to solve the Travelling salesman problem for about n = 100 to 200
cities.
Th
TSP is an NP-hard problem. (As far as we know) there is no algorithm for NP-hard problems which runs in polynomial time, so you ask for something that doesn't exist.
It's either fast enough to finish in a reasonable time and then it's not exact, or exact but won't finish in your lifetime for 100 cities.