I have a problem to solve. Below is the problem statement.
I am currently at a location X. I have to start from X, and travel to these cities-A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V and then return back to X.
In what sequence i should cover these cities so that my round-trip distance is minimized?
Data: n x n matrix containing the distance across individual cities, and also distance between X and cities.
I know this is a Traveling salesmen problem,which is NP hard
I am looking for the best approximation technique/algorithm to use to solve this.
I have tried TSP Nearest Neighbours approach( which i consider as basic) and Clarke-Wright algorithm (not benificial.)
I'm looking for any leads/papers/open source projects(preferrably in python).
Note: Maximum cities <=50.I'm also looking for the methods which can give near to optimal result in least possible time.