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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.

Shubham R
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    Is that all the cities or can n be bigger? – merlyn Jan 03 '19 at 12:49
  • @merlyn This is just for an example, maximum cities can be 50. – Shubham R Jan 03 '19 at 13:46
  • "I'm looking for any leads/papers/open source projects(preferrably in python)." asking for off-site resources is off-topic on StackOverflow. To discuss algorithms such as this (and if you can reword it to be on topic) you might be best posting on [Computer Science](https://cs.stackexchange.com/tour) but be sure to check what is considered on topic there too – Scriptable Jan 03 '19 at 13:58
  • @Shubham 50 seems small enough that modern TSP solvers can simply find the optimal solution. – merlyn Jan 03 '19 at 14:01
  • You will have to define what **best** is. – domen Jan 03 '19 at 14:28
  • You've already tagged `Genetic Algorithm` so why not try to implement that? Biologically inspired algorithms are strong for TSP. You can also try `Particle Swarm Optimisation`. – McGuile Jan 03 '19 at 14:35
  • Adding to above mentioned approaches, you can also try `Ant Colony Optimiszation` – guroosh Feb 12 '19 at 10:38

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