travelling salesman problem

The travelling salesman problem is a common problem with both practical applicatiosn and used as a challenge for optimisation techniques. A salesperson needs to visit certain locations that are linked by roads or railways, with different travelling costs or times associated wut them. The task is to plan a route that visits each taregt location, but with the minimum cost for the travel. The full solution is known to be NP complete, that is effectively impossible, but various statistical techniques and machine learning may achieve near optimal performance in most real cases.