Why is crossing paths bad in Traveling Salesman? I'm learning about Traveling Salesman in an online course (sorry I can't share the link it's paid only) and the first step to solving it then just state &quot;as a heuristic we avoid crossed paths&quot; and never really explained why. Why are crossed paths bad in traveling salesman?
The statement is for Euclidean TSP only, and as you mention yourself, it is only used as a heuristic.
But try to create an example yourself and see what happens when you have crossing links as part of your solution:

From Urban OR:
Property 1: The optimum traveling salesman tour does not intersect itself.