Hard to Solve Instances of the Euclidean Traveling Salesman Problem

08/08/2018
by   Stefan Hougardy, et al.
0

The well known 4/3 conjecture states that the integrality ratio of the subtour LP is at most 4/3 for metric Traveling Salesman instances. We present a family of Euclidean Traveling Salesman instances for which we prove that the integrality ratio of the subtour LP converges to 4/3. These instances (using the rounded Euclidean norm) turn out to be hard to solve exactly with Concorde, the fastest existing exact TSP solver. For a 200 vertex instance from our family of Euclidean Traveling Salesman instances Concorde needs about 1,000,000 times more runtime than for a TSPLIB instance of similar size. From our runtime results we deduce that a 1000 vertex instance of our family would take Concorde about 10^27 times longer to solve than a TSPLIB instance of similar size. Thus our new family of Euclidean Traveling Salesman instances may be useful benchmark instances for TSP algorithms.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset