Hard to Solve Instances of the Euclidean Traveling Salesman Problem

Stefan Hougardy; Xianghui Zhong

doi:10.1007/s12532-020-00184-5

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arXiv · 1808.02859

Hard to Solve Instances of the Euclidean Traveling Salesman Problem

Stefan Hougardy·Xianghui Zhong

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Abstract

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 several days of CPU time. This is more than 1,000,000 times the runtime for a TSPLIB instance of similar size. Thus our new family of Euclidean Traveling Salesman instances may serve as new benchmark instances for TSP algorithms.

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BibTeX RIS

Stefan Hougardy, Xianghui Zhong. 2020-03-17. Hard to Solve Instances of the Euclidean Traveling Salesman Problem. https://doi.org/10.1007/s12532-020-00184-5

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