Hard to solve instances of the Euclidean Traveling Salesman Problem

  • 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 , the fastest existing exact TSP solver. For a 200 vertex instance from our family of Euclidean Traveling Salesman instances needs several days of CPU time. This is more than 1,000,000 times more runtime than 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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Metadaten
Author:Stefan Hougardy, Xianghui Zhong
DOI:https://doi.org/10.1007/s12532-020-00184-5
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2020
Tag:Software; Theoretical Computer Science
Volume:13
Issue:1
Page Number:24
First Page:51
Last Page:74
Mathematical Programming Computation :MPC 2021 - Issue 1
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