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Exploiting planarity in separation routines for the symmetric traveling salesman problem

Exploiting planarity in separation routines for the symmetric traveling salesman problem
Exploiting planarity in separation routines for the symmetric traveling salesman problem
At present, the most successful approach for solving large-scale instances of the Symmetric Traveling Salesman Problem to optimality is branch-and-cut. The success of branch-and-cut is due in large part to the availability of effective separation procedures; that is, routines for identifying violated linear constraints.
For two particular classes of constraints, known as comb and domino-parity constraints, it has been shown that separation becomes easier when the underlying graph is planar. We continue this line of research by showing how to exploit planarity in the separation of three other classes of constraints: subtour elimination, 2-matching and simple domino-parity constraints.
traveling salesman problem, planar graphs, cutting planes
1572-5286
220-230
Letchford, Adam N.
43c21ba9-1849-4c67-ba88-d03c300c50e4
Pearson, Nicholas A.
891c15b6-6ec9-4061-ae8a-2c5d469d1af7
Letchford, Adam N.
43c21ba9-1849-4c67-ba88-d03c300c50e4
Pearson, Nicholas A.
891c15b6-6ec9-4061-ae8a-2c5d469d1af7

Letchford, Adam N. and Pearson, Nicholas A. (2008) Exploiting planarity in separation routines for the symmetric traveling salesman problem. Discrete Optimization, 5 (2), 220-230. (doi:10.1016/j.disopt.2007.05.002).

Record type: Article

Abstract

At present, the most successful approach for solving large-scale instances of the Symmetric Traveling Salesman Problem to optimality is branch-and-cut. The success of branch-and-cut is due in large part to the availability of effective separation procedures; that is, routines for identifying violated linear constraints.
For two particular classes of constraints, known as comb and domino-parity constraints, it has been shown that separation becomes easier when the underlying graph is planar. We continue this line of research by showing how to exploit planarity in the separation of three other classes of constraints: subtour elimination, 2-matching and simple domino-parity constraints.

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More information

Submitted date: October 2006
Published date: 31 March 2008
Keywords: traveling salesman problem, planar graphs, cutting planes
Organisations: Operational Research

Identifiers

Local EPrints ID: 50854
URI: http://eprints.soton.ac.uk/id/eprint/50854
ISSN: 1572-5286
PURE UUID: cb6cfb4e-c6ce-416f-a675-438bc0490c9f

Catalogue record

Date deposited: 08 Apr 2008
Last modified: 13 Mar 2019 20:49

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