The University of Southampton
University of Southampton Institutional Repository

Good triangulations yield good tours

Good triangulations yield good tours
Good triangulations yield good tours
Consider the following heuristic for planar Euclidean instances of the traveling salesman problem (TSP): select a subset of the edges which induces a planar graph, and solve either the TSP or its graphical relaxation on that graph. In this paper, we give several motivations for considering this heuristic, along with extensive computational results. It turns out that the Delaunay and greedy triangulations make effective choices for the induced planar graph. Indeed, our experiments show that the resulting tours are on average within 0.1% of optimality.
Scope and purpose
The traveling salesman problem (TSP) is a fundamental and well-known problem in combinatorial optimisation. It has many applications, for example in vehicle routing and machine scheduling. This paper proposes several heuristics methods for the Euclidean TSP, based on the use of triangulations, and gives extensive computational results.
delaunay triangulation, traveling salesman problem
0305-0548
638-647
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) Good triangulations yield good tours. Computers & Operations Research, 35 (2), 638-647. (doi:10.1016/j.cor.2006.03.025).

Record type: Article

Abstract

Consider the following heuristic for planar Euclidean instances of the traveling salesman problem (TSP): select a subset of the edges which induces a planar graph, and solve either the TSP or its graphical relaxation on that graph. In this paper, we give several motivations for considering this heuristic, along with extensive computational results. It turns out that the Delaunay and greedy triangulations make effective choices for the induced planar graph. Indeed, our experiments show that the resulting tours are on average within 0.1% of optimality.
Scope and purpose
The traveling salesman problem (TSP) is a fundamental and well-known problem in combinatorial optimisation. It has many applications, for example in vehicle routing and machine scheduling. This paper proposes several heuristics methods for the Euclidean TSP, based on the use of triangulations, and gives extensive computational results.

Full text not available from this repository.

More information

Published date: February 2008
Keywords: delaunay triangulation, traveling salesman problem
Organisations: Operational Research

Identifiers

Local EPrints ID: 50725
URI: http://eprints.soton.ac.uk/id/eprint/50725
ISSN: 0305-0548
PURE UUID: 08e9beaf-9759-48b5-bc97-c5a8f2c9769b

Catalogue record

Date deposited: 27 Mar 2008
Last modified: 13 Mar 2019 20:50

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×