Abstract
In this chapter we deal with the problem of solving symmetric TSP (STSP) instances to optimality. Of course, STSP instances are particular cases of asymmetric TSP (ATSP) instances, those for which the distance between any two cities is irrelevant of the direction. Therefore we could transform any instance of the STSP to an asymmetric one and use the results of Chapter 4 to solve it. In fact the techniques of Chapter 4 do not perform well when the costs of the arcs (i,j) and (j,i) only slightly differ. Progress in the solution techniques for the STSP is such that it is common to transform an ATSP into a symmetric one to solve it to optimality (see [474]).
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Naddef, D. (2007). Polyhedral Theory and Branch-and-Cut Algorithms for the Symmetric TSP. In: Gutin, G., Punnen, A.P. (eds) The Traveling Salesman Problem and Its Variations. Combinatorial Optimization, vol 12. Springer, Boston, MA. https://doi.org/10.1007/0-306-48213-4_2
Download citation
DOI: https://doi.org/10.1007/0-306-48213-4_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-44459-8
Online ISBN: 978-0-306-48213-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)