On Semidefinite Programming Relaxations of the Traveling Salesman Problem

CentER Discussion Paper Series No. 2008-96

19 Pages Posted: 9 Dec 2008

See all articles by Etienne de Klerk

Etienne de Klerk

Tilburg University

Dmitrii V. Pasechnik

Tilburg University - Center for Economic Research (CentER)

Renata Sotirov

Tilburg University - Tilburg University School of Economics and Management

Date Written: November 12, 2008

Abstract

We consider a new semidefinite programming (SDP) relaxation of the symmetric traveling salesman problem (TSP), that may be obtained via an SDP relaxation of the more general quadratic assignment problem (QAP). We show that the new relaxation dominates the one in the paper: D. Cvetkovic, M. Cangalovic and V. Kovacevic-Vujcic. Semidefinite Programming Methods for the Symmetric traveling Salesman Problem. In Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization, 1999, 126-136, Springer-Verlag, London, UK. Unlike the bound of Cvetkovic et al., the new SDP bound is not dominated by the Held-Karp linear programming bound, or vice versa.

Keywords: traveling salesman problem, semidefinite programming, quadratic assignment problem, association schemes

JEL Classification: C61

Suggested Citation

de Klerk, Etienne and Pasechnik, Dmitrii V. and Sotirov, Renata, On Semidefinite Programming Relaxations of the Traveling Salesman Problem (November 12, 2008). CentER Discussion Paper Series No. 2008-96. Available at SSRN: https://ssrn.com/abstract=1313648 or http://dx.doi.org/10.2139/ssrn.1313648

Etienne De Klerk (Contact Author)

Tilburg University ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Dmitrii V. Pasechnik

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Renata Sotirov

Tilburg University - Tilburg University School of Economics and Management ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

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