On semidefinite programming relaxations of the traveling salesman problem

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 [D. Cvetković, M. Cangalović, and V. Kovačević-Vujčić, Semidefinite programming methods for the symmetric traveling salesman problem, in Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization, Springer-Verlag, London, UK, 1999, pp. 126–136]. Unlike the bound of Cvetković et al., the new SDP bound is not dominated by the Held–Karp linear programming bound, or vice versa.