A comparison of lower bounds for the symmetric circulant traveling salesman problem
de Klerk,E. Dobre,C.
de Klerk,E.
Dobre,C.
Abstract
When the matrix of distances between cities is symmetric and circulant, the traveling salesman problem (TSP) reduces to the so-called symmetric circulant traveling salesman problem (SCTSP), that has applications in the design of reconfigurable networks, and in minimizing wallpaper waste. The complexity of the SCTSP is open, but conjectured to be NP-hard, and we compare different lower bounds on the optimal value that may be computed in polynomial time. We derive a new linear programming (LP) relaxation of the SCTSP from the semidefinite programming (SDP) relaxation in [E. de Klerk, D.V. Pasechnik, R. Sotirov, On semidefinite programming relaxation of the traveling salesman problem, SIAM Journal of Optimization 19 (4) (2008) 1559–1573]. Further, we discuss theoretical and empirical comparisons between this new bound and three well-known bounds from the literature, namely the Held-Karp bound [M. Held, R.M. Karp, The traveling salesman problem and minimum spanning trees, Operations Research 18 (1970) 1138–1162], the 1-tree bound, and the closed-form bound for SCTSP proposed in [J.A.A. van der Veen, Solvable cases of TSP with various objective functions, Ph.D. Thesis, Groningen University, The Netherlands, 1992].
Description
Date
2011
Journal Title
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Volume Title
Publisher
Research Projects
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Keywords
semidefinite programming, traveling salesman problem, circulant matrices
Citation
de Klerk, E & Dobre, C 2011, 'A comparison of lower bounds for the symmetric circulant traveling salesman problem', Discrete Applied Mathematics, vol. 159, no. 16, pp. 1815-1826. https://doi.org/10.1016/j.dam.2011.01.026
License
info:eu-repo/semantics/openAccess