Abstract
It is well-known that for the symmetric travelling salesman problem search methods using the 1-tree relaxation introduced by Held and Karp are much more efficient than those using the assignment relaxation due to the sharper bounds obtained. Held and Karp noted an analogous relationship between the asymmetric travelling salesman problem and the minimum one-arborescence problem. We implemented a LIFO implicit enumeration algorithm based on this idea and found that it is inferior to the assignment relaxation for two reasons: the relatively large computation time required to compute a minimum one-arborescence; and, more importantly, the fact that the bounds obtained from the two relaxations are about the same for asymmetric problems.
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© 1980 The Mathematical Programming Society
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Smith, T.H.C. (1980). A LIFO implicit enumeration algorithm for the asymmetric travelling salesman problem using a one-arborescence relaxation. In: Padberg, M.W. (eds) Combinatorial Optimization. Mathematical Programming Studies, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120889
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DOI: https://doi.org/10.1007/BFb0120889
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