Abstract
The problem of finding the shortest closed path connectingN randomly chosen points is one of the classicNp-complete problems. We show that the length of tour depends logarithmically on the cooling rateQ in a simulated Monte Carlo anneal. We speculate that this is a general property of allNp-complete problems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi,Science 220:671 (1983).
N. Metropliset al., J. Chem. Phys. 21:1087 (1953).
S. Kirkpatrick,J. Stat. Phys. 34:975 (1984).
M. P. Vecchi and S. Kirkpatrick,IEEE Trans. Comput. Aided Design: Integrated Circuits CAD-2:215 (1983).
W. E. Smith, R. G. Paxman, and H. H. Barrett,J. Opt. Soc. Am. A 2:491 (1985).
D. Vanderbilt and S. G. Louie,J. Comput. Phys. 56:259 (1984).
G. S. Grest, C. M. Soukoulis, and K. Levin,Phys. Rev. Lett. 56:1148 (1986).
M. R. Garey and D. S. Johnson,Computers and Intractability: A Guide to the Theory of Np-Completeness (Freeman, San Francisco, 1979).
D. Huse and D. Fisher,Phys. Rev. Lett. 57:2203 (1986).
E. Bonomi and J.-L. Lutton,SIAM Rev. 26:551 (1984).
R. W. Brady,Nature 317:804 (1985).
M. W. Padberg and S. Hong, On the symmetric travelling salesman problem: A computational study,Mathematical Programming Study 12, M. W. Padberg ed. (North-Holland, 1980), p. 78.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Randelman, R.E., Grest, G.S. N-city traveling salesman problem: Optimization by simulated annealings. J Stat Phys 45, 885–890 (1986). https://doi.org/10.1007/BF01020579
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01020579