Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm
- V. Černý
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We present a Monte Carlo algorithm to find approximate solutions of the traveling salesman problem. The algorithm generates randomly the permutations of the stations of the traveling salesman trip, with probability depending on the length of the corresponding route. Reasoning by analogy with statistical thermodynamics, we use the probability given by the Boltzmann-Gibbs distribution. Surprisingly enough, using this simple algorithm, one can get very close to the optimal solution of the problem or even find the true optimum. We demonstrate this on several examples.
We conjecture that the analogy with thermodynamics can offer a new insight into optimization problems and can suggest efficient algorithms for solving them.
- Kittel, C.,Thermal Physics, John Wiley and Sons, New York, New York, 1969.
- Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., andTeller, E.,Equation of State Calculations by Fast Computing Machines, Journal of Chemical Physics, Vol. 21, pp. 1087–1092, 1953.
- Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm
Journal of Optimization Theory and Applications
Volume 45, Issue 1 , pp 41-51
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
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- Traveling salesman problem
- Monte Carlo optimization
- importance sampling
- Industry Sectors
- V. Černý (1)
- Author Affiliations
- 1. Institute of Physics and Biophysics, Comenius University, Mlynska Dolina, Bratislava, Czechoslovakia