Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm

  • V. Černý
Contributed Papers


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.

Key Words

Traveling salesman problem Monte Carlo optimization importance sampling 


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    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.Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • V. Černý
    • 1
  1. 1.Institute of Physics and BiophysicsComenius UniversityBratislavaCzechoslovakia

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