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

@article{Cern1985ThermodynamicalAT,
  title={Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm},
  author={Vladim{\'i}r Cern{\'y}},
  journal={Journal of Optimization Theory and Applications},
  year={1985},
  volume={45},
  pages={41-51}
}
  • V. Cerný
  • Published 1985
  • Mathematics
  • Journal of Optimization Theory and Applications
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… Expand
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References

Equation of state calculations by fast computing machines
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