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Computer Simulation Studies in Condensed-Matter Physics VII pp 193–198Cite as

Optimization by Multicanonical Annealing and the Traveling-Salesman Problem

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Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 78))

Abstract

We demonstrate a powerful and general simulated annealing method to study combinatorial optimization problems. It combines the multicanonical method, which samples directly the microcanonical entropy of the system, with an elaborate but straightforward annealing scheme. The idea is to fully utilize the information about the local entropy obtained during short Monte Carlo simulations for optimization in an iterative fashion. We present results of an extensive investigation of the traveling salesman problem in a unit square.

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References

  1. The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, edited by E. L. Lawler, J. K. Lenstra, A. H. G. Ringnooy Kan, and D. B. Shmoys (Wiley, Chichester, 1985).

    Google Scholar 

  2. M. Padberg and G. Rinaldi, SIAM Rev. 33, 60 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  3. S. Kirkpatrick, C.D. Jr. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  4. V. Cerny, J. Optimization Theory Appl. 45, 41 (1985).

    Article  MATH  MathSciNet  Google Scholar 

  5. S. Lin and B. W. Kernighan, Oper. Res. 21, 498 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  6. D. Johnson, Nature 330, 525 (1987).

    Article  ADS  Google Scholar 

  7. D. Johnson, Nature Proceedings of the 17th Colloquium on Automata, Language, and Programming (Springer-Verlag, Berlin, 1990), pp. 446–461.

    Google Scholar 

  8. J. P. Valleau and D. N. Card, J. Chem. Phys. 57, 5457 (1972).

    Article  ADS  Google Scholar 

  9. G. M. Torrie and J. P. Valleau, J. Comput. Phys. 23, 187 (1977).

    Article  ADS  Google Scholar 

  10. B. A. Berg and T. Neuhaus, Phys. Lett. B267, 249 (1991).

    ADS  Google Scholar 

  11. B. A. Berg and T. Neuhaus, Phys. Rev. Lett. 68, 9 (1992).

    Article  ADS  Google Scholar 

  12. B. A. Berg and T. Celik, Phys. Rev. Lett. 69, 2292 (1992).

    Article  ADS  Google Scholar 

  13. B. A. Berg, Int. J. Mod. Phys. C3, 1083 (1992).

    ADS  Google Scholar 

  14. J. Lee, Phys. Rev. Lett. 71, 211 (1993).

    Article  ADS  Google Scholar 

  15. J. Lee, Phys. Rev. Lett. 71, 2353 (1993) (erratum).

    Article  ADS  Google Scholar 

  16. A. Hüller, Z. Phys. B 88, 79 (1992).

    Article  ADS  Google Scholar 

  17. J. Lee and M. Y. Choi, preprints, FSU-SCRI-93-107.

    Google Scholar 

  18. J. Beardwood, J. H. Halton, and J. M. Hammersley, Proc. Camb. Philo. Soc. 55, 299 (1959).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  19. J. Beardwood, J. H. Halton, and J. M. Hammersley, J. M. Steele, Ann. Prob. 9, 365 (1981).

    Article  Google Scholar 

  20. G. A. Croes, Oper. Res. 6, 791 (1958).

    Article  MathSciNet  Google Scholar 

  21. S. Lin, Bell Syst. Tech. J. 44, 2245 (1965).

    MATH  Google Scholar 

  22. W. Krauth and M. Mèzard, Europhys. Lett. 8, 213 (1989).

    Article  ADS  Google Scholar 

  23. E. Bonomi and J.-L. Lutton, SIAM Rev. 26, 551 (1984).

    Article  MATH  MathSciNet  Google Scholar 

  24. B. K. Ambati, J. Ambati, and M. M. Mokhtar.

    Google Scholar 

  25. [16] See, e.g., Finite Size Scaling and Numerical Simulation of Statistical Systems, edited by Privman, V. (World Scientific, Singapore, 1990).

    Google Scholar 

  26. F. Favata and R. Walker, R., Biol. Cybern. 64, 463 (1991).

    Article  MATH  Google Scholar 

  27. R. Durbin and D. Willshaw, Nature 336, 689 (1987).

    Article  ADS  Google Scholar 

  28. R. Durbin and D. Willshaw, Biol. Cybern. 65, 31 (1991).

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Supercomputer Computations Research Institute (SCRI), Florida State University, Tallahassee, FL, 32306-4052, USA

    J. Lee

  2. Department of Physics, Seoul National University, Seoul, 151-742, Korea

    M. Y. Choi

Authors
  1. J. Lee
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  2. M. Y. Choi
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Editor information

Editors and Affiliations

  1. Center for Simulational Physics, The University of Georgia, Athens, GA, 30602, USA

    David P. Landau Ph. D. , K. K. Mon Ph. D  & Heinz-Bernd Schüttler Ph. D. ,  & 

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© 1994 Springer-Verlag Berlin Heidelberg

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Lee, J., Choi, M.Y. (1994). Optimization by Multicanonical Annealing and the Traveling-Salesman Problem. In: Landau, D.P., Mon, K.K., Schüttler, HB. (eds) Computer Simulation Studies in Condensed-Matter Physics VII. Springer Proceedings in Physics, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79293-9_19

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  • DOI: https://doi.org/10.1007/978-3-642-79293-9_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-79295-3

  • Online ISBN: 978-3-642-79293-9

  • eBook Packages: Springer Book Archive

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