Abstract
A quantitative study is presented of the typical behavior of the simulated annealing algorithm based on a cooling schedule presented previously by the authors. The study is based on the analysis of numerical results obtained by systematically applying the algorithm to a 100-city traveling salesman problem. The expectation and the variance of the cost are analyzed as a function of the control parameter of the cooling schedule. A semiempirical average-case performance analysis is presented from which estimates are obtained on the expectation of the average final result obtained by the simulated annealing algorithm as a function of the distance parameter, which determines the decrement of the control parameter.
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References
E. H. L. Aarts and P. J. M. van Laarhoven,Philips J. Res. 40:193–226 (1985).
E. H. L. Aarts and P. J. M. van Laarhoven, inProceedings International Conference on Computer-Aided Design (Santa Clara, November 1985), pp. 206–208.
K. Binder,Monte Carlo Methods in Statistical Physics (Springer-Verlag, Berlin, 1986).
V. Černy,J. Optim. Theory Appl. 45:41–51 (1985).
G. S. Grest, C. M. Soukoulis, and K. Levin,Phys. Rev. Lett. 56:1148–1151 (1986).
B. Hajek, inProceedings 24th Conference on Decision and Control (Ft. Lauderdale, December 1985), pp. 755–760.
R. Jonker and T. Volgenant,Oper. Res. 32:837–846 (1984).
S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi,Science 220:671–680 (1983).
S. Kirkpatrick and G. Toulouse,J. Phys. (Paris) 46:1277–1292 (1985).
P. J. M. van Laarhoven and E. H. L. Aarts,Simulated Annealing: Theory and Applications (Kluwer, Dordrecht, 1987).
E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan, and D. B. Shmoys,The Traveling Salesman Problem (Wiley, Chichester, 1985).
S. Lin and B. W. Kernighan,Oper. Res. 21:498–516 (1973).
M. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller,J. Chem. Phys. 21:1087–1092 (1953).
E. Palmer,Graphical Evolution (Wiley Interscience, New York, 1985).
F. Romeo and A. L. Sangiovanni-Vincentelli, inProceedings 1985 Chapel Hill Conference on VLSI (May 1985), pp. 393–417.
G. H. Sasaki and B. Hajek,J. ACM, to appear.
S. Solla, G. Sorkin, and S. White, inDisordered Systems and Biological Organization (Springer-Verlag, Berlin, 1985).
S. R. White, inProceedings International Conference Computer Design (Port Chester, November 1984), pp. 646–651.
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Aarts, E.H.L., Korst, J.H.M. & van Laarhoven, P.J.M. A quantitative analysis of the simulated annealing algorithm: A case study for the traveling salesman problem. J Stat Phys 50, 187–206 (1988). https://doi.org/10.1007/BF01022991
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DOI: https://doi.org/10.1007/BF01022991