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Scale Invariance Properties in the Simulated Annealing Algorithm

Author

Listed:
  • M. A. Fleischer

    (University of Maryland)

  • S. H. Jacobson

    (University of Illinois at Urbana-Champaign)

Abstract

The Boltzmann distribution used in the steady-state analysis of the simulated annealing algorithm gives rise to several scale invariant properties. Scale invariance is first presented in the context of parallel independent processors and then extended to an abstract form based on lumping states together to form new aggregate states. These lumped or aggregate states possess all of the mathematical characteristics, forms and relationships of states (solutions) in the original problem in both first and second moments. These scale invariance properties therefore permit new ways of relating objective function values, conditional expectation values, stationary probabilities, rates of change of stationary probabilities and conditional variances. Such properties therefore provide potential applications in analysis, statistical inference and optimization. Directions for future research that take advantage of scale invariance are also discussed.

Suggested Citation

  • M. A. Fleischer & S. H. Jacobson, 2002. "Scale Invariance Properties in the Simulated Annealing Algorithm," Methodology and Computing in Applied Probability, Springer, vol. 4(3), pages 219-241, September.
    • Handle: RePEc:spr:metcap:v:4:y:2002:i:3:d:10.1023_a:1022596700741
    DOI: 10.1023/A:1022596700741
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    References listed on IDEAS

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    1. Leyuan Shi & Sigurdur Ólafsson, 2000. "Nested Partitions Method for Global Optimization," Operations Research, INFORMS, vol. 48(3), pages 390-407, June.
    2. James P. Hobert, 2002. "On the applicability of regenerative simulation in Markov chain Monte Carlo," Biometrika, Biometrika Trust, vol. 89(4), pages 731-743, December.
    3. Mark Fleischer & Sheldon H. Jacobson, 1999. "Information Theory and the Finite-Time Behavior of the Simulated Annealing Algorithm: Experimental Results," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 35-43, February.
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