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Sequential Monte Carlo simulated annealing

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  • Enlu Zhou
  • Xi Chen

Abstract

In this paper, we propose a population-based optimization algorithm, Sequential Monte Carlo Simulated Annealing (SMC-SA), for continuous global optimization. SMC-SA incorporates the sequential Monte Carlo method to track the converging sequence of Boltzmann distributions in simulated annealing. We prove an upper bound on the difference between the empirical distribution yielded by SMC-SA and the Boltzmann distribution, which gives guidance on the choice of the temperature cooling schedule and the number of samples used at each iteration. We also prove that SMC-SA is more preferable than the multi-start simulated annealing method when the sample size is sufficiently large. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Enlu Zhou & Xi Chen, 2013. "Sequential Monte Carlo simulated annealing," Journal of Global Optimization, Springer, vol. 55(1), pages 101-124, January.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:1:p:101-124
    DOI: 10.1007/s10898-011-9838-3
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    References listed on IDEAS

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    1. Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436, June.
    2. Reuven Rubinstein, 1999. "The Cross-Entropy Method for Combinatorial and Continuous Optimization," Methodology and Computing in Applied Probability, Springer, vol. 1(2), pages 127-190, September.
    3. R. L. Yang, 2000. "Convergence of the Simulated Annealing Algorithm for Continuous Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 691-716, March.
    4. Orcun Molvalioglu & Zelda B. Zabinsky & Wolf Kohn, 2007. "Multi-particle Simulated Annealing," Springer Optimization and Its Applications, in: Aimo Törn & Julius Žilinskas (ed.), Models and Algorithms for Global Optimization, pages 215-222, Springer.
    5. Bruce Hajek, 1988. "Cooling Schedules for Optimal Annealing," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 311-329, May.
    6. Pieter-Tjerk de Boer & Dirk Kroese & Shie Mannor & Reuven Rubinstein, 2005. "A Tutorial on the Cross-Entropy Method," Annals of Operations Research, Springer, vol. 134(1), pages 19-67, February.
    7. M. Locatelli, 2000. "Simulated Annealing Algorithms for Continuous Global Optimization: Convergence Conditions," Journal of Optimization Theory and Applications, Springer, vol. 104(1), pages 121-133, January.
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    Cited by:

    1. John Geweke, 2016. "Sequentially Adaptive Bayesian Learning for a Nonlinear Model of the Secular and Cyclical Behavior of US Real GDP," Econometrics, MDPI, vol. 4(1), pages 1-23, March.
    2. Jinyu Zhang & Kang Gao & Yong Li & Qiaosen Zhang, 2022. "Maximum Likelihood Estimation Methods for Copula Models," Computational Economics, Springer;Society for Computational Economics, vol. 60(1), pages 99-124, June.
    3. Bin Liu, 2017. "Posterior exploration based sequential Monte Carlo for global optimization," Journal of Global Optimization, Springer, vol. 69(4), pages 847-868, December.
    4. Ng, Kenyon & Turlach, Berwin A. & Murray, Kevin, 2019. "A flexible sequential Monte Carlo algorithm for parametric constrained regression," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 13-26.
    5. Tsionas, Mike G., 2018. "A Bayesian approach to find Pareto optima in multiobjective programming problems using Sequential Monte Carlo algorithms," Omega, Elsevier, vol. 77(C), pages 73-79.
    6. Geweke, John & Durham, Garland, 2019. "Sequentially adaptive Bayesian learning algorithms for inference and optimization," Journal of Econometrics, Elsevier, vol. 210(1), pages 4-25.

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