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Convergence of the Simulated Annealing Algorithm for Continuous Global Optimization

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  • R. L. Yang

    (Northern Jiaotong University)

Abstract

A class of simulated annealing algorithms for continuous global optimization is considered in this paper. The global convergence property is analyzed with respect to the objective value sequence and the minimum objective value sequence induced by simulated annealing algorithms. The convergence analysis provides the appropriate conditions on both the generation probability density function and the temperature updating function. Different forms of temperature updating functions are obtained with respect to different kinds of generation probability density functions, leading to different types of simulated annealing algorithms which all guarantee the convergence to the global optimum.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:104:y:2000:i:3:d:10.1023_a:1004697811243
    DOI: 10.1023/A:1004697811243
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    References listed on IDEAS

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    1. Bruce Hajek, 1988. "Cooling Schedules for Optimal Annealing," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 311-329, May.
    2. L. Ingber, 1993. "Simulated annealing: Practice versus theory," Lester Ingber Papers 93sa, Lester Ingber.
    3. L. Ingber, 1989. "Very fast simulated re-annealing," Lester Ingber Papers 89vf, Lester Ingber.
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    Cited by:

    1. Dawid Tarłowski, 2017. "On the convergence rate issues of general Markov search for global minimum," Journal of Global Optimization, Springer, vol. 69(4), pages 869-888, December.
    2. V. Bartkutė & L. Sakalauskas, 2009. "Statistical Inferences for Termination of Markov Type Random Search Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 141(3), pages 475-493, June.
    3. Gerber, Mathieu & Bornn, Luke, 2018. "Convergence results for a class of time-varying simulated annealing algorithms," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1073-1094.
    4. Marc Robini & Pierre-Jean Reissman, 2013. "From simulated annealing to stochastic continuation: a new trend in combinatorial optimization," Journal of Global Optimization, Springer, vol. 56(1), pages 185-215, May.
    5. Enlu Zhou & Xi Chen, 2013. "Sequential Monte Carlo simulated annealing," Journal of Global Optimization, Springer, vol. 55(1), pages 101-124, January.
    6. Antti Solonen, 2013. "Proposal adaptation in simulated annealing for continuous optimization problems," Computational Statistics, Springer, vol. 28(5), pages 2049-2065, October.
    7. Alan Lockett & Risto Miikkulainen, 2014. "Evolutionary annealing: global optimization in measure spaces," Journal of Global Optimization, Springer, vol. 58(1), pages 75-108, January.

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