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Proposal adaptation in simulated annealing for continuous optimization problems

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  • Antti Solonen

Abstract

In recent years, adaptive Markov Chain Monte Carlo (MCMC) methods have become a standard tool for Bayesian parameter estimation. In adaptive MCMC, the past iterations are used to tune the proposal distribution of the algorithm. The same adaptation mechanisms can be used in Simulated Annealing (SA), a popular optimization method based on MCMC. The difficulty in using adaptation directly in SA is that the target function changes along the iterations in the annealing process, and the adaptation should keep up with the annealing. In this paper, a mechanism for automatically tuning the proposal distribution in SA is proposed. The approach is based on the Adaptive Metropolis algorithm of Haario et al. (Bernoulli 7(2):223–242, 2001 ), combined with a weighting mechanism to account for the cooling target. The proposed adaptation mechanism does not add any computational complexity to the problem in terms of objective function evaluations. The effect of adaptation is demonstrated using two benchmark problems, showing that the proposed adaptation mechanism can significantly improve optimization results compared to non-adaptive SA. The approach is presented for continuous optimization problems and generalization to integer and mixed-integer problems is a topic of future research. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Antti Solonen, 2013. "Proposal adaptation in simulated annealing for continuous optimization problems," Computational Statistics, Springer, vol. 28(5), pages 2049-2065, October.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:5:p:2049-2065
    DOI: 10.1007/s00180-013-0395-8
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    References listed on IDEAS

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    1. 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.
    2. L. Ingber, 1996. "Adaptive simulated annealing (ASA): Lessons learned," Lester Ingber Papers 96as, Lester Ingber.
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    2. Wen-Li Dong & Xing Li & Zheng Peng, 2019. "A Simulated Annealing-Based Barzilai–Borwein Gradient Method for Unconstrained Optimization Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(04), pages 1-12, August.

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