ACM Transactions on Mathematical Software (TOMS)
Simulated annealing algorithms for continuous global optimization: convergence conditions
Journal of Optimization Theory and Applications
Convergence of the simulated annealing algorithm for continuous global optimization
Journal of Optimization Theory and Applications
Statistics and Computing
GNU Scientific Library Reference Manual - Third Edition
GNU Scientific Library Reference Manual - Third Edition
Locating and characterizing the stationary points of the extended rosenbrock function
Evolutionary Computation
Paper: The parallel genetic algorithm as function optimizer
Parallel Computing
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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.