Simulated stochastic approximation annealing for global optimization with a square-root cooling schedule

• Autores: Faming Liang, Yichen Cheng, Guang Lin
• Localización: Journal of the American Statistical Association, ISSN 0162-1459, Vol. 109, Nº 506, 2014, págs. 847-863
• Idioma: inglés
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• Resumen

  • Simulated annealing has been widely used in the solution of optimization problems. As known by many researchers, the global optima cannot be guaranteed to be located by simulated annealing unless a logarithmic cooling schedule is used. However, the logarithmic cooling schedule is so slow that no one can afford to use this much CPU time. This article proposes a new stochastic optimization algorithm, the so-called simulated stochastic approximation annealing algorithm, which is a combination of simulated annealing and the stochastic approximation Monte Carlo algorithm. Under the framework of stochastic approximation, it is shown that the new algorithm can work with a cooling schedule in which the temperature can decrease much faster than in the logarithmic cooling schedule, for example, a square-root cooling schedule, while guaranteeing the global optima to be reached when the temperature tends to zero. The new algorithm has been tested on a few benchmark optimization problems, including feed-forward neural network training and protein-folding. The numerical results indicate that the new algorithm can significantly outperform simulated annealing and other competitors. Supplementary materials for this article are available online.