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.
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Torn, A., and Zilinskas, A., Global Optimization, Springer Verlag, Berlin, Germany, 1989.
Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P., Optimization by Simulated Annealing, Science, Vol. 220, pp. 671–680. 1983.
Cerny, V., Thermodynamical Approach to the Travelling Salesman Problem: An Efficient Simulation Algorithm, Journal of Optimization Theory and Applications, Vol. 45, pp. 41–45, 1985.
Van laarhoven, P. J. M., and Aarts, E. H. L., Simulated Annealing: Theory and Applications, D. Reidel Publishing Company, Dordrecht, Holland, 1987.
Romeo, F., and Sangiovanni-vincentelli, A., A Theoretical Framework for Simulated Annealing, Algorithmica, Vol. 6, pp. 302–345, 1991.
Hajek, B., Cooling Schedules for Optimal Annealing, Mathematics of Operations Research, Vol. 13, pp. 311–329, 1988.
Geman, S., and Hwang, C. R., Diffusions for Global Optimization, SIAM Journal on Control and Optimization, Vol. 24, pp. 1031–1043, 1986.
Chiang, T. S., Hwang, C. R., and Sheu, S. J., Diffusion for Global Optimization in R n, SIAM Journal on Control and Optimization, Vol. 25, pp. 737–753, 1987.
Gelfand, S. B., and Mitter, S. K., Recursive Stochastic Algorithms for Global Optimization in R n, SIAM Journal on Control and Optimization, Vol. 29, pp. 999–1018, 1991.
Jeng, F. C., and Woods, J. W., Simulated Annealing in Compound Gaussian Random Fields, IEEE Transactions on Information Theory, Vol. 36, pp. 94–107, 1990.
Gelfand, S. B., and Mitter, S. K., Metropolis-Type Annealing Algorithms for Global Optimization in R d, SIAM Journal on Control and Optimization, Vol. 31, pp. 111–131, 1993.
Szu, H. H., Nonconvex Optimization, Proceedings of the Society of Photo-Optical Instrumentation Engineers, Vol. 698, pp. 59–65, 1986.
Szu, H. H., and Hartley, P. L., Fast Simulated Annealing, Physics Letters, Vol. 122A, pp. 157–162, 1987.
Ingber, L., Very Fast Simulated Reannealing, Mathematical and Computer Modelling, Vol. 12, pp. 967–973, 1989.
Ingber, L., Simulated Annealing: Practice versus Theory, Mathematical and Computer Modelling, Vol. 18, pp. 29–57, 1993.
Belisle, C. J. P., Convergence Theorems for a Class of Simulated Annealing Algorithms on R d, Journal of Applied Probability, Vol. 29, pp. 885–895, 1992.
Dekkers, A., and Aarts, E. H. L., Global Optimization and Simulated Annealing, Mathematical Programming, Vol. 50, pp. 367–393, 1991.
Romeijn, H. E., and Smith, R. L., Simulated Annealing for Constrained Global Optimization, Journal of Global Optimization, Vol. 5, pp. 101–126, 1994.
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Yang, R.L. Convergence of the Simulated Annealing Algorithm for Continuous Global Optimization. Journal of Optimization Theory and Applications 104, 691–716 (2000). https://doi.org/10.1023/A:1004697811243
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DOI: https://doi.org/10.1023/A:1004697811243