Abstract
We present an analytically derived cooling schedule for a simulated annealing algorithm applicable to both continuous and discrete global optimization problems. An adaptive search algorithm is used to model an idealized version of simulated annealing which is viewed as consisting of a series of Boltzmann distributed sample points. Our choice of cooling schedule ensures linearity in the expected number of sample points needed to become arbitrarily close to a global optimum.
Similar content being viewed by others
References
Aarts E.H.L., Van Laarhoven P.J.M. (1989): Simulated annealing: an introduction. Statistica Neerlandica 43, 31–52
Ali M.M., Khompatraporn C., Zabinsky Z.B. (2005): A numerical evaluation of several global optimization algorithms on selected benchmark test problems. J. Glob. Optim. 31(4): 635–672
Alrefaei M.H., Andradóttir S. (1999): A simulated annealing algorithm with constant temperature for discrete stochastic optimization. Manag. Sci. 45(5): 748–764
Bélisle C.J.P. (1992): Convergence theorems for a class of simulated annealing algorithms on R n. J. Appl. Probab. 29, 885–895
Bohachevsky I.O., Johnson M.E., Stein M.L. (1986): Generalized simulated annealing for function optimization. Technometrics 28, 209–217
Cohn H., Fielding M. (1999): Simulated annealing: searching for an optimal temperature schedule. SIAM J. Optim. 9(3): 779–802
Corana A., Marchesi M., Martini C., Ridella S. (1987): Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm. ACM T. Math. Software 13, 262–280
Dekker A., Aarts E.H.L. (1991): Global optimization and simulated annealing. Math. Program. 50, 367–393
Fielding M. (2000): Simulated annealing with an optimal fixed temperature. SIAM J. Optim. 11(2): 289–307
Hajek B. (1988): Cooling schedules for optimal annealing. Math. Oper. Res. 13, 311–329
Kirkpatrick S., Gelatt C.D., Vecchi M.P. (1983): Optimization by simulated annealing. Science 220, 671–680
Locatelli M. (2000): Simulated annealing algorithms for continuous global optimization: convergence conditions. J. Optim. Theory Appl. 104, 121–133
Locatelli M. (2000): Convergence of a simulated annealing algorithm for continuous global optimization. J. Glob. Optim.18, 219–234
Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., Teller E. (1953): Equations of state calculations by fast computing machines. J. Chem. Phys. 21, 1087–1092
Pincus M. (1968): A closed form solution for certain programming problems. Oper. Res. 16, 690–694
Pintér J.D. (1996): Global Optimization in Action (Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications). Kluwer Academic Publishers, Dordrecht/Boston/London
Rubinstein R.Y. (1981): Simulation and the Monte Carlo Method. Wiley, New York
Romeijn H.E., Smith R.L. (1994): Simulated annealing for constrained global optimization. J. Glob. Optim. 5, 101–126
Romeijn H.E., Smith R.L. (1994): Simulated annealing and adaptive search in global optimization. Probab. Eng. Inform. Sci. 8, 571–590
Shen, Y., Zabinsky, Z.B., Smith, R.L.: Annealing adaptive search with a Markov chain Monte Carlo sampler for global optimization. Technical Report, Industrial Engineering, University of Washington, Seattle, WA (2005)
Shen, Y.: Annealing adaptive search with hit-and-run sampling methods for global optimization. PhD dissertation, University of Washington (2005)
Smith R.L. (1984): Efficient Monte Carlo procedures for generating points uniformly distributed over bounded region. Oper. Res. 32, 1296–1308
Zabinsky Z.B. (2003): Stochastic Adaptive Search for Global Optimization. Kluwer Academic Publishers, Boston/Dordrecht/London
Zabinsky Z.B., Graesser D.L., Tuttle M.E., Kim G.I. (1992): Global Optimization of Composite Laminate Using Improving Hit-and-Run. In: Floudas C.A., Pardalos P.M. (eds). Recent Advances in Global Optimization. Princeton University Press, Princeton, NJ
Zabinsky Z.B., Smith R.L. (1992): Pure adaptive search in global optimization. Math. Program. 53, 323–338
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shen, Y., Kiatsupaibul, S., Zabinsky, Z.B. et al. An analytically derived cooling schedule for simulated annealing. J Glob Optim 38, 333–365 (2007). https://doi.org/10.1007/s10898-006-9068-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-006-9068-2