Advertisement

Statistics and Computing

, Volume 2, Issue 4, pp 221–230 | Cite as

A segmented algorithm for simulated annealing

  • A. C. Atkinson
Papers

Abstract

The properties of a parameterized form of generalized simulated annealing for function minimization are investigated by studying the properties of repeated minimizations from random starting points. This leads to the comparison of distributions of function values and of numbers of function evaluations. Parameter values which yield searches repeatedly terminating close to the global minimum may require unacceptably many function evaluations. If computational resources are a constraint, the total number of function evaluations may be limited. A sensible strategy is then to restart at a random point any search which terminates, until the total allowable number of function evaluations has been exhausted. The response is now the minimum of the function values obtained. This strategy yields a surprisingly stable solution for the parameter values of the simulated annealing algorithm. The algorithm can be further improved by segmentation in which each search is limited to a maximum number of evaluations, perhaps no more than a fifth of the total available. The main tool for interpreting the distributions of function values is the boxplot. The application is to the optimum design of experiments.

Keywords

D-optimality exact design generalized simulated annealing nonlinear optimization renewal process segmented algorithm simulated annealing 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Atkinson, A. C. (1969) Constrained maximisation and the design of experiments.Technometrics,11, 616–618.Google Scholar
  2. Atkinson, A. C. and Donev, A. N. (1992)Optimum Experimental Designs, Clarendon Press, Oxford.Google Scholar
  3. Bohachevsky, I. O., Johnson, M. E. and Stein, M. L. (1986) Generalized simulated annealing for function optimization.Technometrics,28, 209–217.Google Scholar
  4. Corana, A., Marchesi, M., Martini, C. and Ridella, S. (1987) Minimizing multimodal functions of continuous variables with the ‘simulated annealing’ algorithm.ACM Transactions on Mathematical Software,13, 272–280.Google Scholar
  5. Davis, L. (ed.) (1991)Handbook of Genetic Algorithms, van Nostrand Reinhold, New York.Google Scholar
  6. Fedorov, V. V. (1972)Theory of Optimal Experiments, Academic Press, New York.Google Scholar
  7. Glover, F. (1989) Tabu search, part I.ORSA Journal on Computing,1, 190–206.Google Scholar
  8. Haines, L. M. (1987) The application of the annealing algorithm to the construction of exact optimal designs for linear-regression models.Technometrics,29, 439–447.Google Scholar
  9. Johnson, D. S., Aragon, C. R., McGeoch, L. A. and Schevon, C. (1989) Optimization by simulated annealing: an experimental evaluation; part 1, graph partitioning.Operations Research,37, 865–892.Google Scholar
  10. Kirkpatrick, S., Gelatt, C. D. and Vecchi, M. P. (1983) Optimization by simulated annealing.Science,220, 671–680.Google Scholar
  11. Kjærulff, U. (1992) Optimal decomposition of probabilistic networks by simulated annealing.Statistics and Computing,2, 7–17.Google Scholar
  12. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953) Equation of state calculations using fast computing machines.Journal of Chemical Physics,21, 1087–1092.Google Scholar
  13. Meyer, R. K. and Nachtsheim, C. J. (1988) Constructing exactD-optimal experimental designs by simulated annealing.American Journal of Mathematical and Management Sciences,8, 329–359.Google Scholar
  14. Silvey, S. D. (1980)Optimal Design, Chapman and Hall, London.Google Scholar
  15. Woodruff, D. L. and Rocke, D. M. (1992) Computation of minimum volume ellipsoid estimates using heuristic search. Technical report, Graduate School of Management, University of California, Davis.Google Scholar
  16. Zhigljavsky, A. A. (1991)Theory of Global Random Search, Kluwer, Dordrecht.Google Scholar

Copyright information

© Chapman & Hall 1992

Authors and Affiliations

  • A. C. Atkinson
    • 1
  1. 1.Department of StatisticsLondon School of EconomicsLondonUK

Personalised recommendations