TERMINATION OF SIMULATED ANNEALING ALGORITHM SOLVING SEMI-SUPERVISED LINEAR SVMS PROBLEMS

Vaida Bartkute-Norkuniene

2012

Abstract

In creating heuristic search algorithms one has to deal with the practical problem of terminating and optimality testing. To solve these problems, we can use information gained from the set of the best function values (order statistics) provided during optimization. In this paper, we consider the application of order statistics to establish the optimality in heuristic optimization algorithms and to stop the Simulated Annealing algorithm when the confidence interval of the minimum becomes less than admissible value. The accuracy of the solution achieved during optimization and the termination criterion of the algorithm are introduced in a statistical way. We build a method for the estimation of confidence intervals of the minimum using order statistics, which is implemented for optimality testing and terminating in Simulated Annealing algorithm. A termination criterion - length of the confidence interval of the extreme value of the objective function - is introduced. The efficiency of this approach is discussed using the results of computer modelling. One test function and two semi-supervised SVMs linear classification problems illustrate the applicability of the method proposed.

References

  1. Astorino, A., Fuduli, A., 2007. Nonsmooth Optimization Techniques for Semisupervised Classification. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 29, No. 12, p. 2135-2142.
  2. Asuncion, A., Newman, D. J., 2007. UCI Machine Learning Repository. School of Information and Computer Science, University of California, Irvine, CA. (http://www.ics.uci.edu/˜mlearn/ MLRepository. html)
  3. Bartkute, V., Sakalauskas, L., 2004. Order statistics for testing optimality in stochastic optimization. Proceedings of the 7th International Conference Computer data analysis and Modelling”, Minsk, p. 128-131
  4. Bartkute, V., Sakalauskas, L., 2009a. Statistical Inferences for Termination of Markov Type Random Search Algorithms. Journal of Optimization Theory and Applications, vol. 141, p. 475-493.
  5. Bartkute-Norkuniene V., 2009b. Stochastic Optimization Algorithms for Support Vector Machines Classification. Informatica, vol. 20, No. 2, p. 173-186.
  6. Bennett, K. P., Demiriz, A., 1999. Semi-supervised support vector machines. In M. S. Kearns, S. A. Solla, and D. A. Cohn, editors, NIPS, vol. 11, p. 368-374.
  7. Cortes, C., Vapnik, V., 1995. Support-vector networks. Machine Learning, vol. 20, No. 3, p. 273-297.
  8. Galambosh, Y., 1984. Asymptotic Theory of Extremal Order Statistics, Nauka, Moscow (in Russian).
  9. Granville, V., Krivanek, M., Rasson, J. P., 1994. Simulated annealing: a proof of convergence. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol 16, No. 6, p. 652-656.
  10. Hall, P., 1982. On estimating the endpoint of a distribution. Annals of Statistic, vol. 10, p. 556-568.
  11. Huang, T. M., Kecman, V., 2004. Semi-supervised Learning from Unbalanced Labeled Data - An Improvement, in 'Knowledge Based and Emergent Technologies Relied Intelligent Information and Engineering Systems', Eds. Negoita, M. Gh., at al., Lecture Notes on Computer Science, vol. 3215, p. 765-771.
  12. Mockus, J., 1967. Multi-Extremal Problems in Engineering Design. Nauka, Moscow, (in Russian).
  13. Yang, R. L., 2000. Convergence of the simulated annealing algorithm for continuous global optimization. Journal of Optimization Theory and Applications, vol. 104, No. 3, p. 691-716.
  14. Zilinskas, A., Zhigljavsky, A., 1991. Methods of the global extreme searching. Nauka, Moscow, (in Russian).
  15. Zilinskas, A., Zhigljavsky, A., 2007. Stochastic global optimization. Springer.
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Paper Citation


in Harvard Style

Bartkute-Norkuniene V. (2012). TERMINATION OF SIMULATED ANNEALING ALGORITHM SOLVING SEMI-SUPERVISED LINEAR SVMS PROBLEMS . In Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-8425-97-3, pages 150-156. DOI: 10.5220/0003759301500156


in Bibtex Style

@conference{icores12,
author={Vaida Bartkute-Norkuniene},
title={TERMINATION OF SIMULATED ANNEALING ALGORITHM SOLVING SEMI-SUPERVISED LINEAR SVMS PROBLEMS},
booktitle={Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2012},
pages={150-156},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003759301500156},
isbn={978-989-8425-97-3},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - TERMINATION OF SIMULATED ANNEALING ALGORITHM SOLVING SEMI-SUPERVISED LINEAR SVMS PROBLEMS
SN - 978-989-8425-97-3
AU - Bartkute-Norkuniene V.
PY - 2012
SP - 150
EP - 156
DO - 10.5220/0003759301500156