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Universal Alignment Probabilities and Subset Selection for Ordinal Optimization

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Abstract

We examine in this paper the subset selection procedure in the context of ordinal optimization introduced in Ref. 1. Major concepts including goal softening, selection subset, alignment probability, and ordered performance curve are formally introduced. A two-parameter model is devised to calculate alignment probabilities for a wide range of cases using two different selection rules: blind pick and horse race. Our major result includes the suggestion of quantifiable subset selection sizes which are universally applicable to many simulation and modeling problems, as demonstrated by the examples in this paper.

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References

  1. Ho, Y. C., Sreenivas, R. S., and Vakili, P., Ordinal Optimization in DEDS, Journal of Discrete Event Dynamic Systems, Vol. 2, pp. 61–68, 1992.

    Google Scholar 

  2. Ho, Y. C., Overview of Ordinal Optimization, Proceedings of the 33rd IEEE Conference on Decision and Control, Lake Buena Vista, Florida, pp. 1975–1977, 1994.

    Google Scholar 

  3. Ahlswede, R., Search Problems, Wiley, New York, New York, 1987.

    Google Scholar 

  4. Zhagljavsky, A. A., Theory of Global Random Search, Kluwer Academic Publishers, Dordrecht, Netherlands, 1991.

    Google Scholar 

  5. Ruml, W., Ngo, J. T., Marks, J., and Sheiber, S., Easily Searched Encodings for Number Partitioning, Journal of Optimization Theory and Applications, Vol. 89, pp. 251–291, 1996.

    Google Scholar 

  6. Deng, M., and Ho, Y. C., Sampling-Selection Method for Stochastic Optimization Problem, Preprint, 1996.

  7. Vakili, P., Mollamustaflaglu, L., and Ho, Y. C., Massively Parallel Simulation of a Class of Discrete Event Systems, Proceedings of the IEEE Frontiers MPC 1992 Symposium, Washington, DC, pp. 412–419, 1992.

  8. Patsis, N. T., Chen, C. H., and Larson, M. E., SIMD Parallel Discrete Event Dynamic System Simulation, IEEE Transactions on Control Systems Technology, Vol. 5, pp. 30–41, 1997.

    Google Scholar 

  9. Gupta, S. S., and Panchapakesan, S., Multiple Decision Procedures: Theory and Methodology of Selecting and Ranking Populations, Wiley, New York, New York, 1979.

    Google Scholar 

  10. Santner, T. J., and Tamhane, A. C., Design of Experiments: Ranking and Selection, Marcel Dekker, New York, New York, 1984.

    Google Scholar 

  11. Goldsman, D., and Nelson, B., Ranking, Selection, and Multiple Comparison in Computer Simulation, Proceedings of the 1994 Winter Simulation Conference, 1994.

  12. David, H. A., Order Statistics, 2nd Edition, Wiley, New York, New York, 1982.

    Google Scholar 

  13. Ho, Y. C., and Deng, M., The Problem of Large Search Space in Stochastic Optimization, Proceedings of the 1994 Conference in Decision and Control, pp. 1470–1475, 1994.

  14. Deng, M., Ho, Y. C., and Hu, J. Q., Effect of Correlated Estimation Errors in Ordinal Optimization, Proceedings of the 1992 Winter Simulation Conference, pp. 466–475, 1992.

  15. Pearson, K., Tables of the Incomplete Beta Function, 2nd Edition, Cambridge University Press, London, England, 1968.

    Google Scholar 

  16. Vakili, P., A Standard Clock Technique for Efficient Simulation, Operations Research Letters, Vol. 10, pp. 445–452, 1991.

    Google Scholar 

  17. Dai, L. Y., Convergence Properties of Ordinal Comparison in the Simulation of Discrete Event Dynamic Systems, Proceedings of the 34th IEEE Conference on Decision and Control, pp. 2604–2609, 1995.

  18. Dai, L. Y., The Effects of Correlation on Ordinal Comparison of Discrete Event Dynamic Systems, Unpublished Manuscript, 1995.

  19. Xie, X. L., Dynamics and Convergence Rate of Ordinal Comparison of Stochastic Discrete Event Systems, Unpublished Manuscript, 1995.

  20. Deng, M., Sampling-Selection and Space Narrowing Methods for Stochastic Optimization, PhD Thesis, Division of Engineering and Applied Sciences, Harvard University, 1995.

  21. Balakrishnan, N., and Cohen, A. C., Order Statistics and Inference, Academic Press, New York, New York, 1991.

    Google Scholar 

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Authors and Affiliations

  1. Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts

    T. W. Edward Lau

  2. Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts

    Y. C. Ho

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  1. T. W. Edward Lau
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  2. Y. C. Ho
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Lau, T.W.E., Ho, Y.C. Universal Alignment Probabilities and Subset Selection for Ordinal Optimization. Journal of Optimization Theory and Applications 93, 455–489 (1997). https://doi.org/10.1023/A:1022614327007

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