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Estimating optimal stopping rules in the multiple best choice problem with minimal summarized rank via the cross-entropy method

Published: 18 May 2009 Publication History
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  • Abstract

    The best choice problem is an important class of the theory of optimal stopping rules. In this article, we present the Cross-Entropy method for solving the multiple best choice problem with the minimal expected ranks of selected objects. Computational results showed that the Cross-Entropy method is producing high-quality solution.

    References

    [1]
    M. Adel El-Baz, "A genetic algorithm for facility layout problems of different manufacturing environments", Comp.and ind.engin., vol. 47, pp. 233-246, 2004.
    [2]
    F.t. Bruss, T.S. Ferguson, "Minimizing the expected rank with full information", J. Appl. Prob., vol.30, pp. 616-626, 1993.
    [3]
    Y. S. Chow, H. Robbins, D. Siegmund, Great Expectations: The Theory of Optimal Stopping, Boston: Houghton Mifflin, 1971.
    [4]
    Y.S. Chow, S. Moriguti, H. Robbins, S.M. Samuels, "Optimal selection based on relative rank", Israel J. Math., vol.2, pp. 81-90, 1964.
    [5]
    E. B. Dynkin, A. A. Yushkevich, Theorems and Problems on Markov Processes, New York: Plenum, 1969.
    [6]
    C.P. Gabor, T.R. Halliday, "Sequential mate choice by multiply mating smooth newts: females become more choosy", Behavioral Ecology, vol. 8, pp 162-166, 1997.
    [7]
    J. P. Gilbert, F. Mosteller, "Recognizing the maximum of sequence," J. Am. Stat. Assoc., vol. 61, pp. 35-73, 1966.
    [8]
    J. Cianini-Pettitt, "Optimal selection based on relative ranks with a random number of individuals," Adv. Appl. Prob., vol. 11, pp. 720-736, 1979.
    [9]
    M. L. Nikolaev, "On a generalization of the best choice problem", Theory Prob. Appl., vol. 22, pp. 187-190, 1977.
    [10]
    M. L. Nikolaev, "Optimal multi-stopping rules", Obozr. Prikl. Prom. Mat., vol. 5, pp. 309-348, 1998.
    [11]
    T.E. Pitcher, B.D. Neff, F.H. Rodd, L. Rowe L., "Multiple mating and sequential mate choice in guppies: females trade up", Proceedings of the Royal Society B: Biological Sciences, vol. 270, pp. 1623-1629, 2003.
    [12]
    R. Y. Rubinstein, D. P. Kroese, The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning, New York: Springer-Verlag, 2004.
    [13]
    A. N. Shiryaev, Optimal Stopping Rules, New York: Springer-Verlag, 1978.
    [14]
    G. Yu. Sofronov, D.P. Kroese, J.M. Keith, M.L. Nikolaev, "Simulation of thresholds in the multiple best choice problem", Obozr. Prikl. Prom. Math., vol. 13, pp. 975-983, 2006.
    [15]
    M. Tamaki, "Minimal expected ranks for the secretary problems with uncertain selection", Lecture Notes-Monograph Series, Institute of Mathematical Statistics, vol. 35, pp. 127-139, 2000.
    [16]
    R. Wang, K. Okazaki, "Solving facility layout problem using an improved genetic algorithm", IEICE Trans.Fundam. E88-A, N 2, pp. 606-610, 2005.

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    cover image Guide Proceedings
    CEC'09: Proceedings of the Eleventh conference on Congress on Evolutionary Computation
    May 2009
    3356 pages
    ISBN:9781424429585

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    IEEE Press

    Publication History

    Published: 18 May 2009

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