Skip to main content
Log in

The Equivalence between Ordinal Optimization in Deterministic Complex Problems and in Stochastic Simulation Problems

  • Published:
Discrete Event Dynamic Systems Aims and scope Submit manuscript

Abstract

In the last decade ordinal optimization (OO) has been successfully applied in many stochastic simulation-based optimization problems (SP) and deterministic complex problems (DCP). Although the application of OO in the SP has been justified theoretically, the application in the DCP lacks similar analysis. In this paper, we show the equivalence between OO in the DCP and in the SP, which justifies the application of OO in the DCP.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Dai L (1996). Convergence properties of ordinal comparison in the simulation of discrete event dynamic system. J Optim Theory App 91:363–388.

    Article  MATH  Google Scholar 

  • Deng M, Ho YC, Hu JQ (1992). Effect of correlated estimation errors in ordinal optimization. In Swain JJ Goldsman D Crain RC Wilson JR (eds) Proceedings of the 1992 Winter Simulation Conference, pp. 466–474.

  • Fishman GS (1996). Monte Carlo: Concepts, Algorithms, and Applications. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Gentle JE (1998). Random Number Generation and Monte Carlo Methods. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

  • Guan X, Ho Y-C, Lai F (2001). An ordinal optimization based bidding strategy for electric power suppliers in the daily energy market. IEEE Trans Power Syst 16(4):788–797.

    Article  Google Scholar 

  • Ho YC (1999). An explanation of ordinal optimization: soft computing for hard problems. Inf Sci 113(3–4):169–192.

    Article  MATH  Google Scholar 

  • Ho YC, Sreenivas R, Vakili P (1992). Ordinal optimization of discrete event dynamic systems. Journal of Discrete Event Dynamic Systems 2(2):61–88.

    Article  MATH  Google Scholar 

  • Landau DP, Binder K (2000). A Guide to Monte Carlo Simulations in Statistical Physics. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Lau TWE, Ho YC (1997). Universal alignment probabilities and subset selection for ordinal optimization. J Optim Theory App 93(3):455–489.

    Article  MATH  MathSciNet  Google Scholar 

  • Lee LH, Lau TWE, Ho YC (1999). Explanation of goal softening in ordinal optimization. IEEE Trans Automat Contr 44(1):94–99.

    Article  MATH  MathSciNet  Google Scholar 

  • Li M, Vitányi P (1997). An Introduction to Kolmogorov Complexity and Its Applications, 2nd edition. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

  • Lin SY, Ho YC (2002). Universal alignment probability revisited. J Optim Theory App 113(2):399–407.

    Article  MATH  MathSciNet  Google Scholar 

  • Lin S-Y, Ho Y-C, Lin C-H (2004). An ordinal optimization theory-based algorithm for solving the optimal power flow problem with discrete control variables. IEEE Trans Power Syst 19(1):276–286.

    Article  Google Scholar 

  • Ordinal Optimization References List 2005. http://www.cfins.au.tsinghua.edu.cn/uploads/Resources/Complete _Ordinal_Optimization_Reference_List_v6.doc.

  • Xie X (1997). Dynamics and convergence rate of ordinal comparison of stochastic discrete-event system. IEEE Trans Automat Contr 42(4):586–590.

    Article  MATH  Google Scholar 

  • Yakowitz SJ (1977). Computational Probability and Simulation. Reading, Massachusetts: Addison-Wesley, Advanced Book Program.

    MATH  Google Scholar 

  • Yang MS (1998). Ordinal optimization and its application to complex deterministic problems. Ph.D. dissertation, Harvard University.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Qing-Shan Jia.

Additional information

Acknowledgment of Financial Support

This work was supported by ARO contract DAAD19-01-1-0610, AFOSR contract F49620-01-1-0288, NSF grant ECS-0323685, NSFC Grant No.60274011 and the NCET (No.NCET-04-0094) program of China.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ho, YC., Jia, QS. & Zhao, QC. The Equivalence between Ordinal Optimization in Deterministic Complex Problems and in Stochastic Simulation Problems. Discrete Event Dyn Syst 16, 405–411 (2006). https://doi.org/10.1007/s10626-006-9329-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10626-006-9329-8

Keywords

Navigation