IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v8y2006i3d10.1007_s11009-006-9753-0.html
   My bibliography  Save this article

The Cross-Entropy Method for Continuous Multi-Extremal Optimization

Author

Listed:
  • Dirk P. Kroese

    (The University of Queensland)

  • Sergey Porotsky

    (Optimata Ltd.)

  • Reuven Y. Rubinstein

    (Technion)

Abstract

In recent years, the cross-entropy method has been successfully applied to a wide range of discrete optimization tasks. In this paper we consider the cross-entropy method in the context of continuous optimization. We demonstrate the effectiveness of the cross-entropy method for solving difficult continuous multi-extremal optimization problems, including those with non-linear constraints.

Suggested Citation

  • Dirk P. Kroese & Sergey Porotsky & Reuven Y. Rubinstein, 2006. "The Cross-Entropy Method for Continuous Multi-Extremal Optimization," Methodology and Computing in Applied Probability, Springer, vol. 8(3), pages 383-407, September.
    • Handle: RePEc:spr:metcap:v:8:y:2006:i:3:d:10.1007_s11009-006-9753-0
    DOI: 10.1007/s11009-006-9753-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-006-9753-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-006-9753-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. L. Margolin, 2005. "On the Convergence of the Cross-Entropy Method," Annals of Operations Research, Springer, vol. 134(1), pages 201-214, February.
    2. Reuven Rubinstein, 1999. "The Cross-Entropy Method for Combinatorial and Continuous Optimization," Methodology and Computing in Applied Probability, Springer, vol. 1(2), pages 127-190, September.
    3. Rubinstein, Reuven Y., 1997. "Optimization of computer simulation models with rare events," European Journal of Operational Research, Elsevier, vol. 99(1), pages 89-112, May.
    4. Pieter-Tjerk de Boer & Dirk Kroese & Shie Mannor & Reuven Rubinstein, 2005. "A Tutorial on the Cross-Entropy Method," Annals of Operations Research, Springer, vol. 134(1), pages 19-67, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Govindan, Kannan & Gholizadeh, Hadi, 2021. "Robust network design for sustainable-resilient reverse logistics network using big data: A case study of end-of-life vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 149(C).
    2. Tien Thanh Thach & Radim Bris, 2020. "Improved new modified Weibull distribution: A Bayes study using Hamiltonian Monte Carlo simulation," Journal of Risk and Reliability, , vol. 234(3), pages 496-511, June.
    3. Illana Bendavid & Boaz Golany, 2009. "Setting gates for activities in the stochastic project scheduling problem through the cross entropy methodology," Annals of Operations Research, Springer, vol. 172(1), pages 259-276, November.
    4. Heath, Jeffrey W. & Fu, Michael C. & Jank, Wolfgang, 2009. "New global optimization algorithms for model-based clustering," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3999-4017, October.
    5. Illana Bendavid & Boaz Golany, 2011. "Predetermined intervals for start times of activities in the stochastic project scheduling problem," Annals of Operations Research, Springer, vol. 186(1), pages 429-442, June.
    6. Le Cadre, Hélène & Mou, Yuting & Höschle, Hanspeter, 2022. "Parametrized Inexact-ADMM based coordination games: A normalized Nash equilibrium approach," European Journal of Operational Research, Elsevier, vol. 296(2), pages 696-716.
    7. Zdravko I. Botev & Dirk P. Kroese, 2008. "An Efficient Algorithm for Rare-event Probability Estimation, Combinatorial Optimization, and Counting," Methodology and Computing in Applied Probability, Springer, vol. 10(4), pages 471-505, December.
    8. Zheng Peng & Donghua Wu & Quan Zheng, 2013. "A Level-Value Estimation Method and Stochastic Implementation for Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 493-523, February.
    9. Illana Bendavid & Boaz Golany, 2011. "Setting gates for activities in the stochastic project scheduling problem through the cross entropy methodology," Annals of Operations Research, Springer, vol. 189(1), pages 25-42, September.
    10. Zheng Peng & Donghua Wu & Wenxing Zhu, 2016. "The robust constant and its applications in random global search for unconstrained global optimization," Journal of Global Optimization, Springer, vol. 64(3), pages 469-482, March.
    11. Charles Audet & Jean Bigeon & Romain Couderc, 2021. "Combining Cross-Entropy and MADS Methods for Inequality Constrained Global Optimization," SN Operations Research Forum, Springer, vol. 2(3), pages 1-26, September.
    12. Hao Su & Qun Niu & Zhile Yang, 2023. "Optimal Power Flow Using Improved Cross-Entropy Method," Energies, MDPI, vol. 16(14), pages 1-33, July.
    13. Satyajith Amaran & Nikolaos V. Sahinidis & Bikram Sharda & Scott J. Bury, 2016. "Simulation optimization: a review of algorithms and applications," Annals of Operations Research, Springer, vol. 240(1), pages 351-380, May.
    14. Caballero, Rafael & Hernández-Díaz, Alfredo G. & Laguna, Manuel & Molina, Julián, 2015. "Cross entropy for multiobjective combinatorial optimization problems with linear relaxations," European Journal of Operational Research, Elsevier, vol. 243(2), pages 362-368.
    15. Min Xie & Yuxin Du & Peijun Cheng & Wei Wei & Mingbo Liu, 2019. "A Cross-Entropy-Based Hybrid Membrane Computing Method for Power System Unit Commitment Problems," Energies, MDPI, vol. 12(3), pages 1-18, February.
    16. Ye, Chengjin & Ding, Yi & Song, Yonghua & Lin, Zhenzhi & Wang, Lei, 2018. "A data driven multi-state model for distribution system flexible planning utilizing hierarchical parallel computing," Applied Energy, Elsevier, vol. 232(C), pages 9-25.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nguyen, Hoa T.M. & Chow, Andy H.F. & Ying, Cheng-shuo, 2021. "Pareto routing and scheduling of dynamic urban rail transit services with multi-objective cross entropy method," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 156(C).
    2. Ali Eshragh & Jerzy Filar & Michael Haythorpe, 2011. "A hybrid simulation-optimization algorithm for the Hamiltonian cycle problem," Annals of Operations Research, Springer, vol. 189(1), pages 103-125, September.
    3. Mattrand, C. & Bourinet, J.-M., 2014. "The cross-entropy method for reliability assessment of cracked structures subjected to random Markovian loads," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 171-182.
    4. Hao Su & Qun Niu & Zhile Yang, 2023. "Optimal Power Flow Using Improved Cross-Entropy Method," Energies, MDPI, vol. 16(14), pages 1-33, July.
    5. Ferdinand Bollwein & Stephan Westphal, 2022. "Oblique decision tree induction by cross-entropy optimization based on the von Mises–Fisher distribution," Computational Statistics, Springer, vol. 37(5), pages 2203-2229, November.
    6. Jiaqiao Hu & Michael C. Fu & Steven I. Marcus, 2007. "A Model Reference Adaptive Search Method for Global Optimization," Operations Research, INFORMS, vol. 55(3), pages 549-568, June.
    7. K.-P. Hui & N. Bean & M. Kraetzl & Dirk Kroese, 2005. "The Cross-Entropy Method for Network Reliability Estimation," Annals of Operations Research, Springer, vol. 134(1), pages 101-118, February.
    8. Fahimnia, Behnam & Sarkis, Joseph & Eshragh, Ali, 2015. "A tradeoff model for green supply chain planning:A leanness-versus-greenness analysis," Omega, Elsevier, vol. 54(C), pages 173-190.
    9. Joshua C. C. Chan & Liana Jacobi & Dan Zhu, 2022. "An automated prior robustness analysis in Bayesian model comparison," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 583-602, April.
    10. Reuven Y. Rubinstein, 2006. "How Many Needles are in a Haystack, or How to Solve #P-Complete Counting Problems Fast," Methodology and Computing in Applied Probability, Springer, vol. 8(1), pages 5-51, March.
    11. Ad Ridder & Bruno Tuffin, 2012. "Probabilistic Bounded Relative Error Property for Learning Rare Event Simulation Techniques," Tinbergen Institute Discussion Papers 12-103/III, Tinbergen Institute.
    12. Tito Homem-de-Mello, 2007. "A Study on the Cross-Entropy Method for Rare-Event Probability Estimation," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 381-394, August.
    13. Ali Kadhem, Athraa & Abdul Wahab, Noor Izzri & Aris, Ishak & Jasni, Jasronita & Abdalla, Ahmed N., 2017. "Computational techniques for assessing the reliability and sustainability of electrical power systems: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 80(C), pages 1175-1186.
    14. Zheng Peng & Donghua Wu & Quan Zheng, 2013. "A Level-Value Estimation Method and Stochastic Implementation for Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 493-523, February.
    15. Qun Niu & Ming You & Zhile Yang & Yang Zhang, 2021. "Economic Emission Dispatch Considering Renewable Energy Resources—A Multi-Objective Cross Entropy Optimization Approach," Sustainability, MDPI, vol. 13(10), pages 1-33, May.
    16. J Morio & R Pastel, 2012. "Plug-in estimation of d-dimensional density minimum volume set of a rare event in a complex system," Journal of Risk and Reliability, , vol. 226(3), pages 337-345, June.
    17. Alibrandi, Umberto, 2014. "A response surface method for stochastic dynamic analysis," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 44-53.
    18. Tai-Yu Ma & Jean-Patrick Lebacque, 2012. "Dynamic System Optimal Routing In Multimodal Transit Network," Working Papers hal-00740347, HAL.
    19. Zheng Peng & Donghua Wu & Wenxing Zhu, 2016. "The robust constant and its applications in random global search for unconstrained global optimization," Journal of Global Optimization, Springer, vol. 64(3), pages 469-482, March.
    20. Agbeyegbe, Terence D., 2020. "Bayesian analysis of output gap in Barbados," Latin American Journal of Central Banking (previously Monetaria), Elsevier, vol. 1(1).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:8:y:2006:i:3:d:10.1007_s11009-006-9753-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.