IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v195y2022i2d10.1007_s10957-022-02097-w.html
   My bibliography  Save this article

Pure Random Search with Virtual Extension of Feasible Region

Author

Listed:
  • E. A. Tsvetkov

    (Lebedev Physical Institute of the Russian Academy of Sciences)

  • R. A. Krymov

    (Moscow Institute of Physics and Technology)

Abstract

We propose a modification of the pure random search algorithm for cases when the global optimum point can be located near the boundary of a feasible region. If the feasible region is cube-shaped, the worst case occurs when the global optimum point is located at the vertex of a cube. In these cases, the sample size for the pure random search should be increased significantly because the success probability of the single trial is decreased. The proposed modification is based on the virtual extension of the feasible region. The extended region contains $$\varepsilon $$ ε -neighbourhoods of all points of the original region. All random points that fall outside the original feasible region are mapped to the nearest points on its boundary before the values of an objective function at these points are calculated. This extension of the feasible region also leads to an increase in the sample size due to the increased volume. We compare sample sizes required to hit into the neighbourhood of the global optimum point with a given probability for the proposed method and the original pure random search algorithm with a corrected sample size. We consider ball-shaped and cube-shaped feasible regions and find the sufficient conditions for the proposed algorithm to be more efficient. We offer a practical recommendation for cases, in which the feasible region is defined by a system of linear inequalities.

Suggested Citation

  • E. A. Tsvetkov & R. A. Krymov, 2022. "Pure Random Search with Virtual Extension of Feasible Region," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 575-595, November.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:2:d:10.1007_s10957-022-02097-w
    DOI: 10.1007/s10957-022-02097-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-022-02097-w
    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/s10957-022-02097-w?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. Samuel H. Brooks, 1958. "A Discussion of Random Methods for Seeking Maxima," Operations Research, INFORMS, vol. 6(2), pages 244-251, April.
    2. Francisco J. Solis & Roger J.-B. Wets, 1981. "Minimization by Random Search Techniques," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 19-30, February.
    3. Donald R. Jones & Joaquim R. R. A. Martins, 2021. "The DIRECT algorithm: 25 years Later," Journal of Global Optimization, Springer, vol. 79(3), pages 521-566, March.
    4. Boris Polyak & Pavel Shcherbakov, 2017. "Why Does Monte Carlo Fail to Work Properly in High-Dimensional Optimization Problems?," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 612-627, May.
    Full references (including those not matched with items on IDEAS)

    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. Giulia Pedrielli & K. Selcuk Candan & Xilun Chen & Logan Mathesen & Alireza Inanalouganji & Jie Xu & Chun-Hung Chen & Loo Hay Lee, 2019. "Generalized Ordinal Learning Framework (GOLF) for Decision Making with Future Simulated Data," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(06), pages 1-35, December.
    2. Rinnooy Kan, A. H. G. & Timmer, G. T., 1985. "Stochastic Global Optimization Methods Part I: Clustering Methods," Econometric Institute Archives 272329, Erasmus University Rotterdam.
    3. Taymaz, Erol, 1993. "A Calibration Algorithm for Micro-Simulation Models," Working Paper Series 374, Research Institute of Industrial Economics.
    4. D. Bulger & W. P. Baritompa & G. R. Wood, 2003. "Implementing Pure Adaptive Search with Grover's Quantum Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 517-529, March.
    5. Prietula, Michael J. & Watson, Harry S., 2008. "When behavior matters: Games and computation in A Behavioral Theory of the Firm," Journal of Economic Behavior & Organization, Elsevier, vol. 66(1), pages 74-94, April.
    6. Liu, Congzheng & Letchford, Adam N. & Svetunkov, Ivan, 2022. "Newsvendor problems: An integrated method for estimation and optimisation," European Journal of Operational Research, Elsevier, vol. 300(2), pages 590-601.
    7. Pavel Shcherbakov & Mingyue Ding & Ming Yuchi, 2021. "Random Sampling Many-Dimensional Sets Arising in Control," Mathematics, MDPI, vol. 9(5), pages 1-16, March.
    8. Mojtaba Akbari & Saber Molla-Alizadeh-Zavardehi & Sadegh Niroomand, 2020. "Meta-heuristic approaches for fixed-charge solid transportation problem in two-stage supply chain network," Operational Research, Springer, vol. 20(1), pages 447-471, March.
    9. Pronzato, Luc & Walter, Eric & Venot, Alain & Lebruchec, Jean-Francois, 1984. "A general-purpose global optimizer: Implimentation and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 26(5), pages 412-422.
    10. Liu, Xueying & Fu, Meiling, 2015. "Cuckoo search algorithm based on frog leaping local search and chaos theory," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1083-1092.
    11. Ran Etgar & Yuval Cohen, 2022. "Optimizing termination decision for meta-heuristic search techniques that converge to a static objective-value distribution," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(1), pages 249-271, March.
    12. Ricardo Navarro & Chyon Hae Kim, 2020. "Niching Multimodal Landscapes Faster Yet Effectively: VMO and HillVallEA Benefit Together," Mathematics, MDPI, vol. 8(5), pages 1-37, April.
    13. Martín Alejandro Valencia-Ponce & Esteban Tlelo-Cuautle & Luis Gerardo de la Fraga, 2021. "Estimating the Highest Time-Step in Numerical Methods to Enhance the Optimization of Chaotic Oscillators," Mathematics, MDPI, vol. 9(16), pages 1-15, August.
    14. Barkema, Alan Dean, 1985. "Farm survival under uncertainty," ISU General Staff Papers 1985010108000017535, Iowa State University, Department of Economics.
    15. Regis, Rommel G., 2010. "Convergence guarantees for generalized adaptive stochastic search methods for continuous global optimization," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1187-1202, December.
    16. 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.
    17. Xiong, Xiaoping & Qing, Guohua, 2023. "A hybrid day-ahead electricity price forecasting framework based on time series," Energy, Elsevier, vol. 264(C).
    18. Soumya D. Mohanty & Ethan Fahnestock, 2021. "Adaptive spline fitting with particle swarm optimization," Computational Statistics, Springer, vol. 36(1), pages 155-191, March.
    19. Riccardo Pellegrini & Andrea Serani & Giampaolo Liuzzi & Francesco Rinaldi & Stefano Lucidi & Matteo Diez, 2022. "A Derivative-Free Line-Search Algorithm for Simulation-Driven Design Optimization Using Multi-Fidelity Computations," Mathematics, MDPI, vol. 10(3), pages 1-13, February.
    20. Tvrdik, Josef & Krivy, Ivan & Misik, Ladislav, 2007. "Adaptive population-based search: Application to estimation of nonlinear regression parameters," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 713-724, October.

    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:joptap:v:195:y:2022:i:2:d:10.1007_s10957-022-02097-w. 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.