IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v156y2007i1p25-4410.1007-s10479-007-0232-y.html
   My bibliography  Save this article

Solving fractional problems with dynamic multistart improving hit-and-run

Author

Listed:
  • Mirjam Dür
  • Charoenchai Khompatraporn
  • Zelda Zabinsky

Abstract

Fractional programming has numerous applications in economy and engineering. While some fractional problems are easy in the sense that they are equivalent to an ordinary linear program, other problems like maximizing a sum or product of several ratios are known to be hard, as these functions are highly nonconvex and multimodal. In contrast to the standard Branch-and-Bound type algorithms proposed for specific types of fractional problems, we treat general fractional problems with stochastic algorithms developed for multimodal global optimization. Specifically, we propose Improving Hit-and-Run with restarts, based on a theoretical analysis of Multistart Pure Adaptive Search (cf. the dissertation of Khompatraporn ( 2004 )) which prescribes a way to utilize problem specific information to sample until a certain level α of confidence is achieved. For this purpose, we analyze the Lipschitz properties of fractional functions, and then utilize a unified method to solve general fractional problems. The paper ends with a report on numerical experiments. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Mirjam Dür & Charoenchai Khompatraporn & Zelda Zabinsky, 2007. "Solving fractional problems with dynamic multistart improving hit-and-run," Annals of Operations Research, Springer, vol. 156(1), pages 25-44, December.
    • Handle: RePEc:spr:annopr:v:156:y:2007:i:1:p:25-44:10.1007/s10479-007-0232-y
    DOI: 10.1007/s10479-007-0232-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-007-0232-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-007-0232-y?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. H. P. Benson, 2002. "Global Optimization Algorithm for the Nonlinear Sum of Ratios Problem," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 1-29, January.
    2. Robert L. Smith, 1984. "Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions," Operations Research, INFORMS, vol. 32(6), pages 1296-1308, December.
    3. Chadha, S. S., 2002. "Fractional programming with absolute-value functions," European Journal of Operational Research, Elsevier, vol. 141(1), pages 233-238, August.
    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. Luca Anzilli & Silvio Giove, 2020. "Multi-criteria and medical diagnosis for application to health insurance systems: a general approach through non-additive measures," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 559-582, December.
    2. Corrente, Salvatore & Figueira, José Rui & Greco, Salvatore, 2014. "The SMAA-PROMETHEE method," European Journal of Operational Research, Elsevier, vol. 239(2), pages 514-522.
    3. Stephen Baumert & Archis Ghate & Seksan Kiatsupaibul & Yanfang Shen & Robert L. Smith & Zelda B. Zabinsky, 2009. "Discrete Hit-and-Run for Sampling Points from Arbitrary Distributions Over Subsets of Integer Hyperrectangles," Operations Research, INFORMS, vol. 57(3), pages 727-739, June.
    4. Luca Consolini & Marco Locatelli & Jiulin Wang & Yong Xia, 2020. "Efficient local search procedures for quadratic fractional programming problems," Computational Optimization and Applications, Springer, vol. 76(1), pages 201-232, May.
    5. Hazan, Aurélien, 2017. "Volume of the steady-state space of financial flows in a monetary stock-flow-consistent model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 589-602.
    6. Dimitris Bertsimas & Allison O'Hair, 2013. "Learning Preferences Under Noise and Loss Aversion: An Optimization Approach," Operations Research, INFORMS, vol. 61(5), pages 1190-1199, October.
    7. Qi Fan & Jiaqiao Hu, 2018. "Surrogate-Based Promising Area Search for Lipschitz Continuous Simulation Optimization," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 677-693, November.
    8. Reuven Rubinstein, 2009. "The Gibbs Cloner for Combinatorial Optimization, Counting and Sampling," Methodology and Computing in Applied Probability, Springer, vol. 11(4), pages 491-549, December.
    9. Jing Voon Chen & Julia L. Higle & Michael Hintlian, 2018. "A systematic approach for examining the impact of calibration uncertainty in disease modeling," Computational Management Science, Springer, vol. 15(3), pages 541-561, October.
    10. Luis V. Montiel & J. Eric Bickel, 2014. "A Generalized Sampling Approach for Multilinear Utility Functions Given Partial Preference Information," Decision Analysis, INFORMS, vol. 11(3), pages 147-170, September.
    11. Kiatsupaibul, Seksan & J. Hayter, Anthony & Liu, Wei, 2017. "Rank constrained distribution and moment computations," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 229-242.
    12. Pavel Shcherbakov & Mingyue Ding & Ming Yuchi, 2021. "Random Sampling Many-Dimensional Sets Arising in Control," Mathematics, MDPI, vol. 9(5), pages 1-16, March.
    13. Etienne de Klerk & Monique Laurent, 2018. "Comparison of Lasserre’s Measure-Based Bounds for Polynomial Optimization to Bounds Obtained by Simulated Annealing," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1317-1325, November.
    14. Cheng, Haiyan & Sandu, Adrian, 2009. "Efficient uncertainty quantification with the polynomial chaos method for stiff systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(11), pages 3278-3295.
    15. Sorawit Saengkyongam & Anthony Hayter & Seksan Kiatsupaibul & Wei Liu, 2020. "Efficient computation of the stochastic behavior of partial sum processes," Computational Statistics, Springer, vol. 35(1), pages 343-358, March.
    16. Arandarenko, Mihail & Corrente, Salvatore & Jandrić, Maja & Stamenković, Mladen, 2020. "Multiple criteria decision aiding as a prediction tool for migration potential of regions," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1154-1166.
    17. Cyril Bachelard & Apostolos Chalkis & Vissarion Fisikopoulos & Elias Tsigaridas, 2023. "Randomized geometric tools for anomaly detection in stock markets," Post-Print hal-04223511, HAL.
    18. Ru, Zice & Liu, Jiapeng & Kadziński, Miłosz & Liao, Xiuwu, 2023. "Probabilistic ordinal regression methods for multiple criteria sorting admitting certain and uncertain preferences," European Journal of Operational Research, Elsevier, vol. 311(2), pages 596-616.
    19. Jan Heufer, 2014. "Generating Random Optimising Choices," Computational Economics, Springer;Society for Computational Economics, vol. 44(3), pages 295-305, October.
    20. Zdravko I. Botev & Pierre L'Ecuyer & Gerardo Rubino & Richard Simard & Bruno Tuffin, 2013. "Static Network Reliability Estimation via Generalized Splitting," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 56-71, February.

    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:annopr:v:156:y:2007:i:1:p:25-44:10.1007/s10479-007-0232-y. 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.