IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v60y2014i2p289-306.html
   My bibliography  Save this article

Finding multiple roots of a box-constrained system of nonlinear equations with a biased random-key genetic algorithm

Author

Listed:
  • Ricardo Silva
  • Mauricio Resende
  • Panos Pardalos

Abstract

Several numerical methods for solving nonlinear systems of equations assume that derivative information is available. Furthermore, these approaches usually do not consider the problem of finding all solutions to a nonlinear system. Rather, most methods output a single solution. In this paper, we address the problem of finding all roots of a system of equations. Our method makes use of a biased random-key genetic algorithm (BRKGA). Given a nonlinear system, we construct a corresponding optimization problem, which we solve multiple times, making use of a BRKGA, with areas of repulsion around roots that have already been found. The heuristic makes no use of derivative information. We illustrate the approach on seven nonlinear equations systems with multiple roots from the literature. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Ricardo Silva & Mauricio Resende & Panos Pardalos, 2014. "Finding multiple roots of a box-constrained system of nonlinear equations with a biased random-key genetic algorithm," Journal of Global Optimization, Springer, vol. 60(2), pages 289-306, October.
    • Handle: RePEc:spr:jglopt:v:60:y:2014:i:2:p:289-306
    DOI: 10.1007/s10898-013-0105-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-013-0105-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-013-0105-7?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. Hirsch, M.J. & Pardalos, P.M. & Resende, M.G.C., 2010. "Speeding up continuous GRASP," European Journal of Operational Research, Elsevier, vol. 205(3), pages 507-521, September.
    2. H.A. Oliveira, Jr. & A. Petraglia & L. Ingber & M.A.S. Machado & M.R. Petraglia, . "Stochastic global optimization and its applications with fuzzy adaptive simulated annealing," Lester Ingber Books, Lester Ingber, number 12a2.
    3. M. Ericsson & M.G.C. Resende & P.M. Pardalos, 2002. "A Genetic Algorithm for the Weight Setting Problem in OSPF Routing," Journal of Combinatorial Optimization, Springer, vol. 6(3), pages 299-333, September.
    4. L. Ingber, 2012. "Adaptive simulated annealing," Lester Ingber Papers 12as, Lester Ingber.
    5. James C. Bean, 1994. "Genetic Algorithms and Random Keys for Sequencing and Optimization," INFORMS Journal on Computing, INFORMS, vol. 6(2), pages 154-160, May.
    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. Alla Kammerdiner & Alexander Semenov & Eduardo L. Pasiliao, 2022. "Multidimensional Assignment Problem for Multipartite Entity Resolution," Journal of Global Optimization, Springer, vol. 84(2), pages 491-523, October.
    2. Jun Pei & Zorica Dražić & Milan Dražić & Nenad Mladenović & Panos M. Pardalos, 2019. "Continuous Variable Neighborhood Search (C-VNS) for Solving Systems of Nonlinear Equations," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 235-250, April.
    3. Gisela C V Ramadas & Ana Maria A C Rocha & Edite M G P Fernandes, 2015. "Testing Nelder-Mead Based Repulsion Algorithms for Multiple Roots of Nonlinear Systems via a Two-Level Factorial Design of Experiments," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-30, April.

    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. R. M. A. Silva & M. G. C. Resende & P. M. Pardalos, 2015. "A Python/C++ library for bound-constrained global optimization using a biased random-key genetic algorithm," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 710-728, October.
    2. Ayşegül Altın & Bernard Fortz & Mikkel Thorup & Hakan Ümit, 2013. "Intra-domain traffic engineering with shortest path routing protocols," Annals of Operations Research, Springer, vol. 204(1), pages 65-95, April.
    3. Andrade, Carlos E. & Toso, Rodrigo F. & Gonçalves, José F. & Resende, Mauricio G.C., 2021. "The Multi-Parent Biased Random-Key Genetic Algorithm with Implicit Path-Relinking and its real-world applications," European Journal of Operational Research, Elsevier, vol. 289(1), pages 17-30.
    4. Sha Lin & Xin-Jiang He, 2022. "Analytically Pricing European Options under a New Two-Factor Heston Model with Regime Switching," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 1069-1085, March.
    5. Gonçalves, José Fernando & Resende, Mauricio G.C., 2015. "A biased random-key genetic algorithm for the unequal area facility layout problem," European Journal of Operational Research, Elsevier, vol. 246(1), pages 86-107.
    6. José Fernando Gonçalves & Mauricio G. C. Resende, 2011. "A parallel multi-population genetic algorithm for a constrained two-dimensional orthogonal packing problem," Journal of Combinatorial Optimization, Springer, vol. 22(2), pages 180-201, August.
    7. Mauricio Resende, 2012. "Biased random-key genetic algorithms with applications in telecommunications," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 130-153, April.
    8. Hime Aguiar e Oliveira, 2022. "Deterministic sampling from uniform distributions with Sierpiński space-filling curves," Computational Statistics, Springer, vol. 37(1), pages 535-549, March.
    9. L. A. C. Roque & D. B. M. M. Fontes & F. A. C. C. Fontes, 2014. "A hybrid biased random key genetic algorithm approach for the unit commitment problem," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 140-166, July.
    10. Julliany S. Brandão & Thiago F. Noronha & Celso C. Ribeiro, 2016. "A biased random-key genetic algorithm to maximize the number of accepted lightpaths in WDM optical networks," Journal of Global Optimization, Springer, vol. 65(4), pages 813-835, August.
    11. Mohamed Abdel-Basset & Reda Mohamed & Nazeeruddin Mohammad & Karam Sallam & Nour Moustafa, 2021. "An Adaptive Cuckoo Search-Based Optimization Model for Addressing Cyber-Physical Security Problems," Mathematics, MDPI, vol. 9(10), pages 1-27, May.
    12. Xin‐Jiang He & Wenting Chen, 2021. "A semianalytical formula for European options under a hybrid Heston–Cox–Ingersoll–Ross model with regime switching," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(1), pages 343-352, January.
    13. Nazari-Heris, M. & Mohammadi-Ivatloo, B. & B. Gharehpetian, G., 2017. "Short-term scheduling of hydro-based power plants considering application of heuristic algorithms: A comprehensive review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 74(C), pages 116-129.
    14. Hiwa Golpira & Rafael R. Sola-Guirado, 2022. "Data-Driven Simulator: Redesign of Chickpea Harvester Reels," Agriculture, MDPI, vol. 12(2), pages 1-11, February.
    15. Paola Festa & Panos Pardalos, 2012. "Efficient solutions for the far from most string problem," Annals of Operations Research, Springer, vol. 196(1), pages 663-682, July.
    16. L. Ingber, 2017. "Quantum Path-Integral qPATHINT Algorithm," Lester Ingber Papers 17qa, Lester Ingber.
    17. John M. Abowd & Francis Kramarz & Sébastien Pérez-Duarte & Ian M. Schmutte, 2018. "Sorting Between and Within Industries: A Testable Model of Assortative Matching," Annals of Economics and Statistics, GENES, issue 129, pages 1-32.
    18. Vo Le & Kent Matthews & David Meenagh & Patrick Minford & Zhiguo Xiao, 2014. "Banking and the Macroeconomy in China: A Banking Crisis Deferred?," Open Economies Review, Springer, vol. 25(1), pages 123-161, February.
    19. Liu, Chunping & Minford, Patrick, 2014. "Comparing behavioural and rational expectations for the US post-war economy," Economic Modelling, Elsevier, vol. 43(C), pages 407-415.
    20. Ivorra, Benjamin & Mohammadi, Bijan & Manuel Ramos, Angel, 2015. "A multi-layer line search method to improve the initialization of optimization algorithms," European Journal of Operational Research, Elsevier, vol. 247(3), pages 711-720.

    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:jglopt:v:60:y:2014:i:2:p:289-306. 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.