IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v222y2012i1p1-9.html
   My bibliography  Save this article

Local search based heuristics for global optimization: Atomic clusters and beyond

Author

Listed:
  • Locatelli, Marco
  • Schoen, Fabio

Abstract

Finding good solutions to large scale, hard, global optimization problems, is a demanding task with many relevant applications. It is well known that, in order to tackle a difficult problem, an algorithm has to incorporate all of the available information on the problem domain. However, as we will show in this paper, some general purpose methods and the ideas on which they are built can provide guidance towards the efficient solution of difficult instances. Most of this paper will be devoted to heuristic techniques applied to the problem of finding a minimum energy configuration of a cluster of atoms in R3. This is a very relevant problem with a large set of applications which has triggered considerable research efforts in the last decade. We will show how some relatively simple ideas can be used to generate fairly efficient methods which have been employed to discover many new cluster structures. In this paper we will introduce some of the main algorithmic ideas which have proven to be particularly successful in the field of global optimization applied to atomic cluster conformation problems. We will mainly discuss Basin Hopping methods, as well as their population–based variant, and some specific technique based on “direct moves”. These methods, although designed for the specific problem, have a much wider applicability. In fact, one of the aims of this paper is also that of suggesting that similar ideas can be employed in order to design innovative methods even for totally different global optimization problems, like, e.g., circle packing and space trajectory planning.

Suggested Citation

  • Locatelli, Marco & Schoen, Fabio, 2012. "Local search based heuristics for global optimization: Atomic clusters and beyond," European Journal of Operational Research, Elsevier, vol. 222(1), pages 1-9.
  • Handle: RePEc:eee:ejores:v:222:y:2012:i:1:p:1-9
    DOI: 10.1016/j.ejor.2012.04.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037722171200286X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2012.04.010?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. Bernardetta Addis & Andrea Cassioli & Marco Locatelli & Fabio Schoen, 2011. "A global optimization method for the design of space trajectories," Computational Optimization and Applications, Springer, vol. 48(3), pages 635-652, April.
    2. A. Cassioli & D. Di Lorenzo & M. Locatelli & F. Schoen & M. Sciandrone, 2012. "Machine learning for global optimization," Computational Optimization and Applications, Springer, vol. 51(1), pages 279-303, January.
    3. Nuno Lourenço & Francisco Baptista Pereira, 2011. "PSO-CGO: A Particle Swarm Algorithm for Cluster Geometry Optimization," International Journal of Natural Computing Research (IJNCR), IGI Global, vol. 2(1), pages 1-20, January.
    4. B. Addis & M. Locatelli & F. Schoen, 2008. "Disk Packing in a Square: A New Global Optimization Approach," INFORMS Journal on Computing, INFORMS, vol. 20(4), pages 516-524, November.
    5. Jonathan P. K. Doye & Robert H. Leary & Marco Locatelli & Fabio Schoen, 2004. "Global Optimization of Morse Clusters by Potential Energy Transformations," INFORMS Journal on Computing, INFORMS, vol. 16(4), pages 371-379, November.
    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. Qunfeng Liu, 2013. "Linear scaling and the DIRECT algorithm," Journal of Global Optimization, Springer, vol. 56(3), pages 1233-1245, July.
    2. Javier Cano & Cesar Alfaro & Javier Gomez & Abraham Duarte, 2022. "Out of the Niche: Using Direct Search Methods to Find Multiple Global Optima," Mathematics, MDPI, vol. 10(9), pages 1-20, 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. Marco Locatelli & Fabio Schoen, 2016. "Global optimization based on local searches," Annals of Operations Research, Springer, vol. 240(1), pages 251-270, May.
    2. Lai, Xiangjing & Hao, Jin-Kao & Yue, Dong & Lü, Zhipeng & Fu, Zhang-Hua, 2022. "Iterated dynamic thresholding search for packing equal circles into a circular container," European Journal of Operational Research, Elsevier, vol. 299(1), pages 137-153.
    3. Xiangjing Lai & Jin-Kao Hao & Renbin Xiao & Fred Glover, 2023. "Perturbation-Based Thresholding Search for Packing Equal Circles and Spheres," INFORMS Journal on Computing, INFORMS, vol. 35(4), pages 725-746, July.
    4. Marco Baioletti & Valentino Santucci & Marco Tomassini, 2024. "A performance analysis of Basin hopping compared to established metaheuristics for global optimization," Journal of Global Optimization, Springer, vol. 89(3), pages 803-832, July.
    5. Xiangyang Huang & LiGuo Huang, 2023. "Spreading Points Using Gradient and Tabu," SN Operations Research Forum, Springer, vol. 4(2), pages 1-11, June.
    6. Huang, Wenqi & Ye, Tao, 2011. "Global optimization method for finding dense packings of equal circles in a circle," European Journal of Operational Research, Elsevier, vol. 210(3), pages 474-481, May.
    7. Pedro Duarte Silva, A., 2017. "Optimization approaches to Supervised Classification," European Journal of Operational Research, Elsevier, vol. 261(2), pages 772-788.
    8. Piotr Łukasiak & Jacek Błażewicz & Maciej Miłostan, 2010. "Some operations research methods for analyzing protein sequences and structures," Annals of Operations Research, Springer, vol. 175(1), pages 9-35, March.
    9. Fu, Zhanghua & Huang, Wenqi & Lü, Zhipeng, 2013. "Iterated tabu search for the circular open dimension problem," European Journal of Operational Research, Elsevier, vol. 225(2), pages 236-243.
    10. Dellepiane, Umberto & Palagi, Laura, 2015. "Using SVM to combine global heuristics for the Standard Quadratic Problem," European Journal of Operational Research, Elsevier, vol. 241(3), pages 596-605.
    11. Bernardetta Addis & Andrea Cassioli & Marco Locatelli & Fabio Schoen, 2011. "A global optimization method for the design of space trajectories," Computational Optimization and Applications, Springer, vol. 48(3), pages 635-652, April.
    12. János Pintér & Frank Kampas, 2013. "Benchmarking nonlinear optimization software in technical computing environments," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 133-162, April.
    13. F. Lampariello & G. Liuzzi, 2015. "A filling function method for unconstrained global optimization," Computational Optimization and Applications, Springer, vol. 61(3), pages 713-729, July.
    14. Hu, Xiaoxuan & Zhu, Waiming & Ma, Huawei & An, Bo & Zhi, Yanling & Wu, Yi, 2021. "Orientational variable-length strip covering problem: A branch-and-price-based algorithm," European Journal of Operational Research, Elsevier, vol. 289(1), pages 254-269.
    15. Zeng, Zhizhong & Yu, Xinguo & He, Kun & Huang, Wenqi & Fu, Zhanghua, 2016. "Iterated Tabu Search and Variable Neighborhood Descent for packing unequal circles into a circular container," European Journal of Operational Research, Elsevier, vol. 250(2), pages 615-627.
    16. B. Addis & M. Locatelli & F. Schoen, 2008. "Disk Packing in a Square: A New Global Optimization Approach," INFORMS Journal on Computing, INFORMS, vol. 20(4), pages 516-524, November.
    17. Ralf Borndörfer & Fabian Danecker & Martin Weiser, 2023. "Newton’s Method for Global Free Flight Trajectory Optimization," SN Operations Research Forum, Springer, vol. 4(3), pages 1-41, September.
    18. António Leitão & Francisco Pereira & Penousal Machado, 2015. "Island models for cluster geometry optimization: how design options impact effectiveness and diversity," Journal of Global Optimization, Springer, vol. 63(4), pages 677-707, December.
    19. Obuchowska, Wiesława T., 2012. "Feasibility in reverse convex mixed-integer programming," European Journal of Operational Research, Elsevier, vol. 218(1), pages 58-67.
    20. A. Grosso & A. Jamali & M. Locatelli & F. Schoen, 2010. "Solving the problem of packing equal and unequal circles in a circular container," Journal of Global Optimization, Springer, vol. 47(1), pages 63-81, May.

    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:eee:ejores:v:222:y:2012:i:1:p:1-9. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.