IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v61y2015i3p713-729.html
   My bibliography  Save this article

A filling function method for unconstrained global optimization

Author

Listed:
  • F. Lampariello
  • G. Liuzzi

Abstract

We consider the problem of finding a global minimum point of a given continuously differentiable function. The strategy is adopted of a sequential nonmonotone improvement of local optima. In particular, to escape the basin of attraction of a local minimum, a suitable Gaussian-based filling function is constructed using the quadratic model (possibly approximated) of the objective function, and added to the objective to fill the basin. Then, a procedure is defined where some new minima are determined, and that of them with the lowest function value is selected as the subsequent restarting point, even if its basin is higher than the starting one. Moreover, a suitable device employing repeatedly the centroid of all the minima determined, is introduced in order to improve the efficiency of the method in the solution of difficult problems where the number of local minima is very high. The algorithm is applied to a set of test functions from the literature and the numerical results are reported along with those obtained by applying a standard Monotonic Basin Hopping method for comparison. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:61:y:2015:i:3:p:713-729
    DOI: 10.1007/s10589-015-9728-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-015-9728-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-015-9728-6?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. Giampaolo Liuzzi & Stefano Lucidi & Veronica Piccialli, 2010. "A partition-based global optimization algorithm," Journal of Global Optimization, Springer, vol. 48(1), pages 113-128, September.
    3. Hansen, Pierre & Mladenovic, Nenad, 2001. "Variable neighborhood search: Principles and applications," European Journal of Operational Research, Elsevier, vol. 130(3), pages 449-467, 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. Efrat Taig & Ohad Ben-Shahar, 2019. "Gradient Surfing: A New Deterministic Approach for Low-Dimensional Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 855-878, March.

    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. Maenhout, Broos & Vanhoucke, Mario, 2010. "A hybrid scatter search heuristic for personalized crew rostering in the airline industry," European Journal of Operational Research, Elsevier, vol. 206(1), pages 155-167, October.
    2. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2018. "Minimizing Piecewise-Concave Functions Over Polyhedra," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 580-597, May.
    3. Fernandez del Pozo, J. A. & Bielza, C. & Gomez, M., 2005. "A list-based compact representation for large decision tables management," European Journal of Operational Research, Elsevier, vol. 160(3), pages 638-662, February.
    4. Amina Lamghari & Roussos Dimitrakopoulos & Jacques Ferland, 2015. "A hybrid method based on linear programming and variable neighborhood descent for scheduling production in open-pit mines," Journal of Global Optimization, Springer, vol. 63(3), pages 555-582, November.
    5. J. Redondo & J. Fernández & I. García & P. Ortigosa, 2009. "A robust and efficient algorithm for planar competitive location problems," Annals of Operations Research, Springer, vol. 167(1), pages 87-105, March.
    6. Patricia Domínguez-Marín & Stefan Nickel & Pierre Hansen & Nenad Mladenović, 2005. "Heuristic Procedures for Solving the Discrete Ordered Median Problem," Annals of Operations Research, Springer, vol. 136(1), pages 145-173, April.
    7. Ali Shahabi & Sadigh Raissi & Kaveh Khalili-Damghani & Meysam Rafei, 2021. "Designing a resilient skip-stop schedule in rapid rail transit using a simulation-based optimization methodology," Operational Research, Springer, vol. 21(3), pages 1691-1721, September.
    8. Janssens, Jochen & Talarico, Luca & Sörensen, Kenneth, 2016. "A hybridised variable neighbourhood tabu search heuristic to increase security in a utility network," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 221-230.
    9. Wilson, Duncan T. & Hawe, Glenn I. & Coates, Graham & Crouch, Roger S., 2013. "A multi-objective combinatorial model of casualty processing in major incident response," European Journal of Operational Research, Elsevier, vol. 230(3), pages 643-655.
    10. 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.
    11. Felipe, Ángel & Ortuño, M. Teresa & Righini, Giovanni & Tirado, Gregorio, 2014. "A heuristic approach for the green vehicle routing problem with multiple technologies and partial recharges," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 71(C), pages 111-128.
    12. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
    13. Fathali, J. & Kakhki, H. Taghizadeh, 2006. "Solving the p-median problem with pos/neg weights by variable neighborhood search and some results for special cases," European Journal of Operational Research, Elsevier, vol. 170(2), pages 440-462, April.
    14. Tengkuo Zhu & Stephen D. Boyles & Avinash Unnikrishnan, 2024. "Battery Electric Vehicle Traveling Salesman Problem with Drone," Networks and Spatial Economics, Springer, vol. 24(1), pages 49-97, March.
    15. Martín Barragán, Belén, 2016. "A Partial parametric path algorithm for multiclass classification," DES - Working Papers. Statistics and Econometrics. WS 22390, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Véronique François & Yasemin Arda & Yves Crama, 2019. "Adaptive Large Neighborhood Search for Multitrip Vehicle Routing with Time Windows," Transportation Science, INFORMS, vol. 53(6), pages 1706-1730, November.
    17. Tino Henke & M. Grazia Speranza & Gerhard Wäscher, 2014. "The Multi-Compartment Vehicle Routing Problem with Flexible Compartment Sizes," FEMM Working Papers 140006, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    18. Timo Hintsch, 2019. "Large Multiple Neighborhood Search for the Soft-Clustered Vehicle-Routing Problem," Working Papers 1904, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    19. Olcay Polat & Can B. Kalayci & Özcan Mutlu & Surendra M. Gupta, 2016. "A two-phase variable neighbourhood search algorithm for assembly line worker assignment and balancing problem type-II: an industrial case study," International Journal of Production Research, Taylor & Francis Journals, vol. 54(3), pages 722-741, February.
    20. Janssens, Jochen & Van den Bergh, Joos & Sörensen, Kenneth & Cattrysse, Dirk, 2015. "Multi-objective microzone-based vehicle routing for courier companies: From tactical to operational planning," European Journal of Operational Research, Elsevier, vol. 242(1), pages 222-231.

    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:coopap:v:61:y:2015:i:3:p:713-729. 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.