IDEAS home Printed from https://ideas.repec.org/a/spr/joheur/v24y2018i2d10.1007_s10732-017-9361-x.html
   My bibliography  Save this article

Scaling-up many-objective combinatorial optimization with Cartesian products of scalarization functions

Author

Listed:
  • Mădălina M. Drugan

    (Vrije Universiteit Brussel)

Abstract

The trade-off between the exploration of large size neighborhoods and the exploitation of Pareto fronts with high cardinality is a challenging task for the metaheuristics for many-objective combinatorial optimization problems. Cartesian products of scalarization functions, or simpler, Cartesian scalarization, is a novel technique that simplifies the search by reducing the number of objectives using sets of scalarization functions. Cartesian scalarization is an alternative to scalarization functions that scales up the local search for many-objective spaces. We introduce a method that automatically generates Cartesian scalarization functions; we use combinatorics to analyze the properties of Cartesian scalarization functions. Cartesian scalarization local search (CsLs) uses a set of Cartesian scalarization functions to generate a quality Pareto local front. We show that CsLs is a well-defined local search algorithm that converges to a Pareto local solution set in finite time. Cartesian scalarization outperforms other Pareto and scalarization local search methods on many-objective combinatorial optimization instances.

Suggested Citation

  • Mădălina M. Drugan, 2018. "Scaling-up many-objective combinatorial optimization with Cartesian products of scalarization functions," Journal of Heuristics, Springer, vol. 24(2), pages 135-172, April.
    • Handle: RePEc:spr:joheur:v:24:y:2018:i:2:d:10.1007_s10732-017-9361-x
    DOI: 10.1007/s10732-017-9361-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10732-017-9361-x
    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/s10732-017-9361-x?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. Aguirre, Hernan E. & Tanaka, Kiyoshi, 2007. "Working principles, behavior, and performance of MOEAs on MNK-landscapes," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1670-1690, September.
    2. Paquete, Luis & Stutzle, Thomas, 2006. "A study of stochastic local search algorithms for the biobjective QAP with correlated flow matrices," European Journal of Operational Research, Elsevier, vol. 169(3), pages 943-959, March.
    3. Luis Paquete & Tommaso Schiavinotto & Thomas Stützle, 2007. "On local optima in multiobjective combinatorial optimization problems," Annals of Operations Research, Springer, vol. 156(1), pages 83-97, December.
    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. Andrzej Jaszkiewicz & Thibaut Lust, 2017. "Proper balance between search towards and along Pareto front: biobjective TSP case study," Annals of Operations Research, Springer, vol. 254(1), pages 111-130, July.
    2. Jaszkiewicz, Andrzej, 2018. "Many-Objective Pareto Local Search," European Journal of Operational Research, Elsevier, vol. 271(3), pages 1001-1013.
    3. Verel, Sébastien & Liefooghe, Arnaud & Jourdan, Laetitia & Dhaenens, Clarisse, 2013. "On the structure of multiobjective combinatorial search space: MNK-landscapes with correlated objectives," European Journal of Operational Research, Elsevier, vol. 227(2), pages 331-342.
    4. Aritra Pal & Hadi Charkhgard, 2019. "A Feasibility Pump and Local Search Based Heuristic for Bi-Objective Pure Integer Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 115-133, February.
    5. Madalina M. Drugan, 2019. "Random walk’s correlation function for multi-objective NK landscapes and quadratic assignment problem," Journal of Combinatorial Optimization, Springer, vol. 38(4), pages 1213-1262, November.
    6. Derbel, Bilel & Humeau, Jérémie & Liefooghe, Arnaud & Verel, Sébastien, 2014. "Distributed localized bi-objective search," European Journal of Operational Research, Elsevier, vol. 239(3), pages 731-743.
    7. Luis Paquete & Tommaso Schiavinotto & Thomas Stützle, 2007. "On local optima in multiobjective combinatorial optimization problems," Annals of Operations Research, Springer, vol. 156(1), pages 83-97, December.
    8. Dubois-Lacoste, Jérémie & López-Ibáñez, Manuel & Stützle, Thomas, 2015. "Anytime Pareto local search," European Journal of Operational Research, Elsevier, vol. 243(2), pages 369-385.
    9. Allmendinger, Richard & Handl, Julia & Knowles, Joshua, 2015. "Multiobjective optimization: When objectives exhibit non-uniform latencies," European Journal of Operational Research, Elsevier, vol. 243(2), pages 497-513.
    10. Diaz, Juan Esteban & López-Ibáñez, Manuel, 2021. "Incorporating decision-maker’s preferences into the automatic configuration of bi-objective optimisation algorithms," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1209-1222.
    11. Marcella S. R. Martins & Mohamed El Yafrani & Myriam Delgado & Ricardo Lüders & Roberto Santana & Hugo V. Siqueira & Huseyin G. Akcay & Belaïd Ahiod, 2021. "Analysis of Bayesian Network Learning Techniques for a Hybrid Multi-objective Bayesian Estimation of Distribution Algorithm: a case study on MNK Landscape," Journal of Heuristics, Springer, vol. 27(4), pages 549-573, August.
    12. Madalina M. Drugan, 2019. "Estimating the number of basins of attraction of multi-objective combinatorial problems," Journal of Combinatorial Optimization, Springer, vol. 37(4), pages 1367-1407, May.
    13. I. F. C. Fernandes & E. F. G. Goldbarg & S. M. D. M. Maia & M. C. Goldbarg, 2020. "Empirical study of exact algorithms for the multi-objective spanning tree," Computational Optimization and Applications, Springer, vol. 75(2), pages 561-605, March.
    14. Justus Bonz, 2021. "Application of a multi-objective multi traveling salesperson problem with time windows," Public Transport, Springer, vol. 13(1), pages 35-57, March.
    15. Martí, Rafael & Campos, Vicente & Resende, Mauricio G.C. & Duarte, Abraham, 2015. "Multiobjective GRASP with Path Relinking," European Journal of Operational Research, Elsevier, vol. 240(1), pages 54-71.

    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:joheur:v:24:y:2018:i:2:d:10.1007_s10732-017-9361-x. 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.