IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i11p1680-d1403892.html
   My bibliography  Save this article

Weight Vector Definition for MOEA/D-Based Algorithms Using Augmented Covering Arrays for Many-Objective Optimization

Author

Listed:
  • Carlos Cobos

    (Information Technology Research Group (GTI), Universidad del Cauca, Popayán 190001, Colombia)

  • Cristian Ordoñez

    (Intelligent Management Systems, Fundación Universitaria de Popayán, Popayán 190001, Colombia)

  • Jose Torres-Jimenez

    (CINVESTAV Tamaulipas, Ciudad Victoria 87130, Mexico)

  • Hugo Ordoñez

    (Information Technology Research Group (GTI), Universidad del Cauca, Popayán 190001, Colombia)

  • Martha Mendoza

    (Information Technology Research Group (GTI), Universidad del Cauca, Popayán 190001, Colombia)

Abstract

Many-objective optimization problems are today ever more common. The decomposition-based approach stands out among the evolutionary algorithms used for their solution, with MOEA/D and its variations playing significant roles. MOEA/D variations seek to improve weight vector definition, improve the dynamic adjustment of weight vectors during the evolution process, improve the evolutionary operators, use alternative decomposition methods, and hybridize with other metaheuristics, among others. Although an essential topic for the success of MOEA/D depends on how well the weight vectors are defined when decomposing the problem, not as much research has been performed on this topic as on the others. This paper proposes using a new mathematical object called augmented covering arrays (ACAs) that enable a better sampling of interactions of M objectives using the least number of weight vectors based on an interaction level (strength), defined a priori by the user. The proposed method obtains better results, measured in inverted generational distance, using small to medium populations (up to 850 solutions) of 30 to 100 objectives over DTLZ and WFG problems against the traditional weight vector definition used by MOEA/D-DE and results obtained by NSGA-III. Other MOEA/D variations can include the proposed approach and thus improve their results.

Suggested Citation

  • Carlos Cobos & Cristian Ordoñez & Jose Torres-Jimenez & Hugo Ordoñez & Martha Mendoza, 2024. "Weight Vector Definition for MOEA/D-Based Algorithms Using Augmented Covering Arrays for Many-Objective Optimization," Mathematics, MDPI, vol. 12(11), pages 1-39, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1680-:d:1403892
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/11/1680/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/11/1680/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Beume, Nicola & Naujoks, Boris & Emmerich, Michael, 2007. "SMS-EMOA: Multiobjective selection based on dominated hypervolume," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1653-1669, September.
    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. Liagkouras, Konstantinos & Metaxiotis, Konstantinos, 2021. "Improving multi-objective algorithms performance by emulating behaviors from the human social analogue in candidate solutions," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1019-1036.
    2. Gong, Wenyin & Cai, Zhihua, 2009. "An improved multiobjective differential evolution based on Pareto-adaptive [epsilon]-dominance and orthogonal design," European Journal of Operational Research, Elsevier, vol. 198(2), pages 576-601, October.
    3. Andrea Ponti & Antonio Candelieri & Ilaria Giordani & Francesco Archetti, 2023. "Intrusion Detection in Networks by Wasserstein Enabled Many-Objective Evolutionary Algorithms," Mathematics, MDPI, vol. 11(10), pages 1-14, May.
    4. David Quintana & Roman Denysiuk & Sandra García-Rodríguez & Antonio Gaspar-Cunha, 2017. "Portfolio implementation risk management using evolutionary multiobjective optimization," Post-Print hal-01881379, HAL.
    5. Yunsong Han & Hong Yu & Cheng Sun, 2017. "Simulation-Based Multiobjective Optimization of Timber-Glass Residential Buildings in Severe Cold Regions," Sustainability, MDPI, vol. 9(12), pages 1-18, December.
    6. Yeudiel Lara Moreno & Carlos Ignacio Hernández Castellanos, 2024. "A Hierarchical Approach to a Tri-Objective Portfolio Optimization Problem Considering an ESG Index," Mathematics, MDPI, vol. 12(19), pages 1-16, October.
    7. Laumanns, Marco & Zenklusen, Rico, 2011. "Stochastic convergence of random search methods to fixed size Pareto front approximations," European Journal of Operational Research, Elsevier, vol. 213(2), pages 414-421, September.
    8. Ivo Couckuyt & Dirk Deschrijver & Tom Dhaene, 2014. "Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization," Journal of Global Optimization, Springer, vol. 60(3), pages 575-594, November.
    9. 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.
    10. Hang Xu, 2024. "A Dynamic Tasking-Based Evolutionary Algorithm for Bi-Objective Feature Selection," Mathematics, MDPI, vol. 12(10), pages 1-23, May.
    11. Sergio Cabello, 2023. "Faster distance-based representative skyline and k-center along pareto front in the plane," Journal of Global Optimization, Springer, vol. 86(2), pages 441-466, June.
    12. Sven Schulz & Udo Buscher & Liji Shen, 2020. "Multi-objective hybrid flow shop scheduling with variable discrete production speed levels and time-of-use energy prices," Journal of Business Economics, Springer, vol. 90(9), pages 1315-1343, November.
    13. Lourdes Uribe & Johan M Bogoya & Andrés Vargas & Adriana Lara & Günter Rudolph & Oliver Schütze, 2020. "A Set Based Newton Method for the Averaged Hausdorff Distance for Multi-Objective Reference Set Problems," Mathematics, MDPI, vol. 8(10), pages 1-29, October.
    14. Houssem R. E. H. Bouchekara & Yusuf A. Sha’aban & Mohammad S. Shahriar & Makbul A. M. Ramli & Abdullahi A. Mas’ud, 2023. "Wind Farm Layout Optimization/Expansion with Real Wind Turbines Using a Multi-Objective EA Based on an Enhanced Inverted Generational Distance Metric Combined with the Two-Archive Algorithm 2," Sustainability, MDPI, vol. 15(3), pages 1-32, January.
    15. Yugong Dang & Hongen Ma & Jun Wang & Zhigang Zhou & Zhidong Xu, 2022. "An Improved Multi-Objective Optimization Decision Method Using NSGA-III for a Bivariate Precision Fertilizer Applicator," Agriculture, MDPI, vol. 12(9), pages 1-23, September.
    16. Álvaro Rubio-Largo & Miguel Vega-Rodríguez & David González-Álvarez, 2015. "Multiobjective swarm intelligence for the traffic grooming problem," Computational Optimization and Applications, Springer, vol. 60(2), pages 479-511, March.
    17. Taimoor Akhtar & Christine Shoemaker, 2016. "Multi objective optimization of computationally expensive multi-modal functions with RBF surrogates and multi-rule selection," Journal of Global Optimization, Springer, vol. 64(1), pages 17-32, January.
    18. Prashant Singh & Ivo Couckuyt & Khairy Elsayed & Dirk Deschrijver & Tom Dhaene, 2017. "Multi-objective Geometry Optimization of a Gas Cyclone Using Triple-Fidelity Co-Kriging Surrogate Models," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 172-193, October.
    19. Braun, Marlon & Shukla, Pradyumn, 2024. "On cone-based decompositions of proper Pareto-optimality in multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 317(2), pages 592-602.
    20. Jesús Martínez-Frutos & David Herrero-Pérez, 2016. "Kriging-based infill sampling criterion for constraint handling in multi-objective optimization," Journal of Global Optimization, Springer, vol. 64(1), pages 97-115, January.

    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:gam:jmathe:v:12:y:2024:i:11:p:1680-:d:1403892. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.