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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
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    References listed on IDEAS

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    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.
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