Reproduction Operator Sensitivity in MOEA/D under Tchebycheff Decomposition: An Empirical Study on Regular and Irregular Pareto Fronts
Resumo
This paper presents a controlled empirical study on the sensitivity of MOEA/D to reproduction operators under fixed Tchebycheff decomposition. Eight operator variants were evaluated in PlatEMO 4.15 on DTLZ and IDTLZ benchmark instances with regular and irregular Pareto fronts, two to five objectives, and different decision-space dimensions. The study does not propose a new algorithm; instead, it isolates the effect of replacing the reproduction mechanism while preserving the same decomposition scheme. Each configuration was executed 30 times independently and compared with the baseline MOEA/D using IGD and a Wilcoxon signed-rank test. The evidence indicates scenario-dependent behavior: ABC and simulated annealing show the strongest aggregated profile on regular many-objective fronts (9 wins, 4 losses, 3 ties each; IGD ratio r = 0.90), MMOPSO shows favorable aggregated IGD ratios on irregular fronts (r = 0.64–0.95), despite limited statistical wins, and NMS degrades performance in nearly every configuration (0–1 wins across all scenario groups). The results support operator selection based on scenario and motivate adaptive mechanisms conditioned on the Pareto-front geometry.
Referências
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Zhang, Q. and Li, H. (2007). MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation, 11(6).
Zhong, Y. B., Xiang, Y., and Liu, H. L. (2014). A multi-objective artificial bee colony algorithm based on division of the searching space. Applied Intelligence, 41(4):987–1011.
Zhou, A., Gao, F., and Zhang, G. (2015). A decomposition based estimation of distribution algorithm for multiobjective traveling salesman problems. Computers & Mathematics with Applications, 70(12):3132–3149.
Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society: Series B, 57(1):289–300.
BIMK Group (2026). PlatEMO release notes: Release highlights of PlatEMO 4.15. [link]. Accessed in 2026.
Deb, K., Thiele, L., Laumanns, M., and Zitzler, E. (2005). Scalable test problems for evolutionary multi-objective optimization. In Evolutionary Multiobjective Optimization: Theoretical Advances and Applications, pages 105–145. Springer.
Dorigo, M., Maniezzo, V., and Colorni, A. (1996). Ant system: optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics, Part B, 26(1):29–41.
Hansen, N. and Ostermeier, A. (2001). Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation, 9(2):159–195.
Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6(2):65–70.
Karaboga, D. and Basturk, B. (2007). A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. Journal of Global Optimization, 39(3):459–471.
Ke, L., Zhang, Q., and Battiti, R. (2013). MOEA/D-ACO: A multiobjective evolutionary algorithm using decomposition and ant colony. IEEE Transactions on Cybernetics, 43(6):1845–1859.
Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220(4598):671–680.
Li, H. and Landa-Silva, D. (2011). An adaptive evolutionary multi-objective approach based on simulated annealing. Evolutionary Computation, 19(4):561–595.
Li, H. and Zhang, Q. (2009). Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II. IEEE Transactions on Evolutionary Computation, 13(2):284–302.
Li, K. (2024). A survey of multi-objective evolutionary algorithm based on decomposition: Past and future. IEEE Transactions on Evolutionary Computation, pages 1–1.
Li, K., Fialho, Á., Kwong, S., and Zhang, Q. (2014). Adaptive operator selection with bandits for a multi-objective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation, 18(1):114–130.
Lin, Q., Li, J., Du, Z., Chen, J., and Ming, Z. (2015). A novel multi-objective particle swarm optimization with multiple search strategies. European Journal of Operational Research, 247(3):732–744.
Nelder, J. A. and Mead, R. (1965). A simplex method for function minimization. The Computer Journal, 7(4):308–313.
Storn, R. and Price, K. (1997). Differential evolution: A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11(4):341–359.
Tian, Y., Cheng, R., Zhang, X., and Jin, Y. (2017). PlatEMO: A MATLAB platform for evolutionary multi-objective optimization. IEEE Computational Intelligence Magazine, 12(4):73–87.
Van Veldhuizen, D. A. and Lamont, G. B. (1998). Evolutionary computation and convergence to a Pareto front. In Late Breaking Papers at the Genetic Programming 1998 Conference, pages 221–228.
Wang, R., Zhang, Q., and Zhang, T. (2015). Pareto adaptive scalarising functions for decomposition based algorithms. In Evolutionary Multi-Criterion Optimization, pages 248–262.
Wang, W., Yang, S., Lin, Q., Coello, C. A. C., Zhang, Q., Wong, K.-S., and Chen, J. (2019). An effective ensemble framework for multiobjective optimization. IEEE Transactions on Cybernetics, 49(3):1120–1133.
Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6):80–83.
Zapotecas-Martínez, S., Derbel, B., Liefooghe, A., Brockhoff, D., Aguirre, H. E., and Tanaka, K. (2015). Injecting CMA-ES into MOEA/D. In Proceedings of the Genetic and Evolutionary Computation Conference, pages 783–790.
Zhang, H., Zhou, A., Zhang, G., and Singh, H. K. (2017). Accelerating MOEA/D by Nelder-Mead method. In 2017 IEEE Congress on Evolutionary Computation (CEC), pages 976–983.
Zhang, Q. and Li, H. (2007). MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation, 11(6).
Zhong, Y. B., Xiang, Y., and Liu, H. L. (2014). A multi-objective artificial bee colony algorithm based on division of the searching space. Applied Intelligence, 41(4):987–1011.
Zhou, A., Gao, F., and Zhang, G. (2015). A decomposition based estimation of distribution algorithm for multiobjective traveling salesman problems. Computers & Mathematics with Applications, 70(12):3132–3149.
Publicado
19/10/2026
Como Citar
LOPES, Isabela Medeiros Belo; FARIAS, Lucas Rodolfo Celestino.
Reproduction Operator Sensitivity in MOEA/D under Tchebycheff Decomposition: An Empirical Study on Regular and Irregular Pareto Fronts. In: ENCONTRO NACIONAL DE INTELIGÊNCIA ARTIFICIAL E COMPUTACIONAL (ENIAC), 23. , 2026, Cuiabá/MT.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2026
.
p. 3710-3720.
ISSN 2763-9061.
DOI: https://doi.org/10.5753/eniac.2026.31545.
