Abstract
In the past several years, it has become apparent that the effectiveness of Pareto dominance-based multiobjective evolutionary algorithms degrades dramatically when solving many-objective optimization problems (MaOPs). Instead, research efforts have been driven toward developing evolutionary algorithms (EAs) that do not rely on Pareto dominance (e.g., decomposition-based techniques) to solve MaOPs. However, it is still a non-trivial issue for many existing non-Pareto-dominance-based EAs to deal with unknown irregular Pareto front shapes. In this paper, we develop the novel “(M-1)+1" framework of relaxed Pareto dominance to address MaOPs, which can simultaneously promote both convergence and diversity. To be specific, we apply M symmetrical cases of relaxed Pareto dominance during the environmental selection step, where each enhances the selection pressure of M-1 objectives by expanding the dominance area of solutions, while remaining unchanged for the one objective left out of that process. Experiments demonstrate that the proposed method is very competitive with or outperforms state-of-the-art methods on a variety of scalable test problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Deb, K., Jain, H.: An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans. Evol. Comput. 18(4), 577–601 (2014)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Ishibuchi, H., Setoguchi, Y., Masuda, H., Nojima, Y.: Performance of decomposition-based many-objective algorithms strongly depends on pareto front shapes. IEEE Trans. Evol. Comput. 21(2), 169–190 (2017)
Ishibuchi, H., Matsumoto, T., Masuyama, N., Nojima, Y.: Effects of dominance resistant solutions on the performance of evolutionary multi-objective and many-objective algorithms. In: Proceedings of Annual Conference on Genetic and Evolutionary Computation (GECCO), pp. 507–515 (2020)
Ishibuchi, H., Matsumoto, T., Masuyama, N., Nojima, Y.: Many-objective problems are not always difficult for pareto dominance-based evolutionary algorithms. In: Proceedings of 24th European Conference on Artificial Intelligence (ECAI) (2020)
K. Ikeda, H. Kita, S.K.: Failure of Pareto-based MOEAs: does non-dominated really mean near to optimal? In: Proceedings of the 2001 Congress on Evolutionary Computation, vol. 2, pp. 957–962 (2001)
Li, K., Deb, K., Zhang, Q., Kwong, S.: An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans. Evol. Comput. 19(5), 694–716 (2015)
Lu, Z., Deb, K., Goodman, E., Banzhaf, W., Boddeti, V.N.: NSGANetV2: evolutionary multi-objective surrogate-assisted neural architecture search. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, J.-M. (eds.) ECCV 2020. LNCS, vol. 12346, pp. 35–51. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-58452-8_3
Lu, Z., Whalen, I., Dhebar, Y., Deb, K., Goodman, E., Banzhaf, W., Boddeti, V.N.: Multi-objective evolutionary design of deep convolutional neural networks for image classification. IEEE Trans. Evol. Comput. (2020). https://doi.org/10.1109/TEVC.2020.3024708
Santos, T., Takahashi, R.H.: On the performance degradation of dominance-based evolutionary algorithms in many-objective optimization. IEEE Trans. Evol. Comput. 22(1), 19–31 (2018)
Sato, H., Aguirre, H.E., Tanaka, K.: Self-controlling dominance area of solutions in evolutionary many-objective optimization. In: Deb, K., et al. (eds.) SEAL 2010. LNCS, vol. 6457, pp. 455–465. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17298-4_49
Sato, H., Aguirre, H.E., Tanaka, K.: Controlling dominance area of solutions and its impact on the performance of MOEAs. In: Proceedings of International Conference on Evolutionary Multi-Criterion Optimization (EMO 2007), pp. 5–20. ACM (2007)
Tian, Y., Cheng, R., Zhang, X., Jin, Y.: PlatEMO: a MATLAB platform for evolutionary multi-objective optimization [educational forum]. IEEE Comput. Intell. Mag. 12(4), 73–87 (2017)
Tian, Y., Cheng, R., Zhang, X., Su, Y., Jin, Y.: A strengthened dominance relation considering convergence and diversity for evolutionary many-objective optimization. IEEE Trans. Evol. Comput. 23(2), 331–345 (2019)
Yuan, Y., Xu, H., Wang, B., Yao, X.: A new dominance relation-based evolutionary algorithm for many-objective optimization. IEEE Trans. Evol. Comput. 20(1), 16–37 (2016)
Zhu, C., Xu, L., Goodman, E.D.: Generalization of Pareto-optimality for many-objective evolutionary optimization. IEEE Trans. Evol. Comput. 20(2), 299–315 (2016)
Acknowledgments
This work was supported by the Natural Science Foundation of China under Grant 61973337, the U.S. National Science Foundation’s BEACON Center, funded under Grant DBI-0939454.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Zhu, S., Xu, L., Goodman, E., Deb, K., Lu, Z. (2021). The (M-1)+1 Framework of Relaxed Pareto Dominance for Evolutionary Many-Objective Optimization. In: Ishibuchi, H., et al. Evolutionary Multi-Criterion Optimization. EMO 2021. Lecture Notes in Computer Science(), vol 12654. Springer, Cham. https://doi.org/10.1007/978-3-030-72062-9_28
Download citation
DOI: https://doi.org/10.1007/978-3-030-72062-9_28
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-72061-2
Online ISBN: 978-3-030-72062-9
eBook Packages: Computer ScienceComputer Science (R0)