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Modified non-dominated sorting genetic algorithm III with fine final level selection

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Abstract

Dominance resistance is a challenge for Pareto-based multi-objective evolutionary algorithms to solve the high-dimensional optimization problems. The Non-dominated Sorting Genetic Algorithm III (NSGA-III) still has such disadvantage even though it is recognized as an algorithm with good performance for many-objective problems. Thus, a variation of NSGA-III algorithm based on fine final level selection is proposed to improve convergence. The fine final level selection is designed in this way. The θ-dominance relation is used to sort the solutions in the critical layer firstly. Then ISDE index and favor convergence are employed to evaluate convergence of individuals for different situations. And some better solutions are selected finally. The effectiveness of our proposed algorithm is validated by comparing with nine state-of-the-art algorithms on the Deb-Thiele-Laumanns-Zitzler and Walking-Fish-Group test suits. And the optimization objectives are varying from 3 to 15. The performance is evaluated by the inverted generational distance (IGD), hypervolume (HV), generational distance (GD). The simulation results show that the proposed algorithm has an average improvement of 55.4%, 60.0%, 63.1% of 65 test instances for IGD, HV, GD indexes over the original NSGA-III algorithm. Besides, the proposed algorithm obtains the best performance by comparing 9 state-of-art algorithms in HV, GD indexes and ranks third for IGD indicator. Therefore, the proposed algorithm can achieve the advantages over the benchmarks.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China [Grant No.51774228].

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Authors and Affiliations

  1. School of Management, Xi’an University of Architecture and Technology, No. 13, middle yanta road, Xi’an, 710055, China

    Qinghua Gu, Rui Wang & Xuexian Li

  2. School of Resource Engineering, Xi’an University of Architecture and Technology, No. 13, middle yanta road, Xi’an, 710055, China

    Qinghua Gu, Song Jiang & Naixue Xiong

  3. Department of Technology, College of Applied Science and Technology, Illinois State University, Normal, IL, USA

    Haiyan Xie

  4. Department of Mathematics and Computer Science, Northeastern State University, Tahlequah, OK, USA

    Naixue Xiong

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  1. Qinghua Gu
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Correspondence to Qinghua Gu.

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Appendix 1

Appendix 1

Table 21 The CPU time consumed by hpaEA, RPD-NSGA-II, RVEA, θ-DEA, MOEA/D-DU, VaEA, 1by1EA, NSGA-III PDMOEAWS and NSGA-III-FS algorithms on DTLZ 1-DTLZ 4
Full size table
Table 22 The CPU time consumed by hpaEA, RPD-NSGA-II, RVEA, θ-DEA, MOEA/D-DU, VaEA, 1by1EA, NSGA-III PDMOEAWS and NSGA-III-FS algorithms on WFG 1-WFG 5
Full size table
Table 23 The CPU time consumed by hpaEA, RPD-NSGA-II, RVEA, θ-DEA, MOEA/D-DU, VaEA, 1by1EA, NSGA-III PDMOEAWS and NSGA-III-FS algorithms on WFG 6-WFG 9
Full size table

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Gu, Q., Wang, R., Xie, H. et al. Modified non-dominated sorting genetic algorithm III with fine final level selection. Appl Intell 51, 4236–4269 (2021). https://doi.org/10.1007/s10489-020-02053-z

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