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A many-objective evolutionary algorithm based on hyperplane projection and penalty distance selection

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Abstract

For many-objective optimization problems, due to the low selection pressure of the Pareto-dominance relation and the ineffectivity of diversity maintenance scheme in the environmental selection, the current Pareto-dominance based multi-objective evolutionary algorithms (MOEAs) fail to balance between convergence and diversity. This paper proposes a many-objective evolutionary algorithm based on hyperplane projection and penalty distance selection (we call it MaOEA-HP). Firstly, the normalization method is used to construct an unit hyperplane and the population is projected onto the unit hyperplane. Then, a harmonic average distance is applied to calculate the crowding density of the projected points on the unit hyperplane. Finally, the perpendicular distance from the individual to the hyperplane as convergence information is added into the diversity maintenance phase, and a penalty distance selection scheme is designed to balance between convergence and diversity of solutions. Compared with six state-of-the-art many-objective evolutionary algorithms, the experimental results on two well-known many-objective optimization test suites show that MaOEA-HP has more advantage than the other algorithms, could improve the convergence and ensure the uniform distribution.

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Notes

  1. The code of MaOEA-DDFC was provided by its authors.

  2. The code of KnEA is from http://www.soft-computing.de/jin-pub_year.html.

  3. The code of SPEA2 + SDE and GrEA are from http://www.cs.bham.ac.uk/~limx/publication.html.

  4. See Footnote 3.

  5. The code of NSGA-III is from http://web.ntnu.edu.tw/~tcchiang/publications/nsga3cpp/nsga3cpp.htm.

  6. The code of MOEA/D is from http://dces.essex.ac.uk/staff/zhang/webofmoead.htm.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 61175126) and the International S&T Cooperation Program of China (Grant No. 2015DFG12150).

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  1. College of Information and Communication Engineering, Harbin Engineering University, Harbin, 150000, People’s Republic of China

    Xiaojun Bi & Chao Wang

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  1. Xiaojun Bi
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Bi, X., Wang, C. A many-objective evolutionary algorithm based on hyperplane projection and penalty distance selection. Nat Comput 17, 877–899 (2018). https://doi.org/10.1007/s11047-017-9633-2

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