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Enhanced θ dominance and density selection based evolutionary algorithm for many-objective optimization problems

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Abstract

Many multi-objective evolutionary algorithms (MOEAs) have been developed for many-objective optimization. This paper proposes a new enhanced 𝜃 dominance and density selection based evolutionary algorithm (called 𝜃-EDEA) for many-objective optimization problems. We firstly construct an m-dimension hyper-plane using the extreme point on the each dimension. Then we replace the distance between the origin point and projection of solution on the reference line of 𝜃 dominance which recently is proposed in 𝜃 dominance based evolutionary algorithm (𝜃-DEA), with the perpendicular distance between each solution and the hyper-plane to develop an enhanced 𝜃 dominance. Finally, in order to maintain better diversity, 𝜃-EDEA employs density based selection mechanism to select the solution for the next population in the environment selection phase. 𝜃-EDEA still inherits clustering operator and ranking operator of 𝜃-DEA to balance diversity and convergence. The performance of 𝜃-EDEA is validated and compared with five state-of-the-art algorithms on two well-known many-objective benchmark problems with three to fifteen objectives. The results show that 𝜃-EDEA is capable of obtaining a solution set with better convergence and diversity.

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Notes

  1. The code of NSGA-III is from http://learntsinghuaeducn:8080/2012310563/ManyEAsrar.

  2. The code of GrEA is from http://www.tech.dmu.ac.uk/syang/publications.html.

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

  4. The code of HypE is from http://www.tik.ee.ethz.ch/pisa.

  5. The code of 𝜃-DEA is from http://learntsinghuaeducn:8080/2012310563/ManyEAsrar.

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Acknowledgments

This work is supported by Natural Science Foundation of China under Grant No. 61472375 and No. 41571403, Joint Funds of Equipment Pre-Research and Ministry of Education of China under Grant No. 6141A02022320.

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Authors and Affiliations

  1. School of Computer, China University of Geosciences, Wuhan, 430074, China

    Chong Zhou, Guangming Dai & Maocai Wang

  2. Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences, Wuhan, 430074, China

    Chong Zhou, Guangming Dai & Maocai Wang

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  1. Chong Zhou
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Correspondence to Guangming Dai.

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Zhou, C., Dai, G. & Wang, M. Enhanced θ dominance and density selection based evolutionary algorithm for many-objective optimization problems. Appl Intell 48, 992–1012 (2018). https://doi.org/10.1007/s10489-017-0998-9

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