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Decomposition-based multiobjective evolutionary algorithm with density estimation-based dynamical neighborhood strategy

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Abstract

The multiobjective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multiobjective optimization problem (MOP) into several scalar subproblems and then optimizes them cooperatively in their respective neighborhoods. Since the neighborhood size remains constant during the evolution process, striking a balance between diversity and convergence is a challenging for the conventional MOEA/D. In this study, a density estimation-based dynamical neighborhood (DEDN) strategy is proposed and integrated into MOEA/D to form MOEA/D-DEDN. In the MOEA/D-DEDN, an angle-based evolutionary state evaluation (AESE) scheme is first developed to evaluate the evolutionary state of the algorithm. Second, a distance-based density estimation (DDE) scheme is designed to calculate the population density for all the subproblems. Finally, the neighborhood size and penalty parameters of each subproblem are adjusted based on the AESE scheme and DDE schemes during the evolutionary process to overcome the disadvantages of computational resource waste and premature convergence. The performance of the proposed MOEA/D-DEDN is validated using the ZDT, DTLZ, and UF test suits in terms of IGD, HV, and Spacing metrics. The experimental results show that MOEA/D-DEDN has a significant improvement over the traditional MOEA/D and six state-of-the-art MOEA/D variants. Furthermore, to verify its effectiveness and usefulness, the proposed MOEA/D-DEDN is applied to address MOPs for three engineering applications: trajectory planning for parafoil UAVs, structural optimization for space trusses, and parameters optimization for wastewater treatment processes.

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The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by the Industry University Research Cooperation Project of Jiangsu Province (Grant number BY2020247), the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. SJCX23_1855), and the Innovation and Entrepreneurship Training Program for College Students of Jiangsu Province (Grant numbers 202211049074Y and 202211049125 H). The authors would like to thank the Editor-in-Chief, the Associate Editor and anonymous reviewers for their invaluable suggestions, which have been incorporated to improve the quality of the paper. We would also like to thank Editage (http://www.editage.cn) for English language editing.

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  1. Faculty of Automation, Huaiyin Institute of Technology, Huai’an, 223003, China

    Yuanhui Qin, Jian Ren, Dan Yang, Hongbiao Zhou, Hengrui Zhou & Congguo Ma

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Qin, Y., Ren, J., Yang, D. et al. Decomposition-based multiobjective evolutionary algorithm with density estimation-based dynamical neighborhood strategy. Appl Intell 53, 29863–29901 (2023). https://doi.org/10.1007/s10489-023-05105-2

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