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A many-objective evolutionary algorithm with adaptive convergence calculation

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Abstract

Since different reference points are crucial for calculating convergence, we design a many-objective evolutionary algorithm with an adaptive convergence calculation method (ACC-MaOEA). This algorithm uses the adaptive convergence calculation method to estimate the shape of the Pareto front (PF) and adaptively determines a reference point to calculate convergence based on the shape. It estimates the PF shape by comparing the distances from the ideal and key points to two parallel planes. If the PF is concave, the ideal point is used as the reference point, and the distance from the solution to a plane through the ideal point is calculated to approximate convergence; if the PF is convex, the nadir point is used as the reference point, and the distance from the solution to a plane through the nadir point is calculated to approximate convergence. To avoid the overestimation of the nadir point, we first adopt a ratio-based infinite norm indicator to determine a potential region in which the optimal solution exists and then estimate the PF shape in this region and adaptively calculate convergence. Additionally, we use a determinantal point process to sample solutions with good convergence and diversity. We compare ACC-MaOEA with state-of-the-art algorithms on 21 test problems and up to 15 objectives. The experimental results show that ACC-MaOEA significantly outperforms its competitors, especially on regular PF problems.

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Acknowledgements

This research is supported by the Natural Science Foundation of Anhui Province, China (Grant No. 1808085MF174, 1808085QF181), the National Natural Science foundation of China (Grant No. 61976101), the Key projects of Natural Science Foundation of Anhui Provincial Department of Education (KJ2019A0603), the Key Research & Development Project of Anhui Province (Grant No. 201904a05020072), the Natural Science Research Project of Anhui Province (Graduate Research Project, Grant No. YJS20210463), the funding plan for scientic research activities of academic and technicalleaders and reserve candidates in Anhui Province (Grant No. 2021H264), the top talent project of disciplines (majors) in Colleges and universities in Anhui Province (Grant No. gxbjZD2022021) and supported by the Graduate Innovation Fund of Huaibei Normal University (Grant No. cx2022041). We thank the language expert of Springer for editing in English.

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  1. Computer Science and Technology, Huaibei Normal University, Huaibei, 340604, China

    Mengzhen Wang, Fangzhen Ge, Debao Chen & Huaiyu Liu

  2. Anhui Engineering Research Center for Intelligent Computing and Application on Cognitive Behavior (ICACB), Huaibei Normal University, Huaibei, 340604, China

    Fangzhen Ge & Debao Chen

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Correspondence to Fangzhen Ge.

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Wang, M., Ge, F., Chen, D. et al. A many-objective evolutionary algorithm with adaptive convergence calculation. Appl Intell 53, 17260–17291 (2023). https://doi.org/10.1007/s10489-022-04296-4

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