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Aitken optimizer: an efficient optimization algorithm based on the Aitken acceleration method

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Abstract

While the optimization algorithm community boasts numerous members, the primary wellspring of inspiration largely stems from collective and social behaviors observed in nature. This paper introduces a new metaphor-free meta-heuristic algorithm called Aitken optimizer (ATK) based on the basic idea of solving groups of equations using iterative methods. ATK is based on the Aitken sequence, which accelerates the immobile point iteration method to improve the algorithm's convergence speed and solution accuracy and reduce the possibility of falling into local optimums. Taking inspiration from the Aitken acceleration method, the ATK integrates two essential rules, namely the Aitken acceleration method search mechanism and the random weighted exponential operator, into its entire search process, which are instrumental in further enhancing the exploration of optimal solutions. ATK was validated using three CEC benchmarks (CEC2017, CEC2020, and CEC2022), and its results were compared with those of three categories of existing optimization algorithms, as follows: (1) the most cited optimizers, including the grey wolf optimizer, whale optimization algorithm, and Harris Hawks optimization, (2) published high-performance algorithms, including BWO, FHO, NRBO, SGA, SCA, CPSOGSA, and KOA, and (3) high-performance optimizers, such as SaDE, JaDE, CJADE, IMODE, EBOwithCMAR, SHADE, LSHADE, AL-SHADE, and LSHADE-cnEpSin. Statistical analysis shows that ATK achieves a winning rate of up to 94.23% across 51 functions in the three test sets compared to 10 competing optimizers. When benchmarked against 9 state-of-the-art high-performance optimizers, ATK's winning rates on the CEC 2017, CEC 2020, and CEC 2022 test suites are 27.59%, 25%, and 66.67%, respectively, with Friedman mean rankings of 2, 3, and 1. The results indicate that ATK, as a high-performance optimizer, demonstrates superior global search capabilities in high-dimensional, non-convex, and multimodal problems, outperforming simpler optimization methods suited for low-dimensional or convex problems. This makes ATK particularly well suited for applications such as engineering design and neural network tuning.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (52165063), Guizhou Provincial Science and Technology Projects [(GCC [2022].006-1), Qiankehe support normal [2022] No.165, [2021] No.445, [2021] No.172, [2021] No.397, [2022] No.008. Qiankehe pingtai rencai-CXTD [2023] No.007, Qiankehe support normal [2023] No.431, No.348, and No.309, Qiankehe support normal [2024] No.093], the Natural Science Foundation of Chongqing (CSTB2022NSCQ-MSX1600), the Science and Technology Platform and Talent Team Building Plan Project of Guizhou Province [2023] No. 134. Finally, the authors would like to thank the Editor and the anonymous reviewers for their constructive comments and valuable suggestions to improve the quality of the article.

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Authors and Affiliations

  1. Key Laboratory of Advanced Manufacturing Technology, Ministry of Education, Guizhou University, Guiyang, 550025, Guizhou, China

    Yongpeng Zhao, Shengwei Fu, Langlang Zhang & Haisong Huang

  2. Information Engineering Institute, Chongqing Vocational and Technical University of Mechatronics, Chongqing, 402760, China

    Haisong Huang

  3. Guizhou Equipment Manufacturing Digital Workshop Modeling and Simulation Engineering Research Center, Guiyang, 550025, Guizhou, China

    Yongpeng Zhao, Shengwei Fu, Langlang Zhang & Haisong Huang

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  1. Yongpeng Zhao
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  2. Shengwei Fu
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Contributions

YZ took part in investigation, methodology, writing—original draft, writing—revised and editing. HH involved in methodology, writing—review and editing. SF took part in investigation, writing—review and editing. LZ involved in writing—review and editing. All authors revised the manuscript.

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Correspondence to Haisong Huang.

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Zhao, Y., Fu, S., Zhang, L. et al. Aitken optimizer: an efficient optimization algorithm based on the Aitken acceleration method. J Supercomput 81, 264 (2025). https://doi.org/10.1007/s11227-024-06709-2

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