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Robust Grey Wolf Optimizer for Multimodal Optimizations: A Cross-Dimensional Coordination Approach

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Abstract

This paper proposes a variant of the Gray Wolf Optimizer (GWO) called the Cross-Dimensional Coordination Gray Wolf Optimizer (CDCGWO), which utilizes a novel learning technique in which all prior best knowledge is gained by candid solutions (wolves) is used to update the best solution (prey positions). This method maintains the wolf's diversity, preventing premature convergence in multimodal optimization tasks. In addition, CDCGWO provides a unique constraint management approach for real-world constrained engineering optimization problems. The CDCGWO's performance on fifteen widely used multimodal numerical test functions, ten complex IEEE CEC06-2019 suit tests, a randomly generated landscape, and twelve constrained real-world optimization problems in a variety of engineering fields, including industrial chemical producer, power system, process design, and synthesis, mechanical design, power-electronic, and livestock feed ration was evaluated. For all 25 numerical functions and 12 engineering problems, the CDCGWO beats all benchmarks and sixteen out of eighteen state-of-the-art algorithms by an average rank of Friedman test of higher than 78 percent, while exceeding jDE100 and DISHchain1e+12 by 21% and 39%, respectively. For all numerical functions and engineering problems, the Bonferroni-Dunn and Holm's tests indicated that CDCGWO is statistically superior to all benchmark and state-of-the-art algorithms, while its performance is statistically equivalent to jDE100 and DISHchain1e+12. The proposed CDCGWO might be utilized to solve challenges involving multimodal search spaces. In addition, compared to rival benchmarks, CDCGWO is suitable for a broader range of engineering applications.

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Data Availability

The resource data and material can be downloaded using the following links and references. https://seyedalimirjalili.com/projects. https://www3.ntu.edu.sg/home/epnsugan/index_files/cec-benchmarking.htm. https://www3.ntu.edu.sg/home/epnsugan/. https://github.com/P-N-Suganthan.

Code Availability

The source code of the models can be available by request.

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Funding

This work was supported by Foundation of Henan Educational Committee under Grant 21B520013, Henan Institute of Science and Technology under Grants 192400410199 and 202102210365, and National Natural Science Foundation of China under Grants U1536201, and 61271392.

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  1. College of Information Engineering, Zhengzhou University of Industrial Technology, Xinzheng, 450064, Henan, China

    Bingkun Wang

  2. Beijing Wodong Tianjun Information Technology Company, Beijing, 100176, China

    Lei Liu

  3. College of Information Science and Technology, Zhengzhou Normal University, Zhengzhou, 450044, China

    Yuchong Li

  4. Department of Electrical Engineering, Imam Khomeini Marine Science University, Nowshahr, Iran

    Mohammad Khishe

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  1. Bingkun Wang
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Wang, B., Liu, L., Li, Y. et al. Robust Grey Wolf Optimizer for Multimodal Optimizations: A Cross-Dimensional Coordination Approach. J Sci Comput 92, 110 (2022). https://doi.org/10.1007/s10915-022-01955-z

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