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A hybridization of grey wolf optimizer and differential evolution for solving nonlinear systems

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Abstract

This paper proposes a new algorithm for solving systems of complex nonlinear equations as an optimization problem. A hybridization algorithm from two inspired algorithms, grey wolf optimizer (GWO) and differential evolution (DE) is named GWO-DE. A new improving encircling prey and new crossover technique is used for updating the new agents of GWO-DE based on the generated agents of DE and GWO. Since GWO-DE has the advantages over GWO and DE, it subdues the inability of GWO and DE for solving unconstrained optimization problems and systems of nonlinear equations. Numerical experiments of 13 unconstrained optimization problems in 100 dimension and seven benchmark systems of nonlinear equations are employed to test the performance of GWO-DE. The non-parametric Wilcoxon statistical test and Friedman test are conducted for this study. Empirical results show that GWO-DE is able to circumvent other algorithms in the literature by getting the optimum solutions for most of systems of nonlinear equations and optimization problems and demonstrates its efficiency in comparison with other existing algorithms.

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Acknowledgements

The authors are thankful to reviewers for considerations, constructive reviews, and beneficial suggestions of the manuscript. These comments have helped us in improving the quality of the manuscript. The research of the 1st author is supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC). The postdoctoral fellowship of the 2nd author is supported by NSERC.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Science, Thompson Rivers University, Kamloops, BC, V2C 0C8, Canada

    Mohamed A. Tawhid & Abdelmonem M. Ibrahim

  2. Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut, Egypt

    Abdelmonem M. Ibrahim

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  1. Mohamed A. Tawhid
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  2. Abdelmonem M. Ibrahim
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Correspondence to Mohamed A. Tawhid.

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Tawhid, M.A., Ibrahim, A.M. A hybridization of grey wolf optimizer and differential evolution for solving nonlinear systems. Evolving Systems 11, 65–87 (2020). https://doi.org/10.1007/s12530-019-09291-8

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