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Volume 9 Issue 1
Jan.  2022

IEEE/CAA Journal of Automatica Sinica

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Aijuan Song, Guohua Wu, Witold Pedrycz and Ling Wang, "Integrating Variable Reduction Strategy With Evolutionary Algorithms for Solving Nonlinear Equations Systems," IEEE/CAA J. Autom. Sinica, vol. 9, no. 1, pp. 75-89, Jan. 2022. doi: 10.1109/JAS.2021.1004278
Citation: Aijuan Song, Guohua Wu, Witold Pedrycz and Ling Wang, "Integrating Variable Reduction Strategy With Evolutionary Algorithms for Solving Nonlinear Equations Systems," IEEE/CAA J. Autom. Sinica, vol. 9, no. 1, pp. 75-89, Jan. 2022. doi: 10.1109/JAS.2021.1004278

Integrating Variable Reduction Strategy With Evolutionary Algorithms for Solving Nonlinear Equations Systems

doi: 10.1109/JAS.2021.1004278
Funds:  This work was supported by the National Natural Science Foundation of China (62073341), and in part by the Natural Science Fund for Distinguished Young Scholars of Hunan Province (2019JJ20026)
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  • Nonlinear equations systems (NESs) are widely used in real-world problems and they are difficult to solve due to their nonlinearity and multiple roots. Evolutionary algorithms (EAs) are one of the methods for solving NESs, given their global search capabilities and ability to locate multiple roots of a NES simultaneously within one run. Currently, the majority of research on using EAs to solve NESs focuses on transformation techniques and improving the performance of the used EAs. By contrast, problem domain knowledge of NESs is investigated in this study, where we propose the incorporation of a variable reduction strategy (VRS) into EAs to solve NESs. The VRS makes full use of the systems of expressing a NES and uses some variables (i.e., core variable) to represent other variables (i.e., reduced variables) through variable relationships that exist in the equation systems. It enables the reduction of partial variables and equations and shrinks the decision space, thereby reducing the complexity of the problem and improving the search efficiency of the EAs. To test the effectiveness of VRS in dealing with NESs, this paper mainly integrates the VRS into two existing state-of-the-art EA methods (i.e., MONES and DR-JADE) according to the integration framework of the VRS and EA, respectively. Experimental results show that, with the assistance of the VRS, the EA methods can produce better results than the original methods and other compared methods. Furthermore, extensive experiments regarding the influence of different reduction schemes and EAs substantiate that a better EA for solving a NES with more reduced variables tends to provide better performance.

     

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  • 1 The statistical tests reported in this paper are calculated by the KEEL3.0 software [32].
    2 http://faculty.csu.edu.cn/guohuawu/zh_CN/zdylm/193832/list/index.htm
    3 Except for VR-DR-JADE, DR-JADE, and MONES, the data of other seven compared methods are from the literature [20] and the detailed results of the eleven methods are reported in the supplementary file2.
    4 The date of DR-JADE comes from [20].
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    Highlights

    • Variable reduction strategy was proposed to reduce nonlinear equations systems
    • A framework of variable reduction strategy and evolutionary algorithms was presented
    • Variable reduction strategy enables a better performance of an original algorithm
    • A better algorithm and a reduction scheme with more reduced variables perform better

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