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Solving Nonlinear Equations Systems with a Two-Phase Root-Finder Based on Niching Differential Evolution

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Bio-Inspired Computing: Theories and Applications (BIC-TA 2020)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1363))

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Abstract

Solving nonlinear equation systems (NESs) is a challenging problems in numerical computation. Two goals should be considered for solving NESs. One is to locate as many roots as possible and the other is to improve the solving precision. In this work, in order to achieve these two goals, a two-phase niching differential evolution (TPNDE) is proposed. The innovation of TPNDE is mainly reflected in the following three aspects. First, a probabilistic mutation mechanism is designed to increase the diversity of the population. Second, a novel reinitialization procedure is proposed to detect converged individuals and explore more new regions that may contain global optima. Third, distribution adjustment local search (DALS) is proposed to deal with the isolated solution and enhance the convergence of the algorithm. To evaluate the performance of TPNDE, we test our TPNDE and 5 state-of-the-art algorithms on 20 NESs with diverse features. The experimental results show that the proposed TPNDE algorithm is better than the other methods.

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Acknowledgements

The National Natural Science Foundation of China (62072201), China Postdoctoral Science Foundation (2020M672359), and the Fundamental Research Funds for the Central Universities (HUST: 2019kfyXMBZ056).

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Authors and Affiliations

  1. Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, 430074, China

    Lianlang Duan & Fei Xu

Authors
  1. Lianlang Duan
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  2. Fei Xu
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Corresponding author

Correspondence to Fei Xu .

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Editors and Affiliations

  1. Huazhong University of Science and Technology, Wuhan, China

    Linqiang Pan

  2. China University of Petroleum, Qingdao, China

    Shangchen Pang

  3. China University of Petroleum, Qingdao, China

    Tao Song

  4. China University of Petroleum, Qingdao, China

    Faming Gong

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Duan, L., Xu, F. (2021). Solving Nonlinear Equations Systems with a Two-Phase Root-Finder Based on Niching Differential Evolution. In: Pan, L., Pang, S., Song, T., Gong, F. (eds) Bio-Inspired Computing: Theories and Applications. BIC-TA 2020. Communications in Computer and Information Science, vol 1363. Springer, Singapore. https://doi.org/10.1007/978-981-16-1354-8_17

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  • DOI: https://doi.org/10.1007/978-981-16-1354-8_17

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-16-1353-1

  • Online ISBN: 978-981-16-1354-8

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