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An Improved Newton-raphson Optimizer with Differential Evolution and Adaptive Strategy.

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Title: An Improved Newton-raphson Optimizer with Differential Evolution and Adaptive Strategy.
Authors: Wang, Bo1 zsa3685@163.com, Zhang, Yong2 zy9091@163.com
Source: Engineering Letters. Jul2026, Vol. 34 Issue 7, p2808-2823. 16p.
Subjects: Newton-Raphson method, Differential evolution, Mathematical optimization, Swarm intelligence, Process optimization, Metaheuristic algorithms
Abstract: Newton-raphson optimizer (NRBO) is a new swarm intelligence meta-heuristic algorithm inspired by Newton-raphson method, which combines Newton-raphson search rule (NRSR) and trap avoidance operator (TAO). Although it performs well in global exploration, the original NRBO has some shortcomings in local harsh utilization, which may lead to poor utilization effect of NRBO, insufficient convergence accuracy, insufficient exploration-mining balance and easy to fall into local optimum. Therefore, this paper proposes an improved version of EDNRBO. By introducing a variety of strategies to solve the above defects. Firstly, the introduction of a nonlinear convergence factor AF in the original NRBO parameter ρ can improve the local search effect of NRBO and improve the convergence accuracy. Secondly, the particle position is updated by combining the advantages of differential evolution and local search. Finally, the adaptive factor (DF) is improved to avoid EDNRBO falling into local optimum. In this study, the CEC2022 benchmark suite was used to evaluate the performance of the EDNRBO algorithm, and compared with the other four optimization algorithms. In addition, the proposed algorithm was qualitatively analyzed with NRBO to further verify the effectiveness of EDNRBO. The algorithm is applied to engineering optimization problems with different complexity. The test data show that it is superior to other comparison algorithms in terms of optimization accuracy, problem adaptability and solution stability. [ABSTRACT FROM AUTHOR]
Copyright of Engineering Letters is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: An Improved Newton-raphson Optimizer with Differential Evolution and Adaptive Strategy.
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  Data: <searchLink fieldCode="AR" term="%22Wang%2C+Bo%22">Wang, Bo</searchLink><relatesTo>1</relatesTo><i> zsa3685@163.com</i><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Yong%22">Zhang, Yong</searchLink><relatesTo>2</relatesTo><i> zy9091@163.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Engineering+Letters%22">Engineering Letters</searchLink>. Jul2026, Vol. 34 Issue 7, p2808-2823. 16p.
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  Data: <searchLink fieldCode="DE" term="%22Newton-Raphson+method%22">Newton-Raphson method</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+evolution%22">Differential evolution</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Swarm+intelligence%22">Swarm intelligence</searchLink><br /><searchLink fieldCode="DE" term="%22Process+optimization%22">Process optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Metaheuristic+algorithms%22">Metaheuristic algorithms</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Newton-raphson optimizer (NRBO) is a new swarm intelligence meta-heuristic algorithm inspired by Newton-raphson method, which combines Newton-raphson search rule (NRSR) and trap avoidance operator (TAO). Although it performs well in global exploration, the original NRBO has some shortcomings in local harsh utilization, which may lead to poor utilization effect of NRBO, insufficient convergence accuracy, insufficient exploration-mining balance and easy to fall into local optimum. Therefore, this paper proposes an improved version of EDNRBO. By introducing a variety of strategies to solve the above defects. Firstly, the introduction of a nonlinear convergence factor AF in the original NRBO parameter ρ can improve the local search effect of NRBO and improve the convergence accuracy. Secondly, the particle position is updated by combining the advantages of differential evolution and local search. Finally, the adaptive factor (DF) is improved to avoid EDNRBO falling into local optimum. In this study, the CEC2022 benchmark suite was used to evaluate the performance of the EDNRBO algorithm, and compared with the other four optimization algorithms. In addition, the proposed algorithm was qualitatively analyzed with NRBO to further verify the effectiveness of EDNRBO. The algorithm is applied to engineering optimization problems with different complexity. The test data show that it is superior to other comparison algorithms in terms of optimization accuracy, problem adaptability and solution stability. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Engineering Letters is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Code: eng
        Text: English
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        PageCount: 16
        StartPage: 2808
    Subjects:
      – SubjectFull: Newton-Raphson method
        Type: general
      – SubjectFull: Differential evolution
        Type: general
      – SubjectFull: Mathematical optimization
        Type: general
      – SubjectFull: Swarm intelligence
        Type: general
      – SubjectFull: Process optimization
        Type: general
      – SubjectFull: Metaheuristic algorithms
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              M: 07
              Text: Jul2026
              Type: published
              Y: 2026
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