<abstract xmlns="http://www.w3.org/1999/xhtml">

In order to solve the system of compatible nonlinear equations, the author proposes a hybrid computational intelligence method of Newton's method and genetic algorithm. First, the Quasi-Newton Methods (QN) method is given. Aiming at the local convergence of the algorithm, it is easy to cause the solution to fail. By embedding the QN operator in the Genetic Algorithm (GA) and defining the appropriate fitness, thus, a hybrid computational intelligence algorithm of CNLE is obtained that combines the advantages of GA and QN method, which has both faster convergence and higher probability of solving. Experimental results show that: The value of the selection probability <italic>pn</italic> of the QN operator also directly affects the solution efficiency. Generally speaking, for strong nonlinear CNLE composed of multimodal functions, <italic>pn</italic> can be larger; For weakly nonlinear CNLE composed of functions with fewer extreme points and stronger monotonicity, <italic>pn</italic> can be smaller. It is demonstrated that the computational results show that this method significantly outperforms the GA and QN methods.
</abstract>

In order to solve the system of compatible nonlinear equations, the author proposes a hybrid computational intelligence method of Newton's method and genetic algorithm. First, the Quasi-Newton Methods (QN) method is given. Aiming at the local convergence of the algorithm, it is easy to cause the solution to fail. By embedding the QN operator in the Genetic Algorithm (GA) and defining the appropriate fitness, thus, a hybrid computational intelligence algorithm of CNLE is obtained that combines the advantages of GA and QN method, which has both faster convergence and higher probability of solving. Experimental results show that: The value of the selection probability pn of the QN operator also directly affects the solution efficiency. Generally speaking, for strong nonlinear CNLE composed of multimodal functions, pn can be larger; For weakly nonlinear CNLE composed of functions with fewer extreme points and stronger monotonicity, pn can be smaller. It is demonstrated that the computational results show that this method significantly outperforms the GA and QN methods.

A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations

Gansu University of Political Science and Law

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

In order to solve the system of compatible nonlinear equations, the author proposes a hybrid computational intelligence method of Newton's method and genetic...

A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations

Published Online: Jul 15, 2022

Page range: 1731 - 1742

Received: Apr 18, 2022

Accepted: Jun 12, 2022

DOI: https://doi.org/10.2478/amns.2022.2.0161

Keywords
Solving compatible nonlinear equations, Newton's method, genetic algorithm, hybrid computing, intelligence

© 2023 Yunfeng Wang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

Figure 2

A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations

Published Online: Jul 15, 2022

Page range: 1731 - 1742

Received: Apr 18, 2022

Accepted: Jun 12, 2022

DOI: https://doi.org/10.2478/amns.2022.2.0161

KeywordsSolving compatible nonlinear equations, Newton's method, genetic algorithm, hybrid computing, intelligence

© 2023 Yunfeng Wang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

Figure 2

Keywords
Solving compatible nonlinear equations, Newton's method, genetic algorithm, hybrid computing, intelligence