Nonlinear equation systems solved by many-objective Hype

Qin, Sha; Zeng, Sanyou; Dong, Wei; Li, Xi

doi:10.1109/cec.2015.7257222

Cited by 16 publications

(9 citation statements)

References 13 publications

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“…In Ref. [46], a complex multi-objective transformation technique was developed, where an NEs problem is formulated as shown in Eq. ( 15) at the bottom of this page, where R.x/ D P n iD1 jf i .x/j is the system function, and C is used to control the shape of the Pareto front.…”

Section: Transformation Techniquesmentioning

confidence: 99%

Nonlinear Equations Solving with Intelligent Optimization Algorithms: A Survey

Gong

Liao

et al. 2021

Complex Syst. Model. Simul.

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Nonlinear Equations (NEs), which may usually have multiple roots, are ubiquitous in diverse fields. One of the main purposes of solving NEs is to locate as many roots as possible simultaneously in a single run, however, it is a difficult and challenging task in numerical computation. In recent years, Intelligent Optimization Algorithms (IOAs) have shown to be particularly effective in solving NEs. This paper provides a comprehensive survey on IOAs that have been exploited to locate multiple roots of NEs. This paper first revisits the fundamental definition of NEs and reviews the most recent development of the transformation techniques. Then, solving NEs with IOAs is reviewed, followed by the benchmark functions and the performance comparison of several state-of-the-art algorithms. Finally, this paper points out the challenges and some possible open issues for solving NEs.

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Section: Transformation Techniquesmentioning

confidence: 99%

Nonlinear Equations Solving with Intelligent Optimization Algorithms: A Survey

Gong

Liao

et al. 2021

Complex Syst. Model. Simul.

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“…NESs are generally transformed into optimization problems to efficiently develop the roots, which possesses several advantages, such as low dependence on problem characteristics, locating multiple solutions in a single run. Currently, popular transformation techniques can be roughly classified into three categories: i) single-objective optimizationbased transformation techniques [22], [24], [25], ii) multiobjective optimization-based transformation techniques [23],…”

Section: B Transformation Techniquesmentioning

confidence: 99%

Integrating Variable Reduction Strategy with Evolutionary Algorithm for Solving Nonlinear Equations Systems

Song,

Wu,

Pedrycz

2020

Preprint

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Nonlinear equations systems (NESs) are widely used in real-world problems while they are also difficult to solve due to their characteristics of nonlinearity and multiple roots. Evolutionary algorithm (EA) is one of the methods for solving NESs, given their global search capability and an 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, the problem domain knowledge of NESs is particularly investigated in this study, using which we propose to incorporate the variable reduction strategy (VRS) into EAs to solve NESs. 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 the variable relationships existing in the equation systems. It enables to reduce partial variables and equations and shrink 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 integrates VRS into two existing state-of-the-art EA methods (i.e., MONES and DR-JADE), respectively. Experimental results show that, with the assistance of VRS, the EA methods can significantly produce better results than the original methods and other compared methods.

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“…The open methods start only one initial value and converges the solution rapidly since they use derivative. Newton-Raphson is an open method and used for the solution of both nonlinear equation and nonlinear equation systems [4].…”

Section: Introductionmentioning

confidence: 99%

“…Besides numerical methods, some solution approaches are proposed in the literature. Nonlinear equation systems have been modelled as multi objective optimization problems [4], [5]. The advantage of modelling the nonlinear equation systems as multi objective optimization problem is that the user can find alternative solutions instead of finding only one solution.…”

Section: Introductionmentioning

confidence: 99%

A New Solution Approach for Non-Linear Equation Systems with Grey Wolf Optimizer

Erdoğmuş

2018

Sakarya University Journal of Computer and Information Sciences

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The aim of this study is to bring a new perspective for the solutions of non-linear equation systems. So this study handles the non-linear equation systems as a constrained optimization problem, while generally is handled unconstrained optimization problem or multi objective optimization problem. The object is to minimize the sum of the squares of nonlinear equations under the nonlinear equality constraints. A recently developed heuristic optimization algorithm called Grey Wolf Optimizer (GWO) is proposed for the solution of nonlinear equation systems. Two results were obtained. Firstly, it has been seen that GWO can be an alternative solution technique for the solution of nonlinear equation systems. Secondly, modelling the systems of nonlinear equations as constrained optimization gives better results.

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Nonlinear equation systems solved by many-objective Hype

Cited by 16 publications

References 13 publications

Nonlinear Equations Solving with Intelligent Optimization Algorithms: A Survey

Nonlinear Equations Solving with Intelligent Optimization Algorithms: A Survey

Integrating Variable Reduction Strategy with Evolutionary Algorithm for Solving Nonlinear Equations Systems

A New Solution Approach for Non-Linear Equation Systems with Grey Wolf Optimizer

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