Research of Ranking Method in Evolution Strategy for Solving Nonlinear System of Equations

Geng, Huantong; Sun, Yijie; Song, Qing; Wu, Tingting

doi:10.1109/icise.2009.922

Cited by 6 publications

(4 citation statements)

References 5 publications

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“…Often, evolutionary algorithms associate candidate solutions to biological individuals, which gradually evolve, and only the fittest survive. For example, article [36] proposes an evolutionary algorithm for solving SNEs which first ranks all candidate solutions of the current population by their fitness values, and then performs mutation operations on the best candidate solutions to generate "offspring" which will serve as the new set of candidate solutions for the next iteration of the evolutionary algorithm. Here, fitness is quantified as a mathematical fitness function.…”

Section: Population-based Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Survey of Methods for Solving Systems of Nonlinear Equations, Part II: Optimization Based Approaches

Kotsireas¹,

Pardalos²,

Semenov³

et al. 2022

Preprint

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This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting a thorough description and analysis of the known methods capable of finding one or many solutions to SNEs, and to assist interested readers seeking to identify solution techniques which are well suited for solving the various classes of SNEs which one may encounter in real world applications.To accomplish these objectives, we present a multi-part survey. In part one, we focused on root-finding approaches which can be used to search for solutions to a SNE without transforming it into an optimization problem. In part two, we introduce the various transformations which have been utilized to transform a SNE into an optimization problem, and we discuss optimization algorithms which can then be used to search for solutions. We emphasize the important characteristics of each method, and we discuss promising directions for future research. In part three, we will present a robust quantitative comparative analysis of methods capable of searching for solutions to SNEs.

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Section: Population-based Methodsmentioning

confidence: 99%

“…Other papers refer to Eq. ( 2) as a nonlinear system of equations, and use the abbreviations "NSE" [36,37] and "NLS" [38]. Eq.…”

Section: Terminologymentioning

confidence: 99%

Survey of Methods for Solving Systems of Nonlinear Equations, Part II: Optimization Based Approaches

Kotsireas¹,

Pardalos²,

Semenov³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Other papers refer to Eq. (1) as a nonlinear system of equations, and use the abbreviations "NSE" [37,38] and "NLS" [39]. Eq.…”

Section: Terminologymentioning

confidence: 99%

Survey of Methods for Solving Systems of Nonlinear Equations, Part I: Root-finding Approaches

Kotsireas¹,

Pardalos²,

Semenov³

et al. 2022

Preprint

View full text Add to dashboard Cite

This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting a thorough description and analysis of the known methods capable of finding one or many solutions to SNEs, and to assist interested readers seeking to identify solution techniques which are well suited for solving the various classes of SNEs which one may encounter in real world applications.To accomplish these objectives, we present a multi-part survey. In part one, we focus on root-finding approaches which can be used to search for solutions to a SNE without transforming it into an optimization problem. In part two, we will introduce the various transformations which have been utilized to transform a SNE into an optimization problem, and we discuss optimization algorithms which can then be used to search for solutions. In part three, we will present a robust quantitative comparative analysis of methods capable of searching for solutions to SNEs.

show abstract

“…The transformed problem is generally a multi-modal or multi-objective optimization problem. At present, EAs that have been applied to solve NESs comprise evolutionary strategy (ES), particle swarm optimization algorithm (PSO), differential evolution algorithm (DE), genetic algorithm (GA), etc.. For example, Tong et al proposed a ranking method in ES for solving NESs [13]. Ouyang et al developed a hybrid PSO [14], which solves NESs by combining PSO with the Nelder-Mead simplex method.…”

Section: Introductionmentioning

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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Research of Ranking Method in Evolution Strategy for Solving Nonlinear System of Equations

Cited by 6 publications

References 5 publications

Survey of Methods for Solving Systems of Nonlinear Equations, Part II: Optimization Based Approaches

Survey of Methods for Solving Systems of Nonlinear Equations, Part II: Optimization Based Approaches

Survey of Methods for Solving Systems of Nonlinear Equations, Part I: Root-finding Approaches

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

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