New Discrete-Time Models of Zeroing Neural Network Solving Systems of Time-Variant Linear and Nonlinear Inequalities

Shi, Yang; Zhang, Yunong

doi:10.1109/tsmc.2017.2751259

Cited by 51 publications

(31 citation statements)

References 56 publications

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“…3) Problem 17: Solving polynomial equations. Therefore, finding the roots of NESs is not only of great significance for solving practical problems but also one of the core problems of mathematics [5].…”

Section: ) Problemmentioning

confidence: 99%

“…The parameter α, which is used to adjust the radius of the repulsion areas, plays a more important role than . 5 Therefore, the influence of different α values on the performance of RADE was empirically studied. The detailed results of RR and SR are shown in Tables S-R-XIII and S-R-XIV in the supplementary material, respectively.…”

Section: ) Effect Of Different Population Sizesmentioning

confidence: 99%

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Finding Multiple Roots of Nonlinear Equation Systems via a Repulsion-Based Adaptive Differential Evolution

Gong

Wang

Cai

et al. 2020

IEEE Trans. Syst. Man Cybern, Syst.

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Abstract-Finding multiple roots of nonlinear equation systems (NESs) in a single run is one of the most important challenges in numerical computation. We tackle this challenging task by combining the strengths of the repulsion technique, diversity preservation mechanism, and adaptive parameter control. First, the repulsion technique motivates the population to find new roots by repulsing the regions surrounding the previously found roots. However, to find as many roots as possible, algorithm designers need to address a key issue: how to maintain the diversity of the population. To this end, the diversity preservation mechanism is integrated into our approach, which consists of the neighborhood mutation and the crowding selection. In addition, we further improve the performance by incorporating the adaptive parameter control. The purpose is to enhance the search ability and remedy the trial-and-error tuning of the parameters of differential evolution (DE) for different problems. By assembling the above three aspects together, we propose a repulsion-based adaptive DE, called RADE, for finding multiple roots of NESs in a single run. To evaluate the performance of RADE, 30 NESs with diverse features are chosen from the literature as the test suite. Experimental results reveal that RADE is able to find multiple roots simultaneously in a single run on all the test problems. Moreover, RADE is capable of providing better results than the compared methods in terms of both root rate and success rate.

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Section: ) Problemmentioning

confidence: 99%

Section: ) Effect Of Different Population Sizesmentioning

confidence: 99%

Finding Multiple Roots of Nonlinear Equation Systems via a Repulsion-Based Adaptive Differential Evolution

Gong

Wang

Cai

et al. 2020

IEEE Trans. Syst. Man Cybern, Syst.

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show abstract

“…In order to investigate its roots, the bilinear transformation is employed, i.e., define ζ = (1 + ω)/(1 − ω) in equation (11), and then the following equation is obtainedčž Instant number General TOA formula…”

Section: B Stability and Convergence Analysesmentioning

confidence: 99%

“…It means that future information is calculated predictively at VOLUME 4, 2016 each time instant t k so that time consumption of computation has no infection on real-time performance [8], [9]. Secondly, time discretization formulas have to meet 0stability constraint [10], [11]. It is a tough requirement that most existing derivative approximation formulas can not satisfy.…”

Section: Introductionmentioning

confidence: 99%

General Third-Order-Accuracy Formulas for Time Discretization Applied to Time-Varying Optimization

Xuan

Zhu

et al. 2020

IEEE Access

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“…As many systems in practical applications always change as time evolves, the corresponding LI should be the time-varying one with coefficients being time-varying [i.e., A(t) and b(t) with t 0]. When the aforementioned approaches are exploited directly to solve the time-varying LI (TVLI), they may be less effective [15]- [20].…”

Section: Introductionmentioning

confidence: 99%

Discrete-Time Zeroing Dynamics With Quadruplicate Error Pattern for Time-Varying Linear Inequality

2021

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New Discrete-Time Models of Zeroing Neural Network Solving Systems of Time-Variant Linear and Nonlinear Inequalities

Cited by 51 publications

References 56 publications

Finding Multiple Roots of Nonlinear Equation Systems via a Repulsion-Based Adaptive Differential Evolution

Finding Multiple Roots of Nonlinear Equation Systems via a Repulsion-Based Adaptive Differential Evolution

General Third-Order-Accuracy Formulas for Time Discretization Applied to Time-Varying Optimization

Discrete-Time Zeroing Dynamics With Quadruplicate Error Pattern for Time-Varying Linear Inequality

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