The Application of Particle Swarm Optimization to Solving Nonlinear Equations

2010 ◽  
Author(s):  
ZhiHong Shuang
Keyword(s):  
Particle Swarm Optimization ◽  
Nonlinear Equations ◽  
Particle Swarm ◽  
Swarm Optimization

Quantum-Behaved Particle Swarm Optimization Algorithm for Solving Nonlinear Equations

2013 ◽  
Vol 756-759 ◽  
pp. 2926-2931 ◽  
Author(s):  
Xiao Feng Zhang ◽  
Gui Fang Sui
Keyword(s):  
Particle Swarm Optimization ◽  
Real Number ◽  
Nonlinear Equations ◽  
Optimization Algorithm ◽  
Traditional Method ◽  
Particle Swarm Optimization Algorithm ◽  
Particle Swarm ◽  
Swarm Optimization ◽  
Simulation Results

A quantum-behaved particle swarm optimization algorithm is presented in this paper for solving nonlinear equations. The positions of particle are coded by probability amplitudes of qubits that are updated by quantum rotation gates in this method. The corresponding real number solution at specified interval can be extracted by this algorithm for solving nonlinear equations. Compared to real traditional method, the simulation results show that this algorithm is more accurate and effective.

scholarly journals Particle Swarm Optimization for Solving a Class of Type-1 and Type-2 Fuzzy Nonlinear Equations

2018 ◽  
Vol 8 (2) ◽  
pp. 103-110 ◽  
Author(s):  
Sheriff Sadiqbatcha ◽  
Saeed Jafarzadeh ◽  
Yiannis Ampatzidis
Keyword(s):  
Particle Swarm Optimization ◽  
Fuzzy Sets ◽  
Nonlinear Equations ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Swarm Optimization ◽  
Fuzzy Variables ◽  
Modified Particle Swarm Optimization ◽  
Fuzzy Polynomials ◽  
Exponential Equations

Abstract This paper proposes a modified particle swarm optimization (PSO) algorithm that can be used to solve a variety of fuzzy nonlinear equations, i.e. fuzzy polynomials and exponential equations. Fuzzy nonlinear equations are reduced to a number of interval nonlinear equations using alpha cuts. These equations are then sequentially solved using the proposed methodology. Finally, the membership functions of the fuzzy solutions are constructed using the interval results at each alpha cut. Unlike existing methods, the proposed algorithm does not impose any restriction on the fuzzy variables in the problem. It is designed to work for equations containing both positive and negative fuzzy sets and even for the cases when the support of the fuzzy sets extends across 0, which is a particularly problematic case.

scholarly journals A Velocity-Combined Local Best Particle Swarm Optimization Algorithm for Nonlinear Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Zhigang Lian ◽  
Songhua Wang ◽  
Yangquan Chen
Keyword(s):  
Particle Swarm Optimization ◽  
Nonlinear Equations ◽  
Optimization Algorithm ◽  
Particle Swarm Optimization Algorithm ◽  
Particle Swarm ◽  
Local Optimum ◽  
The Novel ◽  
Swarm Optimization ◽  
The Given ◽  
Novel Algorithm

Many people use traditional methods such as quasi-Newton method and Gauss–Newton-based BFGS to solve nonlinear equations. In this paper, we present an improved particle swarm optimization algorithm to solve nonlinear equations. The novel algorithm introduces the historical and local optimum information of particles to update a particle’s velocity. Five sets of typical nonlinear equations are employed to test the quality and reliability of the novel algorithm search comparing with the PSO algorithm. Numerical results show that the proposed method is effective for the given test problems. The new algorithm can be used as a new tool to solve nonlinear equations, continuous function optimization, etc., and the combinatorial optimization problem. The global convergence of the given method is established.

scholarly journals A NEW ALGORITHM IN NONLINEAR ANALYSIS OF STRUCTURES USING PARTICLE SWARM OPTIMIZATION

2016 ◽  
Vol 17 (2) ◽  
pp. 157-168 ◽  
Author(s):  
Iman Mansouri ◽  
Ali Shahri ◽  
Hassan Zahedifar
Keyword(s):  
Particle Swarm Optimization ◽  
Nonlinear Analysis ◽  
Nonlinear Equations ◽  
Particle Swarm ◽  
Load Ratio ◽  
Buckling Analysis ◽  
Displacement Control ◽  
Swarm Optimization ◽  
Post Buckling ◽  
Limit Points

Solving systems of nonlinear equations is a difficult problem in numerical computation. Probably the best known and most widely used algorithm to solve a system of nonlinear equations is Newton-Raphson method. A significant shortcoming of this method becomes apparent when attempting to solve problems with limit points. Once a fixed load is defined in the first step, there is no way to modify the load vector should a limit point occur within the increment. To overcome this defect, displacement control methods for passing limit points can be used. In displacement control method, the load ratio in the first step of an increment is defined so that a particular key displacement component will change only by a prescribed amount. In this paper the load ratio is obtained using particle swarm optimization (PSO) algorithm so that the complex behavior of structures can be followed, automatically. Design variable is load ratio and its unbalanced force is also considered as objective function in optimization process. Numerical results are performed under geometrical nonlinear analysis, elastic post-buckling analysis and inelastic post-buckling analysis. The efficiency and accuracy of proposed method are demonstrated by solving these examples.   

Smart teaching mode based on particle swarm image recognition and human-computer interaction deep learning

2020 ◽  
Vol 39 (4) ◽  
pp. 5699-5711
Author(s):  
Shirong Long ◽  
Xuekong Zhao
Keyword(s):  
Feature Extraction ◽  
Particle Swarm Optimization ◽  
Deep Learning ◽  
Real Time ◽  
Image Recognition ◽  
Particle Swarm ◽  
Learning Technology ◽  
Search Performance ◽  
Swarm Optimization ◽  
Teaching Mode

The smart teaching mode overcomes the shortcomings of traditional teaching online and offline, but there are certain deficiencies in the real-time feature extraction of teachers and students. In view of this, this study uses the particle swarm image recognition and deep learning technology to process the intelligent classroom video teaching image and extracts the classroom task features in real time and sends them to the teacher. In order to overcome the shortcomings of the premature convergence of the standard particle swarm optimization algorithm, an improved strategy for multiple particle swarm optimization algorithms is proposed. In order to improve the premature problem in the search performance algorithm of PSO algorithm, this paper combines the algorithm with the useful attributes of other algorithms to improve the particle diversity in the algorithm, enhance the global search ability of the particle, and achieve effective feature extraction. The research indicates that the method proposed in this paper has certain practical effects and can provide theoretical reference for subsequent related research.

Sistem Kontrol Optimal Fuzzy-Particle Swarm Optimization

2018 ◽  
Vol 9 (1) ◽  
pp. 1-5
Author(s):  
Fachrudin Hunaini ◽  
Imam Robandi ◽  
Nyoman Sutantra
Keyword(s):  
Fuzzy Logic ◽  
Particle Swarm Optimization ◽  
Control System ◽  
Membership Function ◽  
Fuzzy Logic Control ◽  
Particle Swarm ◽  
Optimization Method ◽  
Swarm Optimization ◽  
Motion Error ◽  
Logic Control

Fuzzy Logic Control (FLC) is a reliable control system for controlling nonlinear systems, but to obtain optimal fuzzy logic control results, optimal Membership Function parameters are needed. Therefore in this paper Particle Swarm Optimization (PSO) is used as a fast and accurate optimization method to determine Membership Function parameters. The optimal control system simulation is carried out on the automatic steering system of the vehicle model and the results obtained are the vehicle's lateral motion error can be minimized so that the movement of the vehicle can always be maintained on the expected trajectory

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