scholarly journals Quantum-behaved Particle Swarm Optimization Algorithm for Solving Nonlinear Equations

2012 ◽  
Author(s):  
Xiaofeng Zhang ◽  
Guifang Sui
Keyword(s):  
Particle Swarm Optimization ◽  
Nonlinear Equations ◽  
Optimization Algorithm ◽  
Particle Swarm Optimization Algorithm ◽  
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 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.

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