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

Author(s):  
Xiaofeng Zhang ◽  
Guifang Sui
2013 ◽  
Vol 756-759 ◽  
pp. 2926-2931 ◽  
Author(s):  
Xiao Feng Zhang ◽  
Gui Fang Sui

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.


2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Zhigang Lian ◽  
Songhua Wang ◽  
Yangquan Chen

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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