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Solving Complex Transcendental Equations Based on Swarm Intelligence
Author(s) -
YuBo Tian
Publication year - 2009
Publication title -
ieej transactions on electrical and electronic engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.254
H-Index - 30
eISSN - 1931-4981
pISSN - 1931-4973
DOI - 10.1002/tee.20477
Subject(s) - transcendental equation , particle swarm optimization , swarm intelligence , convergence (economics) , genetic algorithm , process (computing) , algorithm , mathematical optimization , computer science , eigenvalues and eigenvectors , mathematics , numerical analysis , physics , quantum mechanics , economics , economic growth , operating system , mathematical analysis
Swarm intelligence (SI) is a kind of intelligence mode enlightened by some intelligent colony behaviors in nature. This paper focuses on the characteristics of global convergence of genetic algorithm (GA) and particle swarm optimization (PSO) in SI and the strategy of parameter tracking (PT), and fusing them together effectively forms a new algorithm that can solve complex transcendental equations accurately in electromagnetic field. In the process of developing the algorithm, the searching area is decreased, solution is simplified, and the calculating speed is accelerated due to the PT. Moreover, the precision of the results is enhanced due to the dynamic searching area. The predicting of the new searching center by using 3‐order difference formula speeds up the calculation further. Based on the developed algorithm, some classical eigenvalue equations that are complex transcendental ones are solved. The computing results show that the algorithm can suitably solve the multi‐root problem of complex transcendental equations. Furthermore, the computing result is complete and accurate, and the algorithm is robust. Copyright © 2009 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.