Premium
Statistical stability analysis for particle swarm optimization dynamics with random coefficients
Author(s) -
Koguma Yuji,
Aiyoshi Eitaro
Publication year - 2012
Publication title -
electronics and communications in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.131
H-Index - 13
eISSN - 1942-9541
pISSN - 1942-9533
DOI - 10.1002/ecj.10388
Subject(s) - randomness , stability (learning theory) , particle swarm optimization , eigenvalues and eigenvectors , mathematical optimization , computer science , simple (philosophy) , mathematics , heuristic , algorithm , statistics , machine learning , philosophy , physics , epistemology , quantum mechanics
Particle swarm optimization (PSO), a meta‐heuristic global optimization method, has attracted special interest for its simple algorithm and high searching ability. The updating formula of PSO involves coefficients with random numbers as parameters to enhance diversification ability in searching for the global optimum. However, the randomness makes stability of the searching points difficult to analyze mathematically, and the users need to adjust the parameter values by trial and error. In this paper, stability of the stochastic dynamics of PSO is analyzed mathematically and an exact stability condition taking the randomness into consideration is presented with an index called the “statistical eigenvalue,” which is a new concept for evaluating the degree of stability of PSO dynamics. The accuracy and effectiveness of the proposed stability discrimination using the presented index are certified in numerical simulation for simple examples. © 2011 Wiley Periodicals, Inc. Electron Comm Jpn, 95(1): 31–42, 2012; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/ecj.10388