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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 409606, 10 pages
Research Article

Convergence Analysis of a Class of Computational Intelligence Approaches

1College of IOT Engineering, Hohai University, Changzhou 213022, China
2Jiangsu Key Laboratory of Power Transmission and Distribution Equipment Technology, Changzhou 213022, China
3Changzhou Key Laboratory of Sensor Networks and Environmental Sensing, Changzhou 213022, China

Received 11 January 2013; Revised 25 March 2013; Accepted 13 April 2013

Academic Editor: Yang Tang

Copyright © 2013 Junfeng Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Computational intelligence approaches is a relatively new interdisciplinary field of research with many promising application areas. Although the computational intelligence approaches have gained huge popularity, it is difficult to analyze the convergence. In this paper, a computational model is built up for a class of computational intelligence approaches represented by the canonical forms of generic algorithms, ant colony optimization, and particle swarm optimization in order to describe the common features of these algorithms. And then, two quantification indices, that is, the variation rate and the progress rate, are defined, respectively, to indicate the variety and the optimality of the solution sets generated in the search process of the model. Moreover, we give four types of probabilistic convergence for the solution set updating sequences, and their relations are discussed. Finally, the sufficient conditions are derived for the almost sure weak convergence and the almost sure strong convergence of the model by introducing the martingale theory into the Markov chain analysis.