Global convergence analysis of the bat algorithm using a markovian framework and dynamical system theory
Article
Chen, S., Peng, G., He, X. and Yang, X. 2018. Global convergence analysis of the bat algorithm using a markovian framework and dynamical system theory. Expert Systems with Applications. 114, pp. 173-182. https://doi.org/10.1016/j.eswa.2018.07.036
Type | Article |
---|---|
Title | Global convergence analysis of the bat algorithm using a markovian framework and dynamical system theory |
Authors | Chen, S., Peng, G., He, X. and Yang, X. |
Abstract | The bat algorithm (BA) has been shown to be effective to solve a wider range of optimization problems. However, there is not much theoretical analysis concerning its convergence and stability. In order to prove the convergence of the bat algorithm, we have built a Markov model for the algorithm and proved that the state sequence of the bat population forms a finite homogeneous Markov chain, satisfying the global convergence criteria. Then, we prove that the bat algorithm can have global convergence. In addition, in order to enhance the convergence performance of the algorithm and to identify the possible effect of parameter settings on convergence, we have designed an updated model in terms of a dynamic matrix. Subsequently, we have used the stability theory of discrete-time dynamical systems to obtain the stable parameter ranges for the algorithm. Furthermore, we use some benchmark functions to demonstrate that BA can indeed achieve global optimality efficiently for these functions. |
Keywords | Bat algorithm; Global convergence; Markov chain theory; Dynamical system theory; Parameters selection; Optimization; Swarm intelligence |
Publisher | Elsevier |
Journal | Expert Systems with Applications |
ISSN | 0957-4174 |
Electronic | 1873-6793 |
Publication dates | |
Online | 18 Jul 2018 |
30 Dec 2018 | |
Publication process dates | |
Deposited | 08 Aug 2018 |
Accepted | 16 Jul 2018 |
Submitted | 06 Mar 2018 |
Output status | Published |
Accepted author manuscript | License |
Copyright Statement | © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/ |
Digital Object Identifier (DOI) | https://doi.org/10.1016/j.eswa.2018.07.036 |
Web of Science identifier | WOS:000446949300013 |
Language | English |
https://repository.mdx.ac.uk/item/87wq3
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