Sufficient Conditions for Global Convergence of Differential Evolution Algorithm
The differential evolution algorithm (DE) is one of the most powerful stochastic real-parameter optimization algorithms. The theoretical studies on DE have gradually attracted the attention of more and more researchers. However, few theoretical researches have been done to deal with the convergence...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/193196 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832556900613357568 |
|---|---|
| author | Zhongbo Hu Shengwu Xiong Qinghua Su Xiaowei Zhang |
| author_facet | Zhongbo Hu Shengwu Xiong Qinghua Su Xiaowei Zhang |
| author_sort | Zhongbo Hu |
| collection | DOAJ |
| description | The differential evolution algorithm (DE) is one of the most powerful stochastic real-parameter optimization algorithms. The theoretical studies on DE have gradually attracted the attention of more and more researchers. However, few theoretical researches have been done to deal with the convergence conditions for DE. In this paper, a sufficient condition and a corollary for the convergence of DE to the global optima are derived by using the infinite product. A DE algorithm framework satisfying the convergence conditions is then established. It is also proved that the two common mutation operators satisfy the algorithm framework. Numerical experiments are conducted on two parts. One aims to visualize the process that five convergent DE based on the classical DE algorithms escape from a local optimal set on two low dimensional functions. The other tests the performance of a modified DE algorithm inspired of the convergent algorithm framework on the benchmarks of the CEC2005. |
| format | Article |
| id | doaj-art-832f40e3dda74301a4d8110543922ad8 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-832f40e3dda74301a4d8110543922ad82025-02-03T05:44:10ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/193196193196Sufficient Conditions for Global Convergence of Differential Evolution AlgorithmZhongbo Hu0Shengwu Xiong1Qinghua Su2Xiaowei Zhang3School of Computer Science and Technology, Wuhan University of Technology, Wuhan, Hubei 430070, ChinaSchool of Computer Science and Technology, Wuhan University of Technology, Wuhan, Hubei 430070, ChinaSchool of Mathematics and Statistics, Hubei Engineering University, Xiaogan, Hubei 432100, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaThe differential evolution algorithm (DE) is one of the most powerful stochastic real-parameter optimization algorithms. The theoretical studies on DE have gradually attracted the attention of more and more researchers. However, few theoretical researches have been done to deal with the convergence conditions for DE. In this paper, a sufficient condition and a corollary for the convergence of DE to the global optima are derived by using the infinite product. A DE algorithm framework satisfying the convergence conditions is then established. It is also proved that the two common mutation operators satisfy the algorithm framework. Numerical experiments are conducted on two parts. One aims to visualize the process that five convergent DE based on the classical DE algorithms escape from a local optimal set on two low dimensional functions. The other tests the performance of a modified DE algorithm inspired of the convergent algorithm framework on the benchmarks of the CEC2005.http://dx.doi.org/10.1155/2013/193196 |
| spellingShingle | Zhongbo Hu Shengwu Xiong Qinghua Su Xiaowei Zhang Sufficient Conditions for Global Convergence of Differential Evolution Algorithm Journal of Applied Mathematics |
| title | Sufficient Conditions for Global Convergence of Differential Evolution Algorithm |
| title_full | Sufficient Conditions for Global Convergence of Differential Evolution Algorithm |
| title_fullStr | Sufficient Conditions for Global Convergence of Differential Evolution Algorithm |
| title_full_unstemmed | Sufficient Conditions for Global Convergence of Differential Evolution Algorithm |
| title_short | Sufficient Conditions for Global Convergence of Differential Evolution Algorithm |
| title_sort | sufficient conditions for global convergence of differential evolution algorithm |
| url | http://dx.doi.org/10.1155/2013/193196 |
| work_keys_str_mv | AT zhongbohu sufficientconditionsforglobalconvergenceofdifferentialevolutionalgorithm AT shengwuxiong sufficientconditionsforglobalconvergenceofdifferentialevolutionalgorithm AT qinghuasu sufficientconditionsforglobalconvergenceofdifferentialevolutionalgorithm AT xiaoweizhang sufficientconditionsforglobalconvergenceofdifferentialevolutionalgorithm |