A decomposition-based differential evolution with reinitialization for nonlinear equations systems

Solving nonlinear equations systems (NESs) is one of the most important challenges in numerical computation, especially to find multiple roots in one run. In this paper, a decomposition-based differential evolution with reinitialization is proposed to tackle this challenging task. The main advantage...

Full description

Saved in:
Bibliographic Details
Published in:Knowledge-based systems 2020-03, Vol.191, p.105312, Article 105312
Main Authors: Liao, Zuowen, Gong, Wenyin, Wang, Ling, Yan, Xuesong, Hu, Chengyu
Format: Article
Language:English
Subjects:
Algorithms
Decomposition
Decomposition technique
Differential equations
Differential evolution
Evolutionary computation
Nonlinear equations
Nonlinear equations systems
Nonlinear systems
Numerical analysis
Optimization
Population
Population control
Reinitialization
Sub-population control strategy
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Solving nonlinear equations systems (NESs) is one of the most important challenges in numerical computation, especially to find multiple roots in one run. In this paper, a decomposition-based differential evolution with reinitialization is proposed to tackle this challenging task. The main advantages of our method are: (i) an improved parameter-free decomposition technique is exploited to partition the population into numerous sub-populations to locate multiple roots of NESs; (ii) to enhance the search ability of optimization algorithm, a sub-population control strategy is presented to control the number of solutions in the sub-populations; and (iii) the sub-population reinitialization mechanism is proposed to enrich the population diversity. To evaluate the performance of our approach, thirty NES problems with different characteristics are selected as the test suite. Moreover, to further indicate the superiority of our method, ten complex NESs with many roots are also tested. Experimental results show that the proposed approach can locate multiple roots in a single run. In addition, it is able to obtain better results compared with other state-of-the-art methods in terms of both root rate and success rate. •An improved differential evolution (DDE/R) is proposed.•Forty nonlinear equations systems are used to test the performance of DDE/R.•DDE/R yields better results than the compared 10 algorithms.
ISSN:0950-7051
1872-7409
DOI:10.1016/j.knosys.2019.105312